The ratio of the length of an actual tile is 4/3, and the ratio of area is 16/9.
What is ratio?
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Given,
the length of tile is 2/3 and width = 1/2
The length of actual tile is 1/2 and width = 3/8
Therefore, the ratio of the actual length of tile = 2/3 ÷ 1/2
=2/3×2/1
=4/3
The area of the tile in the model to the area of tile in actual tile = 2/3×1/2÷(1/2×3/8)
=1/3÷3/16
=1/3×16/3
=16/9
And another method is property of dilation,
The ratio of the areas = (4/3)^2
=16/9
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Help please I don't understand where to get the degrees from. And what degrees are each
SOLUTION:
(i)
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\cos \text{ }\theta \\ \end{gathered}[/tex]Sine of an angle is complementary to the Cosine of an angle so for both to be the same the angle 90 degrees must be divided into.
[tex]\theta=45^0[/tex](ii)
[tex]\begin{gathered} \tan \text{ }\theta\text{ = 0} \\ \theta\text{ = }\tan ^{-1}(0) \\ \theta\text{ = 0} \end{gathered}[/tex](iii)
[tex]\csc \text{ }\theta\text{ > sec }\theta[/tex]As said earlier sine and cosine of angles are complementary so cosecant and secant of angles are also complementary.
[tex]\begin{gathered} \text{When }\theta\text{ = 30} \\ \csc \text{ }\theta\text{ > sec }\theta \\ \frac{1}{\sin30}\text{ > }\frac{1}{\cos30} \\ \\ 2\text{ > 1.15} \\ \\ \csc \text{ }\theta\text{ > sec }\theta\text{ when }\theta=30^0 \end{gathered}[/tex]AyA(-5,6)B (3,6)D(-5,-1)C(3,-1)-20-laFind the area of the rectangle ABCD.B. 72 square unitsA. 40 square unitsC. 56 square unitsD. 36 square units
Given:
Given a rectangle with coordinates A(-5, 6), B(3, 6), C(3, -1) and D(-5, -1).
Required: Area of rectangle ABCD
Explanation:
First, find the length and width of the rectangle.
[tex]\begin{gathered} \text{ Length, }DC=\sqrt{(-5-3)^2+(-1-(-1))^2} \\ =\sqrt{(-8)^2+0^2} \\ =8 \\ \text{ Width, }BC=\sqrt{(3-3)^2+(6-(-1))^2} \\ =\sqrt{0^2+7^2} \\ =7 \end{gathered}[/tex]The are of the rectangle is
[tex]\begin{gathered} A=\text{Length}\times\text{Width} \\ =8\times7 \\ =56 \end{gathered}[/tex]Option C is correct.
Final Answer: Rectangle ABCD has area 56 square units.
Create a scatterplot using the following data relating the number of cigarettes a day smoked by a parent and thenumber of days the child missed school in the last quarter of the school year. Draw your estimate of the line of best fit.Select and give the coordinates of two points on the line. Find the slope of the line you drew. Write a sentence thatsummarizes the relationship between the two variables.
The equation for the line of best fit is given by:
y = mx + b
In which m is the slope
They are given by:
[tex]m=\frac{n\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{n\sum^{}_{}x^2-(\sum^{}_{}x)^2}[/tex][tex]b=\frac{\sum^{}_{}y-m\sum^{}_{}x}{n}[/tex]Sum of x:
Sum of all values of x.
[tex]\sum ^{}_{}x=3\ast0+5+10+12+15+16+2\ast24+28+30+21+36_{}[/tex][tex]\sum ^{}_{}x=221[/tex]Sum of y:
[tex]\sum ^{}_{}y=0+2\ast2+3+2\ast5+2\ast8+10+2\ast12+2\ast15+20[/tex][tex]\sum ^{}_{}y=117[/tex]Sum of squares of x:
[tex]\sum ^{}_{}x^2=3\ast0^2+5^2+10^2+12^2+15^2+16^2+2\ast24^2+28^2+30^2+21^2+36^2_{}[/tex][tex]\sum ^{}_{}x^2=5323[/tex]Sum of xy:
[tex]\sum ^{\infty}_{n\mathop=0}xy=0\ast(0+2+5)+5\ast3+10\ast5+12\ast8+15\ast10+16\ast2[/tex][tex]+24\ast(8+12)+28\ast15+30\ast15+21\ast20+36\ast12_{}[/tex][tex]\sum ^{}_{}xy=2545[/tex]
Slope:
14 students, so n = 14.
Then
[tex]m=\frac{n\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{n\sum^{}_{}x^2-(\sum^{}_{}x)^2}=\frac{14\ast2545-(221\ast117)}{14\ast5323-221^2}=0.38[/tex][tex]b=\frac{\sum^{}_{}y-m\sum^{}_{}x}{n}=\frac{117-0.38\ast221}{14}=2.36[/tex]The line of best fit is y = 0.38x + 2.36. This means that for a parents that smokes x cigarettes a day, the child is expect to miss 0.38x + 2.36 days of school during the quarter.
Graphic
Tell me how I can eliminate the x-terms in this system! ASAP!
4y+3x=-6
Y-X=-5
Options: 2, 3, 4, and 5.
Answer:
3
Step-by-step explanation:
you can eliminate x with 3 if you multiply the second equation with 3
What is the perpendicular slope to your line? I got the Slope along with the slope-intercept. but I keep getting 0.33333 (etc) for the perpendicular and i dont know if it right tells me to show all my work
The perpendicular slope of the given line is -1/3.
What is a perpendicular?In elementary geometry, two geometric objects are perpendicular if they intersect at right angles.The squareness condition can be represented graphically using the squareness symbol ⟂.Can be defined between two lines, between a line and a plane, and between two planes.Two perpendicular lines make a right angle.The word "perpendicular" means "right angle".This is because when two straight lines intersect, they form a right angle.Vertical lines can point in any direction.
Slope formula = y₂-y₁ / x₂₋x₁Now, insert values in the formula and calculate as follows:
Slope = y₂-y₁ / x₂₋x₁Slope = -1 -3 / 4 - (-8)Slope = -4/12 = -1/3Therefore, the perpendicular slope of the given line is -1/3.
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I cant remember the steps on how to work this problem
Answer:
x= 3
y=0
Step-by-step explanation:
y = -x + 3
y = 2x - 6
-x + 3 = 2x -6
3 + 6 = 2x + x
9 = 3x
3 = x
y = -3 + 3
y = 0
Answer:
(3,0)
Step-by-step explanation:
Factor the expression. - 35a - 30
Answer:
-5(7a+ 6)
Explanation:
Given the expression:
-35a - 30
-35a = -5 * 7 * a
-30 = -5 * 6
You can see from the factors that -5 is common to both
Hence -5 is the GCF
Factoring out -5 from the expression will give;
-5(7a+ 6)
This gives the correct factor
Express the confidence interval 0.555 < p < 0.999 in the form p+E
In order to express the confidence interval in the form p ± E, first we have to determine the midpoint of the interval, like this:
[tex]\hat{p}=\frac{0.555+0.999}{2}=0.777[/tex]The value of the error, E, can be calculated by taking the difference between p and the end of the interval, like this:
[tex]E=0.999-0.777=0.222[/tex]Then, we can express 0.555 < p < 0.999 in p + E notation as 0.777 ± 0.222
The confidence interval can be written as 0.777 ± 0.222.
The confidence interval 0.555 < p < 0.999 can be expressed in the form of p ± E.
To find the margin of error (E), we can subtract the lower limit (0.555) from the upper limit (0.999) and divide it by 2:
E = (0.999 - 0.555) / 2
E = 0.222
Therefore, the confidence interval 0.555 < p < 0.999 can be expressed as:
p ± E
where p is the point estimate and E is the margin of error. In this case, the point estimate would be the midpoint of the interval, which is the average of the lower and upper limits:
p = (0.555 + 0.999) / 2
p = 0.777
Hence, the confidence interval can be written as 0.777 ± 0.222.
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Catherine drives to school each day and lives 5 miles away. After school, she drives to Kroger , which is 2 additional miles away from her house. Then she heads home and studies for a test before having dinner. Sketch a graph showing Catherine's distance from her home throughout the day.
The total distance covered by catherine is 10 miles as the problem says, " Catherine drives to school each day and lives 5 miles away. After school, she drives to Kroger , which is 2 additional miles away from her house. Then she heads home and studies for a test before having dinner".
What is distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point. The magnitude or size of displacement between two positions is defined as distance. The distance between two points differs from the distance traveled between them. The total length of the path traveled between two points is referred to as the distance traveled. Travel distance is not a vector. Distance refers to "how much ground an object has covered" while moving, whereas displacement refers to how far an object is out of place. Displacement is a Vector quantity, whereas distance is a Scalar quantity.
Here,
The total distance from home to school=5 miles
She goes to kroger that is 2 miles from her home,
so, 5-2=3 miles
So she travels 3 miles back from school.
Then she goes 2 miles from kroger to home.
5+3+2=10 miles
According to the problem, Catherine's total distance traveled is 10 miles "Catherine lives 5 miles away and drives to school every day. She drives to Kroger after school, which is two miles away from her house. She then returns home to study for a test before eating dinner ".
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
two thirds of a number is negitive 20
Answer:
The number is -30.
Step-by-step explanation:
Given statement,
→ two thirds of a number is negative 20.
The equation will be,
→ (2/3)x = -20
Now the value of x will be,
→ (2/3)x = -20
→ 2x = (-20) × 3
→ x = (-60)/2
→ [ x = -30 ]
Hence, the value of x is -30.
Answer:
[tex]-30[/tex]
Step-by-step explanation:
Set up the equation where [tex]x[/tex] is the unknown number:
[tex]\frac{2}{3}x = -20[/tex]
Divide both sides by [tex]\frac{2}{3}[/tex]:
[tex]x = -20 \div \frac{2}{3}[/tex]
Rewrite division by a fraction as multiplication by its reciprocal:
[tex]x = -\frac{20}{1} \times \frac{3}{2}[/tex]
Multiply:
[tex]x = -\frac{60}{2}[/tex]
Simplify:
[tex]x = -30[/tex]
a jar contains five black buttons and six brown buttons. If 8 buttons are picked at random,what is the probability that at least 4 of them are black?
First, we write out the probability formula:
[tex]Pr(E)=\frac{n(R\text{equired outcome)}}{n(Total\text{ outcome) }}[/tex]Total number of tickets = 13
Pr(both Ashley and Matt win) = Pr(Ashley wins) x Pr(Matt wins)
[tex]\begin{gathered} Pr(\text{Ashley win ) }=\text{ }\frac{1}{13} \\ Pr(\text{Matt win) = }\frac{1}{13} \end{gathered}[/tex][tex]Pr(\text{both wins ) }=\frac{1}{13}\times\frac{1}{13}=\frac{1}{169}[/tex]The final answer is 1/169
In order to express our answer as a percentage, we multiply by a 100%
= 1/169 x 100% = 0.592% ( to 3 significant figures)
I need help solving this practice problem from my trig prep book
The period of a trigonometric function is the distance between each repetition of the function.
In this case, we have:
As we can see in the graph of the function, the distance between each repetition is 2π.
Therefore, the period of f(x) = csc(x) is 2π.
A paddleboat can move at a speed of 14 kilometers per hour in still water. The boat is paddled 10 kilometers downstream in a river in the same time it takes to go 5 kilometers upstream. What is the speed of the river? Round your answer to the nearest tenth.
The speed of the river is 7.5 kilometers per hour.
Let the speed of boat in still water = u = 14 km/h
Let the speed of river = v = x km/h
Upstream speed = u - v = 14 - x
Downstream speed = u + v = 14 +x
Distance paddled upstream = [tex]D_{1}[/tex] = 5 km
Distance paddled downstream = [tex]D_{2}[/tex] = 10 km
Time taken (upstream) = [tex]T_{1}[/tex] = [tex]\frac{D_{1} }{u-v}[/tex]
Time taken (downstream) = [tex]T_{2}[/tex] = [tex]\frac{D_{2} }{u+v}[/tex]
According to question,
[tex]T_{1}[/tex] = [tex]T_{2}[/tex]
[tex]\frac{D_{1} }{u-v}[/tex] = [tex]\frac{D_{2} }{u+v}[/tex]
[tex]\frac{5}{14-x}[/tex] = [tex]\frac{10}{14+x}[/tex]
5(14 + x) = 10(14 - x)
14 + x = 2(14 - x)
14 + x = 28 - 2x
x + 2x = 28 - 14
3x = 14
x = [tex]\frac{14}{3}[/tex]
x = 7.5
Hence, Speed of river is 7.5 km/h.
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How do I find the slope in this problem?
to get the slope of any straight line, we simply need two points off of it, let's use the points in the picture below
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-5)}}} \implies \cfrac{-2}{0 +5} \implies \cfrac{ -2 }{ 5 } \implies {\Large \begin{array}{llll} - \cfrac{2 }{ 5 } \end{array}}[/tex]
Formulate at least three problems that you wish to have answers using statisticsI am sorry there's no additional information or pictures on this question.
In order to create three statistics problems, we can use the concepts of mean, median and mode.
The mean of a data set is the sum of all values divided by the number of values.
The median of a data set is the middle term of the set in crescent order (if the set has an even number of values, the median is the mean between the two middle values).
The mode of a data set is the value that repeats the most in the set.
So, for our three questions, let's use the following data set:
[tex]1,3,5,2,2,8,4,1,2,3,2[/tex]The three problems are:
1) Calculate the mean of the data set
2) Calculate the median and the mode of the data set
3) Which one is greater: mean, median or mode?
13r+ 8v = 47
22v=63-17r
Answer:
D. 5.
Step-by-step explanation:
Yes.
Complete the equation so it has no solution. 9x - 7x + 5 = ___ - 7
Answer: 2x
Step-by-step explanation: The answer is 2x, because on the LHS, 9x - 7x = 2x, so the LHS is 2x + 5, if we make the RHS 2x - 7, the equation will become 2x + 5 = 2x - 7, this makes the equation unsolvable
HELP!!!!!!!!!! I NEED THIS ASAP PLEASE!!!
Graph the systems of equations.
Both the equations are plotted on the graph and they intersect each other on (2, 4).
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, graph the equation as follows:
2x + y = 8-x + 2y = 6So plot as:
(Refer to the graph attached below)The lines of both equation intersect at (2, 4).Therefore, both the equations are plotted on the graph and they intersect each other on (2, 4).
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Somebody please help me I need to send this tomorrow
4. Mr. Wilson has two cats, named Ramses and Kilala. Kilala weighs 6 pounds. Ramses weighs 3 times as much as Kilala. How much does Ramses weigh? Show how you figured this out.
Answer:
18
Step-by-step explanation:
6lb
*3
6lb*3=18
find the perimeter of the following polygon in these sorts of junk food the correct unit in your answer
Solution
Given a trapezoid with the following dimensions
[tex]10ft,10ft,11ft,15ft[/tex]To find the perimeter, P, of the polygon, we add up all the side lengths i.e the formula to find the perimeter, P, of the trapezoid is
[tex]\begin{gathered} P=a+b+c+d \\ \text{Where a, b, c and d are the side lengths} \end{gathered}[/tex]Where
[tex]\begin{gathered} a=10ft \\ b=10ft \\ c=11ft \\ d=15ft \end{gathered}[/tex]Subsitute the values into the formula above
[tex]\begin{gathered} P=10+10+11+15=46 \\ P=46ft \end{gathered}[/tex]Hence, the perimeter is 46ft
solve for y
show your work.
9-4x=-3y
y=9-4x/3
you need to isolate y so you divide 3 on both sides.
y=3-4/3x
What is the answer to: -32/40 - 35/40
Answer:
To subtract fractions, find the LCD and then combine.
Exact Form:
− 67/40
Decimal Form:
− 1.675
Mixed Number Form:
− 1 27/40
Step-by-step explanation:
Please give the brainliest.
Answer:
− 67/40 or -1 27/40
Step-by-step explanation:
Subtract:
-32/40 - 35/40 =
-67/40
Change into a mixed number (optional):
− 67/40 =
− 1 27/40
Solve the system of equations.2y = 42z? +y = 3
The answer is option B
(1, 2) and (-3, -6)
Data can be displayed in many different ways: using tables, graphs, and equations. What are the benefits and drawbacks of each of these models?
Answer:
There are many different ways to portray your findings for an individual to view and understand. However, each have their pros and cons. When using a table, all of the specific numbers of your data can clearly be seen and compared with one another without having to analyze a picture. However, since there is no visual correlation that shows the growth and decline of your data, someone who best comprehends visually may not be able to understand your findings. It sis best to vary your sources of displaying information to make sure that it is all able to be understood by any viewer. When using a graph, you have a clear visual representation of the correlation of your variables in your experimentation. This allows the viewer to comprehend your data as a picture and see the change as the picture moves. However, it take further analysis and cross referencing to get specific quantitative data as you are required to read across and down the graph. And finally, when using equations you can show the direct way that the change was caused in your experiment. Each equation has a specific input and output. However, the drawback is the person viewing your data may have to solve the equations themselves to find out your data or simply be confused as equations don’t directly show data, but rather how to find it. It is important to have a varied combination of these things to allow for your data to be throughly understood by anyone viewing it. I hope this helps! :)
Step-by-step explanation:
how can you determine a reseentative sample of a population
A representative sample is one that accurately depicts the a population> This representative sample can be determined through sampling. The examples of sampling methods used are random sampling, stratified random sampling
Which of the following is an equivalent expression of 18x² +14x + 7?
Answer:
The second one
Step-by-step explanation:
....is just the equation with the order of the terms re-arranged
What is the first step in solving the equation 2a - 4( a - 5 ) = 10
The first step in solving for a in the equation would be:
1.distribute -4 to a and -5, then:
2a-4a+20=10
Now the next steps in solving for a:
2.Add 2a and -4a :
-2a+20=10
3.Substract 20 to both sides
-2a+20-20=10-20
then:
-2a= -10
4.Finally, divide both sides by -2
[tex]\frac{-2a}{-2}=\frac{-10}{-2}=5[/tex]then, a=5
solve the equation A-X=B-A for X.
Answer:
X= -B+2A
Step-by-step explanation:
Hope this helps and sorry if I'm wrong
2.Use the diagram below. Circle the true statements based on the given diagram.
3.Use the diagram below. Circle the angle pairs that are supplementary to each other.
4.Triangle HIJ has ∠I = 17° and ∠H = 84°. Find m∠ J.
5.An isosceles triangle has a base angle of 24°. Find the measure of the apex angle.
Step-by-step explanation:
2.
angle B is congruent to angle B'.
side BC is congruent to side B'C'.
3.
angle pairs 1 and 3, 2 and 3, 5 and 7 are supplementary (together they have 180°).
4.
please burn this into your brain for all times : the sum of all angles in a triangle is always (yes, always) 180°.
so,
angle J + 17 + 84 = 180
angle J = 180 - 17 - 84 = 79°
5.
and here we use it again.
isoceles means that the triangle has 2 equally long legs. that makes also both base angles equally large.
apex angle + 24 + 24 = 180
apex angle = 180 - 24 - 24 = 132°