The sample size should be taken as 545.6 to obtain a margin of error of 0.042 for the estimation of a population proportion.
What is sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component. The sample size chosen for a study is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the sample size have adequate statistical power.
As given in the question,
Confidence level is 95% and the margin of error is 0.042
So,
1 - α = 0.95,
α = 0.05,
E = 0.042
planning value (p) = 0.5
To calculate Sample size the formula is:
[tex]n = \frac{p(1-p)(Z_{a/2})^2}{E^2}[/tex]
From the table we can find that:
[tex]Z_{a/2} = 1.96[/tex]
Putting the values given in the question in formula:
[tex]n = \frac{0.5(0.5)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(3.841)}{0.00176}[/tex]
n = 545.6
Hence the sample size is 545.6
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Find the slope of the linear regression line for the given data below. Round your
answer to two decimal places.
x y
2 25
3 19
48
5 11
6 15
7 14
Round your final result to two decimal places.
Answer:
hey bro listen
Step-by-step explanation:
you can't always
get the answers
here try to
do yourself and
see your potential.
Box A weighs 212.04 kilograms. Box B weighs 212 1/4 kilograms Which statement is true?A) the box weigh the same amountB) Box B weighs 0.10 of a kilogram more than Box AC) Box A weighs 0.15 of a kilogram more than box BD) Vox b weighs 0.21 of a kilogram more than Box A
To be able to compare the weight of the boxes, we need to have their weight in decimal form:
Box A --> 212.04 kilograms
Box B --> 212 1/4 kilograms
Convert 212 1/4 to decimal:
[tex]\begin{gathered} \text{SINCE }\frac{1}{4}=0.25 \\ 212\frac{1}{4}=212.25 \end{gathered}[/tex]Box B --> 212.25
We can see that the weight of box B is more than the weight of box A, so we discard options A and C.
To find how much more is the weight of box B, we subtract the quantities:
[tex]212.25-212.04=0.21[/tex]Answer: Box B weighs 0.21 of a kilogram more than box A
2. (04.01) Which point could be removed in order to make the relation a function? (4 points) {(-9, -8), (-8, 4), (0, -2), (4,8), (0, 8), (1, 2)} (4,8) (0,8) (-9, -8) (1, 2)
Answer:
(0,8)
Step-by-step explanation:
What is needed in order to be a function?
A value of x cannot have more than one value of y. In this question, we have that for x = 0, there are 2 values of y: -2 and 8. So one of those can be removed.
Among the options, we have: (0,8), which is the correct answer
Find the least common denominator of
8/x²+11x+28
and
-2/x^2+4x
The least common denominator of 8/( x²+11x+28 ) and -2/ (x^2+4x) is (x+4).
We have to find the least common denominator of 8/x²+11x+28 and -2/x^2+4x. We can solve this problem by following a few steps.
The denominator of both terms is, x²+11x+28 and x²+4x.
First of all, we have to find the factors of these two terms.
Let's find the factors of x²+11x+28.
x²+11x+28 = x²+11x+28
Or, x²+11x+28 = x²+ 4x+ 7x+ 28 [ we have to break the middle term in such a way as the product of consecutive terms must be 28 ]
Or, x²+11x+28 = x (x+4) +7 (x-4) [ we have to take ( x+ 4) as acommon ]
Or, x²+11x+28 = ( x+4 )( x+7 ).................(1)
Now find the factors of x²+4x.
x²+4x = x (x+4)..................(2) [ We have to take x as a common ]
Therefore, the common term between (1) and (2) is ( x+4 ). So, the least common denominator is ( x+4 ).
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Find Sin A, Cos A, Sin B, and Cos B for the following. Enter answers as fractions in simplest form, not decimals.
Answer:
[tex]\begin{gathered} \sin A=\frac{\sqrt[]{6}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Explanation:
Let x represent unknown side length
We can go ahead and find x using the Pythagorean Theorem as seen below;
[tex]\begin{gathered} (5\sqrt[]{3})^2=5^2+x^2 \\ (25\times3)=25+x^2 \\ 75-25=x^2 \\ 50=x^2 \\ x=\sqrt[]{50}=\sqrt[]{25\times2}=\sqrt[]{25}\times\sqrt[]{2}=5\sqrt[]{2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]Let's find sin A as seen below;
[tex]\begin{gathered} \sin A=\frac{opposite}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \sin A=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \sin A=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Let's find cos A as seen below;
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \cos A=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find sin B as seen below;
[tex]\begin{gathered} \sin B=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \sin B=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find cos B as seen below;
[tex]\begin{gathered} \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \cos B=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Carly has twice as many sisters as Connor.
Connor has twice as many sisters as Alicia.
Alicia has 3 sisters.
How many sisters does Carly have?
Answer:
12
Step-by-step explanation:
Alicia has 3 sisters.
Connor has twice as many sisters.
Twice means "two times".
Connor has 2×3, that is 6 sisters.
Carly has twice (two times) as many sisters as Connor.
Carly has 2×6, or 12 sisters.
Evaluate the polynomial function for the given values of the variable
ANSWERS
• P(2) = 11
,• P(-1) = 14
,• P(0) = 7
EXPLANATION
Every time we have to evaluate a function, what we have to do is replace the variable with the value and solve the operations.
Let's solve P(2),
[tex]P(2)=3(2)^2-4(2)+7[/tex]Solve the powers first,
[tex]P(2)=3\cdot4-4\cdot2+7[/tex]Then the products,
[tex]P(2)=12-8+7[/tex]And then the additions/subtractions,
[tex]P(2)=11[/tex]The process is the same for the other two values,
[tex]P(-1)=3(-1)^2-4(-1)+7=3\cdot1-4(-1)+7=3+4+7=14[/tex]And,
[tex]P(0)=3(0)^2-4(0)+7=3\cdot0-4\cdot0+7=0+0+7=7[/tex]Hence, P(2) = 11, P(-1) = 14 and P(0) = 7.
Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets ofcardboard from which she cuts out 2-in squares from eachPLEASE CHECK PHOTO
Solution:
Given:
When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;
[tex]\begin{gathered} l=(x+4)-2-2=x+4-4=x \\ w=x-2-2=x-4 \\ h=2 \\ \\ The\text{ volume }V=792in^3 \end{gathered}[/tex]The volume of a cuboid is given by;
[tex]\begin{gathered} V=lwh \\ 792=(x)(x-4)(2) \\ Dividing\text{ both sides by 2;} \\ \frac{792}{2}=x(x-4) \\ 396=x^2-4x \\ \\ Collecting\text{ all sides to one side to form a quadratic equation;} \\ 0=x^2-4x-396 \\ x^2-4x-396=0 \end{gathered}[/tex]Solve the quadratic equation by factorization;
[tex]\begin{gathered} x^2-4x-396=0 \\ x^2+18x-22x-396=0 \\ x(x+18)-22(x+18)=0 \\ (x-22)(x+18)=0 \\ x=22,x=-18 \\ \\ Since\text{ the dimension of a box can not be negative, then;} \\ x=22in \end{gathered}[/tex]Hence, the dimension of the original piece of cardboard is;
[tex]\begin{gathered} (x+4)\text{ by }x \\ \\ Substitute\text{ the value of x, the dimension of the cardboard is;} \\ (22+4)\text{ by }22 \\ 26in\text{ by }22in \end{gathered}[/tex]Therefore, the dimensions of the original piece of cardboard are 26 in by 22in
A grocery store sells a bag of 3 oranges for $2.16. What is the cost of oranges, in dollars per orange?
Answer:
0.72
Step-by-step explanation:
The answer is that because all you have to do is just 2.16 divided by 3. Equalling to 0.72. Now we just have to do 0.72 + 0.72 + 0.72 and that would equal $2.16.
plss mark me as a brainlist plss
What is the value of this expression: (−2)3 x 30 x (−4)−2
0
-3/2
-3/4
-1/2
3/2
3/4
1/2
The given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
In the above question, the following mathematical expression is given :
(−2)3 x 30 x (−4)(−20)
We need to find the value of the given expression by solving it using the BODMAS rule
According to the rule, first we'll solve the multiplication then subtraction
Therefore, we get
(−2)3 x 30 x (−4)(−20)
(-6) x 30 x (-)(-)80
We know, that (-) x (-) = +
and (-) x (+) = (-)
Therefore, we get
(-6) x 30 x (-)(-)80
(-6) x 30 x 80
-6 x 2400
- 14400
Hence, the given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
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Consider the graph of the function f. a) Find the domain, range, and zeros of the function. b) write an equation for the function f. (In vertex form, standard form, or intercept form)c) compare the graph of f to the graph of g(x) = x^2.
Solution:
Given the graph;
(a) The domain of a function is the set of values for which the function is real and defined. Thus, the domain D is;
[tex]\begin{gathered} (-\infty,\infty) \\ D:All\text{ }real\text{ }numbers \end{gathered}[/tex]The range is;
[tex]y\leq8[/tex]The zeros of the function are the points y=0;
[tex]x=1,x=5[/tex](b) The equation of a parabola in vertex form is;
[tex]\begin{gathered} y=a(x-h)^2+k \\ Where\text{ }(h,k)\text{ is }the\text{ }vertex; \\ and\text{ }given\text{ }(1,0) \\ \\ 0=a(1-3)^2+8 \\ \\ -8=4a \\ \\ a=-2 \\ \\ \end{gathered}[/tex]Thus, the equation is;
[tex]y=-2(x-3)^2+8[/tex](c) Using the graph below;
The graph of g(x) has its intercept at (0,0).
The transformation goes as;
Vertical stretch 2units, reflection over the x-axis, horizontal shift to the the right 3 units, vertical shift up 8 units
Using (5,0);
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 0=a(5-3)^2+8 \\ 4a=-8 \\ \\ a=-2 \end{gathered}[/tex]is this triangle possible?
Answer: The triangle is not possible.
Step-by-step explanation:
1) Find the missing angle
62+59+x=180
x=59
2) Use the Law of Sine to check if the triangle sides are the same.
The Law of sine means that Sine the angle and divide with the side across it will equal to same.
[tex]\frac{sin(x)}{x} =\frac{sin(y)}{y}[/tex]
Substitute the numbers.
[tex]\frac{sin(59)}{10} =\frac{sin(62)}{10}[/tex]
0.0636 = -0.0739
3) Solve
Since the decimals aren't the same, the triangle is not possible.
find the remainder for the given division. (z^2+3z+1)/(z-2)
Explanation
Given the expression
[tex]\frac{z^{2}+3z+1}{z-2}[/tex]We are asked to find the remainder. We can use the remainder theorem. This can be seen below.
According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.
Therefore, we will have;
[tex]\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}[/tex]
Koharu pie dough recipe uses 6 oz of flour, 4 oz of butter, and 2 oz of water. Complete the sentences to describe the ratios in her recipe. The ratio of ____ to ____ is 3:2
Answer:
The ratio of flour to butter is 3:2
Step-by-step explanation:
:]
Solve the equation _(4t+_) =6t+15
The given expression is : _( 4t + _ ) = 6t + 15
In the 6t + 15,
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
The equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".
What exactly are equations?A mathematical formula known as an equation is one in which two expressions with the same value are separated by the "equal to" sign. For instance, 3x plus 5 equals 15.There are numerous kinds of equations, including linear, quadratic, cubic, and others. The slope-intercept form, standard form, and point-slope form are the three main types of linear equations.So, the equation for P will be:
Let, P be the total money earned when Madeline sells the 'x' number of computers.Let, 80 be the constant as that is the basic pay.Let, 'x' be the number of computers Madeline sells.Now, the equation can be:
P = 20x + 80(Refer the table attached below)
Therefore, the equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".
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How many solutions does the equation 6z − 3z − 7 = −2 + 3 have? (5 points)TwoNoneInfinitely manyOne
Answer:
One solution.
Explanation:
Let us try to solve the equation and see how many solutions it has.
The first step in solving the equation is to first simplify both the right-hand and the left-hand sides. This means adding all the like terms.
[tex]\begin{gathered} 6z−3z−7=−2+3 \\ \Rightarrow3z-7=1 \end{gathered}[/tex]Next, we add 7 to both sides. This gives
[tex]3x-7+7=1+7[/tex][tex]3x=8[/tex]dividing both sides by 3 gives
[tex]\boxed{z=8/3.}[/tex]which is exactly one solution!
Therefore, our equation had one solution.
The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?
Answer:
1/4
Step-by-step explanation:
I'm 95% sure that this is the answer. if im not correct, im sorry for wasting your time having to read all of this, and im sorry i couldnt help.
The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Answer:x=3
Step-by-step explanation: if they are similar lets say for instance BD is congruent to QS.
so TP is congruent to AE and AE is three so TP has to be three.
hope this helps!
Identify the graph of the ellipse given by the equation below.
Answer options are also attached :)
The required graph below which represents the given equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1. Which is the correct answer would be option (C).
What is an ellipse?An ellipse can be defined as a shape that looks like an oval circle.
The equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1 which is given in the question.
An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.
Center of the ellipse : (−7,5)
Vertex 1: (0,5)
Vertex 2: (−14,5)
We have attached the required graph below which represents the given
equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1.
Hence, the correct answer would be an option (C).
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simplify 3y-5y+10y-4y
To simplify 3y-5y+10y-4y, just add and subtract the coefficients of each term. That is, 3 - 5 + 10 - 4 = 4, which means that the final expression is 4y.
Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.figure 1: 9 cubesfigure 2: 13 cubesfigure 3: (blank)figure 4: (blank)figure 5: (blank)
Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.
figure 1: 9 cubes
figure 2: 13 cubes
figure 3: (blank)
figure 4: (blank)
figure 5: (blank)
Let
f(0)=5
so
For n=0
f(1)=5+4=9
f(1)=9
For n=1
f(2)=9+4=13
f(2)=13
For n=2
f(3)=13+4=17
For n=3
f(4)=17+4=21
For n=4
f(5)=21+4=25
For n=5
f(6)=25+4=29
therefore
theanswer is
figure 3: 17figure 4: 21figure 5: 25Samantha borrowed money to buy lawn equipment to start her new lawn service business. She borrowed $800 for 9 months and paid $70.50 in interest. What was the rate of interest.
Using simple interest, the rate of interest on the amount that Samantha borrowed to buy the law equipment is 11.75%.
What is the simple interest?A simple interest system does not accumulate (compound) interest on both the principal and interest, unlike compound interest.
The simple interest uses the following formula, Interest = Principal x Rate x Period.
This simple interest formula can be reversed to find either the principal, rate, or period, as the case may be.
The loan amount = $800
Period of loan = 9 months
Total interest paid = $70.50
Rate of interest = (Interest × 100)/(Principal × Time)
= 11.75% ($70.50 x 100)/($800 x 9/12)
Check:
Interest = $70.50 ($800 x 11.75% x 9/12)
Thus, Samantha's interest rate on the loan is 11.75%.
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Write the equation of the line that passes through the points (4, -1)
and (3,-2).
Ox+y = -5
O y = x-5
O y = -x +3
Oy - 3x + 13
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Given points:
(x₁, y₁) = (4, -1)(x₂, y₂) = (3, -2)Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{-2-(-1)}{3-4}=\dfrac{-1}{-1}=1[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Point-slope Formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and the point (4, -1) into the point-slope formula to create the equation of the line:
[tex]\implies y-(-1)=1(x-4)[/tex]
[tex]\implies y+1=x-4[/tex]
[tex]\implies y+1-1=x-4-1[/tex]
[tex]\implies y=x-5[/tex]
what is 576.984 round in to the nearest tenths
Answer: 577
Step-by-step explanation:
Answer:
577.0
Rounded to the nearest 0.1 or
the Tenths Place.
Step-by-step explanation:
576.984
You rounded to the nearest tenths place. The 9 in the tenths place rounds up to 10 because the digit to the right in the hundredths place is 8.
Because the tenths place was rounded up from 9 to 10, the tenths place becomes 0 and the ones place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0 and we add 1 to the previous place value.
577.0
When the digit to the right is 5 or greater we round away from 0.
576.984 was rounded up and away from zero to 577.0
Please help me with this question
Answer:
The cost of a card is 4 dollars
The cost of a baseball is 18 dollars
Step-by-step explanation:
13c + 9b = 214
3c + 8b = 156
(13c + 9b = 214) × -8
( 3c + 8b = 156) × 9
-104c - 72b = -1712
27c + 72b = 1404
-------------------------------
-77c = -308
÷-77 ÷-77
--------------------
c = 4
3c + 8b = 156
3(4) + 8b = 156
12 + 8b = 156
-12 -12
----------------------
8b = 144
÷8 ÷8
------------------
b = 18
I hope this helps!
three fifths of thr tshirts in a tshirt shop are on sale. five eighths of those tshirts are on sale. one third of those blue tshirts that are on sale are size medium. what fraction of the shops tshirts are blue tshirts that are on sale and are size medium? explain
3/5 of the T-shirts of the shop are on sale
5/8 of those on sale are blue
1/3 of the blue shirts on sale are medium size.
First calculate how many of the shirts on sale are blue:
[tex]\frac{5}{8}\frac{\div3}{5}=\frac{5}{8}\cdot\frac{5}{3}=\frac{25}{24}[/tex]25/24 of the shirts on sale are blue
Then divide that number by three to know how many are medium size:
[tex]\frac{25}{24}\div3=\frac{25}{72}[/tex]25/72 are blue and medium size
factorize the following if possible 5z^2+35z-90
Answer:
5z² + 35z - 90 = 0
5(z² + 7z - 18) = 0
z² + 7z - 18 = 0
(z - 2)(z + 9) = 0
r=−9, s=2
STEPS USING THE DIRECT FACTORING METHOD
5z²+35z−90
This quadratic equation can be resolved using a revolutionary direct factoring technique that does not rely on guesswork. The equation must have the form x2+Bx+C=0 to be solved using the direct factoring approach. To do this, multiply both sides of the equation by 5.
x²+7x−18=0
Let r and s be the factors for the quadratic equation such that x²+Bx+C=(x−r)(x−s) where the sum of factors (r+s)=−B and the product of factors rs=C
r+s=−7
rs=−18
When the average of the two integers is 1/2*-7=-7 /2, the sum of the two numbers r and s are exactly 7. You can also observe that the parabola symbolized by the quadratic equation y=x2+Bx+C has its axis of symmetry in the middle of r and s. An unknown quantity u separates the values of r and s from the center at an equal distance. Describe r and s about the variable u.
r=−7/2−u
s=−7/2+u
Put these in the product equation rs=-18 to solve for the unknown quantity u.
(−27−u)(−27+u)=−18
Simplify by expanding (a−b)(a+b)=a2–b2
49/4−u²=−18
Simplify the expression by subtracting 49/4 on both sides
−u2=−18−49/4=−121/4
To find the value of the unknowable variable u, simplify the expression by multiplying by 1 on both sides and taking the square root.
u2=121/4
u=±√121/4=±11/2
The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.
r=−7/2−11/2=−9
s=−7/2+11/2=2
Therefore, r=−9, s=2
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Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram.
Triangles L M N and P Q R are shown. The length of side L M is 11 and the length of P Q is 22. The length of M N is 7 and the length of Q R is 12. The length of N L is 6 and the length of R P is 12.
Which statement is true?
The statement that is true about the triangle is that D. The triangles are similar by the SSS similarity theorem.
How to illustrate the information?It should be noted that congruence simply refers to a scenario where there are the same triangles.
The SSS Similarity Theorem states that two triangles are similar if all three pairs of matching sides are proportionate.
Compare the shortest sides first, followed by the longest sides, when applying the SSS Similarity Theorem. Two triangles are similar if their corresponding side lengths are proportionate to one another.
Therefore, triangle LMN and PQR are the same.
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The triangles are not similar, but they are congruent.
The triangles are neither similar nor congruent.
The triangles are similar by the SAS similarity theorem.
The triangles are similar by the SSS similarity theorem.
Answer:
d) The triangles are similar by the SSS similarity theorem.
Ellie wants to save her weekly allowance to go to Disneyland, In 3
weeks she has $40. In 7 weeks, she has $60. Let x represent the
number of weeks and let y represent the total amount saved. Write
an equation in slope intercept form that represents this situation
The equation in slope-intercept form that represents the situation is y = 5x + 25.
In 3 weeks Ellie she saved $40 and $60 in 7 weeks.
Let x and y represent the number of weeks and the total amount saved respectively.
The equation of a line in slope intercept form is given as:
y = mx + b where m is the slope and b is the y-intercept.
Now when x = 3, y = $40.
Therefore,
y = mx + b
40 = 3m + b --------------(1)
When x = 7, y = $60
y = mx + b
60 = 7m + b -------------(2)
Subtracting (1) from (2),
7m + b - 3m - b = 60 - 40
4m = 20
m = 5
So,
3m + b = 40
3(5) + b = 40
15 + b = 40
b = 25
Hence, the equation of the line in slope intercept form is y = 5x + 25.
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