Answer:
C is the answer
Given : dilation with a scale factor of 3
To find : Which statement is true
Step-by-step explanation:
Solution: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
if Dilation factor N then image Size is multiplied by N
if Scale factor < 1 then image get reduced
if scale factor > 1 then image get enlarged
scale factor = 1 lead to Same size image
Here is given that Scale factor of 3
=> image will be enlarged to 3 times the original image
Hence correct option is :
C)Each side in the pre-image is multiplied by three to find the corresponding side length in the image
Answer: C
Step-by-step explanation: Edge Unit Test
A framed picture has a total area y, in square inches. The thickness of the frame is
represented by x, in inches. The equation y = (8+2x)(10 + 2x) relates these two
variables.
1. What are the length and width of the picture without the frame?
2. What would a solution to the equation 100 = (8+2x)(10+2x) mean in this
situation?
The given total area including the frame is y = (8+2x)(10+2x).
As per the question the thickness of the frame is x.
The area of a rectangle is given by A=L*B
For a picture with frame it will be A=(L+2t)*(B+2t)
1. Comparing the above equation with the given equation it can be concluded that the Length is 10 and the width is 8.
2. The given equation is 100=(8+2x)(10+2x)
Upon solving it simplifies to [tex]x^2+9x-5=0[/tex]
x=0.525.
Thus the thickness x=0.525.
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A total of $5550 is plit into
Awo investments. Part of the money.
is invested at 4%, and the reminder
is invested at 5"%.. If the total annual
interest from the two investments is
$259, how much is invested at each rate?
a = amount invested at 4%
how much is 4% of "a"? (4/100) * "a", namely 0.04a.
b = amount invested at 5%
how much is 5% of "b"? (5/100) * "b", namely 0.05b.
we know the total amount invested is 5550, so whatever "a" and "b" might be, we know that a + b = 5550.
we also know that the yielded amount in interest is 259, so if we simply add their interest, that'd be 0.04a + 0.05b = 259.
[tex]a+b=5550\implies b=5550-a \\\\[-0.35em] ~\dotfill\\\\ 0.04a+0.05b=259\implies \stackrel{\textit{substituting from above}}{0.04a+0.05(5550-a)~~ = ~~259} \\\\\\ 0.04a+277.5-0.05a=259\implies 277.5-0.01a=259\implies -0.01a=-18.5 \\\\\\ a=\cfrac{-18.5}{-0.01}\implies \boxed{a=1850}\hspace{9em}\stackrel{ 5550~~ - ~~1850 }{\boxed{b=3700}}[/tex]
Can someone help me please
here is the picture
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
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I have no idea how to solve this problem.
(a) The domain of f of g is {1, 8}.
(b) The range of f of g is {0, 1}.
What is the domain and range of f of g?The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.
(a) Domain of f of g:
The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.
To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.
(b) Range of f of g:
The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.
We have:
f(g(1)) = f(8) = 0
f(g(4)) = f(2) = 1
f(g(8)) = f(0) = 1
Therefore, the range of f of g is {0, 1}.
Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get
�
x small greeting cards and
�
y large greeting cards?
Answer: 18.75
Step-by-step explanation:
small greeting cards = 1.80
large greeting cards = 3.85
1.80 x 4 = 7.20
3.85 x 3 = 11.55
7.20 + 11.55 = 18.75
A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Which statements about this situation are true?
The 99% confidence interval of the population mean is (352.32, 371.68).
To find the 99% confidence interval of the population mean, we need to use the following formula:
CI = x; ± zα/2 * (σ/√n)
where:
x' = sample mean (362)
zα/2 = z-score for 99% confidence level (2.576)
σ = population standard deviation (29.6)
n = sample size (40)
Substituting the values, we get:
CI = 362 ± 2.576 * (29.6/√40)
CI = 362 ± 9.68
This means that if we take many random samples of 40 hours from the population, we can be 99% confident that the true population mean of the number of customers per hour falls between 352.32 and 371.68.
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Complete question is:
A large department store found that it averages 362 customers per hour. Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average. Find the 99% confidence interval of the population mean.
What is the meaning of "Finally [tex]s _{i}\circ s_{i}=s _{j}\circ s_{i}=1[/tex] hence [tex]s _{j}=s_{i}\circ r_{i-j}[/tex] and [tex]s _{i}=r_{i-j}\circ s_{j}[/tex]?
This statement describes the relationship between symmetries and rotations
Explaining the meaning of the statement as statedThis statement describes a relation between two symmetry operations, denoted by [tex]s_i[/tex] and [tex]s_j[/tex], and a rotation operation denoted by [tex]r_{i-j}[/tex]. The notation [tex]"s_i \circ s_i"[/tex] and [tex]"s_j \circ s_i"[/tex] denotes the composition of these operations, which means applying one operation after the other.
The statement says that [tex]s_i[/tex] and [tex]s_j[/tex] are both symmetries, and that they have a specific relationship with each other: when [tex]s_i[/tex] is composed with itself, it gives the identity operation (denoted by 1), and when [tex]s_j[/tex] is composed with [tex]s_i[/tex], it also gives the identity operation.
Then the statement concludes that this relationship implies that [tex]s_j[/tex] can be obtained by first applying [tex]s_i[/tex] and then applying a rotation operation [tex]r_{i-j}[/tex], and that [tex]s_i[/tex] can be obtained by first applying a rotation operation [tex]r_{i-j}[/tex] and then applying [tex]s_j[/tex].
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One option in a roulette game is to bet 11on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the 11 you paid to play the game and you are awarded 11. If the ball lands elsewhere, you are awarded nothing and the 11 that you bet is collected. Complete parts (a) through (b) below.
The expected value for playing roulette if a person bet $16 on red is -$0.84.
b. The statement that best describes what this value means is option b. Over the long run, the player can expect to lose about $1.05 for each game played.
What is the expected value?To be able to calculate the expected value, you need to multiply the probability of winning by the amount won hence it will be:
Expected value = (18/38) x $16 - (20/38) x $16
= -$0.84
Based on the fact that the expected value has a negative sign, it implies that, on average, the player tend to lose money over the long run.
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See full question below
one option in a roulette game is to bet $16 on red. (there are 18 red compartments, 18 compartments, and two compartments that are neither red nor black) if the ball lands on red, you get to keep the $16 you paid to play the game and you are awarded $16. If the ball lands elsewhere, you are awarded nothing and the $16 that you bet is collected.
a. what is the expected value for playing roulette if you bet $16 on red?
$__________ (round to the nearest cent)
b. chosen the statment below that best describes what this value means???
Pick One!
a. over the long run, the player can expect to win about $1.05 for each game played
b. over the long run, the player can expect to lost about $1.05 for each game player
c. over the lung run, the player can expect to break even
What is the value of y in the solution to the system of equations shown?
y = 3x − 1
y = −x − 5
Answer:{y,x}={-4,-1}
Step-by-step explanation:
PLEASE HELP!!
A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 6 inches?
Enter your answer in the box.
Surface area of similar cone =
___in²
Surface area of similar cone is 44π square inches
What does a cone in maths ?
A cone is referred to as a "right cone" when its vertex is higher than the base's centre (i.e., when the angle formed by the vertex, base center, and any base radius is a right angle); otherwise, the word "oblique" is used. A cone is referred to as an elliptic cone when the base is assumed to be an ellipse rather than a circle.
The surface area of a cone is given by:
surface area = πr(r + l)
where r is the radius and l is the slant height.
surface area of original cone = π(3)(3 + 12) = 45π
slant height of similar cone = (6/3)(12) = 24 inches
surface area of similar cone = π(6)(6 + 18) = 144π
ratio of surface areas = surface area of similar cone / surface area of original cone
= (144π) / (45π)
= 3.2
Therefore, The exact surface area of the similar cone is 6 times the surface area of the original cone,
6 × 45π = 144π square inches
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MODELING REAL LIFE About 5.2% of a population
contracted the flu last year. A test used to diagnose the
flu was 92% accurate for people who had the flu and
85% accurate for people who did not have it. Find and
interpret the ratio of true positives to false positives.
The ratio of true positives to false positives, given the accuracy of the test would be 239 : 711 .
Here. we have,
First, find the number of people who have the flu:
= 5. 2 % x 10, 000
= 520 people
Those who don't have it:
= 10, 000 - 520
= 9, 480 people
True positive :
= 92 % x 520
= 478 people
False negatives:
= 8 % x 520
= 42 people
False positives:
= 15 % x 9, 480
= 1, 422 people
The ratio of true positives to false positives is therefore:
478 : 1, 422
239 : 711
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In the diagram below, BE intersects AD at C, AB | DE. If CD = 4.2 and AB = 9.6, what is the length of
BC to the nearest tenth of a centimeter?
Dont mind the writing
The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.
How to Find the Length of the Indicated Side?Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:
AC/CE = BC/CD
Given the following:
AC = 7.2 units
CE = 2.4 units
CD = 4.2 units
BC = ?
Plug in the values:
7.2/2.4 = BC/4.2
Cross multiply:
BC = 7.2 * 4.2 / 2.4
BC = 12.6 cm
Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.
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Working with Formulas
HELP PLS
.
the rate of interest is 11.25%.we can use simple interest formula get answer as above
what is simple interest ?
Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.
In the given question,
We can use the formula for simple interest to solve for the rate:
Simple Interest = (Principal x Rate x Time) / 100
Substituting the given values, we get:
$900 = (400 x Rate x 20) / 100
Multiplying both sides by 100 and dividing by 400 x 20, we get:
Rate = $900 / (400 x 20) = 0.1125 or 11.25%
Therefore, the rate of interest is 11.25%.
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Write the equation of the line in slope-intercept form.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{ 5 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{ 5 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -4 = - \cfrac{ 5 }{ 4 } ( x +4) \\\\\\ y-4=- \cfrac{ 5 }{ 4 }x-5\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 4 }x-1 \end{array}}[/tex]
This is for precalc can someone help please
9 belongs to the set N
Answer:
9 belongs to set N, natural, whole, integer, rational, and real number
Step-by-step explanation:
* Natural number: use for counting
* Whole number: includes natural number and zero
* Integer : are whole numbers and their opposite
*Rational number:come from fraction, and their results can be positive integer
*Real number: includes all numbers
what are the answers to these questions?
a) The function of h in terms of r is h=1400/(πr²).
b) The surface area of the can in terms of r is 2800/r+2πr².
c) The corresponding values of r and h that minimize the amount of required material are r≈14.04 cm and h≈2.98 cm.
a) The volume of a cylinder is given by
V = πr²h.
In this case, the volume of the can is
1400 cm³
So we have
1400 = πr²h.
Solving for h, we get
h = 1400/(πr²).
b) The surface area of a cylinder is given by
A = 2πrh+2πr².
Using the expression we obtained for h in part (a), we can substitute it in the equation and get
A = 2πr(1400/(πr²))+2πr²
= 2800/r+2πr².
c) To minimize the amount of required material, we need to find the value of r that minimizes the surface area.
To do this, we take the derivative of the surface area expression with respect to r and set it equal to zero:
dA/dr = -2800/r²+4πr = 0.
Solving for r, we get
r = √(700/π), which is approximately 14.04 cm.
Substituting this value in the expression for h that we obtained in part (a), we get
h = 1400/(π(14.04)²), which is approximately 2.98 cm.
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Confusing
Kerrin is making an input-output table for the rule "add 5." What is the output value for an input value of 5?
Options:
A: 0
B :5
C: 10
D: 25
The calculated output value for an input value of 5 is (c) 10
What is the output value for an input value of 5?From the question, we have the following parameters that can be used in our computation:
Kerrin is making an input-output table for the rule "add 5."
This means that
Output = input + 5
In this case, we have
input = 5
substitute the known values in the above equation, so, we have the following representation
Output = 5 + 5
Evaluate
Output =10
Hence, the output is 10
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What are the solutions to the system of equations?
y=x^2−5x−6
y=2x−6
(−1, 0) and (−6, 0)
(7, 8) and (0, −6)
(−6, 0) and (0, −1)
(−1, 0) and (0, −6)
Please answer- I will report you if you do not answer and only want the points.
The solutions of the system of equations are (0, -6) and (7, 8)
How to find the solution of the system of equations?
Here we have the system of equations:
y=x^2−5x−6
y=2x−6
To solve this, we need to solve the equation:
x^2 - 5x - 6 = 2x - 6
x^2 - 7x = 0
x*(x - 7) = 0
We can see that the two solutions are:
x = 0
x = 7
Evaluating the line in these values we get:
y = 2*0 - 6 = -6
y = 2*7 - 6 = 8
Then the solutions are (0, -6) and (7, 8)
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If 90% of a number is 110, find 9% of that number.
We can set up the equation :
0.9x = 110 ,
where x is the unknown number. To solve for x, we can divide both sides by 0.9 :
x = 110 ÷ 0.9
x = 122.22 (rounded to two decimal places)
So the unknown number is approximately 122.22.
To find 9% of that number, we can multiply 122.22 by 0.09 :
0.09 × 122.22 = 11.00 (rounded to two decimal places)
Therefore, 9% of the number is approximately 11.
simplify (5^4)^2. 5^6. 5^8. 25^6. 25^8
Therefore here, (5⁴)². 5⁶. (5⁸)².(5⁶)². (5⁸)² simplifies to 5⁸².
The simplest version is what?The integer's basic form is represented by its smallest equivalent fraction. How to determine the simplest form: Look for shared components in the denominator and numerator.
By applying the exponentiation laws, let's us gradually simplify this an expression is:
[tex](5^4)^2 = 5^(4*2) = 5^85^6 * 5^8 = 5^(6+8) = 5^1425^6 = (5^2)^6 = 5^(2*6) = 5^1225^8 = (5^2)^8 = 5^(2*8) = 5^16[/tex]
When all of these simplifications are put back into the original statement, we get the following:
[tex](5^4)^2. 5^6. 5^8. 25^6. 25^8 = 5^8 * 5^14 * 5^12 * 5^16 * 5^16[/tex]
Using the rule that is [tex]a^b * a^c = a^(b+c)[/tex],
The first three terms can be combined to create:
[tex]5^8 * 5^14 * 5^12 * 5^16 * 5^16 = 5^(8+14+12) * 5^(16+16) = 5^50 * 5^32[/tex]
Using the same rule again, we can combine these two terms:
5⁵⁰* 5³²
= 5⁵⁰⁺³²
= 5⁸²
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Factor the polynomial completely. If the polynomial is prime, so state.
15y2 - 19y + 6
Answer: 15y2 - 19y + 6 = 0
Step-by-step explanation:
The first term is, 15y2 its coefficient is 15 .The middle term is, -19y its coefficient is -19 .The last term, "the constant", is +6 Step-1 : Multiply the coefficient of the first term by the constant 15 • 6 = 90 Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -19 .
En un grupo de 60 alumnos, 12 sacaron 10 en el examen de matemáticas. ¿Cuál es el porcentaje de alumnos que sacaron 10?
We can see that the percentage is 20%, then 20 percent of the students got a 10.
Which percentage of the students got a 10?To find this, we need to use the formula:
Percentage = 100%(number of students with a 10)/(total number of students)
Here we know the that the revelant numbers are:
Number of students with a 10 = 12
total number of students in the class = 60
Replacing that in the formula we will get the percentage:
P = 100%*(12/60)
P = 20%
So 20% of the total number of students got a 10.
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where should the linear inequality y ≤ 1/4 x- 3 be shaded?
The required direction of the inequality is below the line.
How to find the direction of inequality in graph?If you're not graphing a vertical line, the inequality's sign will tell you which half-plane to shade. Shade above the line when using the or > sign. Shade below the line if the symbol or is used. Larger solutions are to the right and smaller solutions are to the left, respectively, for a vertical line.
According to question:To check the direction, we will take points from the graph and put in the given inequality.
At point (2, 0)
y ≤ x/4 - 3
0 ≤ 2/4 - 3
0 ≤ -25
It is false
Again
At (2, -4)
y ≤ x/4 - 3
-4 ≤ 2/4 - 3
-4 ≤ -2.5
It is true,
Thus, we can say the direction of the inequality is below the line.
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helpppp
in the figure below, m WXZ=72 degrees, and m 2 is three times m 1. Find m 1
Answer:
Step-by-step explanation:
The volume of a juice box is about 24 cubic inches.
One number is 6 3/4 while another number is 2 1/6 smaller. Find the sum of these numbers.
The sum of both numbers is 107/12
How to calculate the sum of both numbers ?One number is 6 3/4
The other smaller number is 2 1/6
The sum of both numbers can be calculated as follows
= 6 3/4 + 2 1/6
= 27/4 + 13/6
= 162 + 52/24
= 214/24
= 107/12
Hence the sum of both numbers is 107/12
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Help please!!!!
Whoever answers right gets brainliest!
Answer:
its 112.7
Step-by-step explanation:
x+2x=3x. 3x = 338
divide 3x and 338 by 3 three is cancelled and x equals to 112.7
[tex]\sf x=13.[/tex]
Step-by-step explanation:1. Formula for area.Assuming that the canvas has a standard rectangle shape, the area should be given by: [tex]\sf A= bh[/tex], where "b" is the base length of the rectangle, and "h" its heignt.
2. Form an equation.We're told that the canvas is "x" inches wide, and that the length of it is "twice as long as the width", thus it is "2x". Now, let's take width as the base, and length as the height.
Since the formula for area is just a product between width and length, and those values are "x" and "2x", respectively, the formula for the area of this canvas is:
[tex]\sf (x)(2x)=338(in^{2} )[/tex]
3. Solve the equation.a) Solve the product.
[tex]\sf (x)(2x)=338(in^{2} )\\ \\\sf 2x^{2} =338(in^{2} )[/tex]
b) Divide by "2" on both sides of the equation.
[tex]\sf \dfrac{2x^{2}}{2} =\dfrac{338(in^{2} )}{2} \\ \\x^{2} =169[/tex]
c) Take the square root of both sides.
[tex]\sf \sqrt{x^{2}} =\sqrt{169} \\ \\x=13[/tex]
4) Final answer.[tex]\sf x=13.[/tex]
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Given Circle C, calculate the length of PQ (Thx for any help!)
Answer:
3π
Step-by-step explanation:
Given
Radius=9
Angle=60°
Since PQ is an arc
Perimeter of an Arc =(θ/360)×2πr
60/360×2π(9)
1/6×18π
3π
The temperature is dropping at 3 degrees per hour. At noon it was 0 degrees, what was the temperature at 1pm? 2pm? 3pm? 6pm? What was the temperature t hours after noon?
The temperature at 1pm is -3°C, at 2pm it's -6°C, at 3pm it's -9°C, and at 6pm it's -18°C. The temperature t hours after noon is T = 0 - 3t
If the temperature is dropping at a rate of 3 degrees per hour, then the temperature t hours after noon can be represented by the equation T = 0 - 3t, where T is the temperature in degrees Celsius.
To find the temperature at a specific time after noon, we need to substitute the corresponding value of t into the equation and solve for T. For example:
At 1pm (t = 1), T = 0 - 3(1) = -3°C
At 2pm (t = 2), T = 0 - 3(2) = -6°C
At 3pm (t = 3), T = 0 - 3(3) = -9°C
At 6pm (t = 6), T = 0 - 3(6) = -18°C
To find the temperature t hours after noon, we can use the same equation: T = 0 - 3t. For example, if we want to find the temperature 4 hours after noon, we can substitute t = 4 into the equation: T = 0 - 3(4) = -12°C. So the temperature 4 hours after noon is -12°C.
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