The angle of rotation = 19.35°
Explanations:The diameter of the ferris wheel = 225 feet
Radius, r = diameter/2
r = 225/2
r = 112.5 feet
The passenger travels 38 feet when the wheel stops
This is the arc length
Arc length = 38 feet
Using the formula for the length of an arc
[tex]\text{Arc length = }\frac{\theta}{360}\times2\text{ }\pi\text{ r}[/tex][tex]\begin{gathered} 38\text{ = }\frac{\theta}{360}\times2\times\frac{22}{7}\times112.5 \\ \theta\text{ = }\frac{38\times360\times7}{2\times22\times112.5} \\ \theta\text{ = }\frac{95760}{4950} \\ \theta\text{ = }19.35^0 \end{gathered}[/tex]The angle of rotation = 19.35°
Find the next three terms in this sequence: 5120, 1280, 320, 80...-160, -400, -64020, 5, 1.2540, 20, 1076, 72, 68
Given the first four terms of this sequence:
[tex](5120,1280,320,80,\ldots)[/tex]We can see a pattern. To analize this pattern, let's first check the difference between those terms.
[tex]\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}[/tex]From those differences, we can verify the following equations:
[tex]\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}[/tex]From this, we can write the general rule for this sequence:
[tex]a_n=\frac{5120}{4^{n-1}}[/tex]This sequence gives us:
[tex]\begin{gathered} a_1=5120 \\ a_2=1280 \\ a_3=320 \\ a_4=80 \\ a_5=20 \\ a_6=5 \\ a_7=1.25 \end{gathered}[/tex]Then, we have the following 3 terms. (20, 5, 1.25)
8. If the slope of the equation y = -3/5x + 4 is changed to 3/5 and the y-intercept is changed to -4, which statement best describes this situation? You can use a calculator to graph or create your own graph.*A The new line is perpendicular to the original line. B The new line is parallel to the original line. C The new line and the original line have the same y-intercept. D The new line and the original line have the same x-intercept.
Answer:
Explanation:
Given that the line
[tex]y=-\frac{3}{5}x+4[/tex]is changed to
[tex]y=\frac{3}{5}x-4[/tex]A triangle has angle measures of 27 degrees , 50 degrees, and x degrees, use the triangle sum theorem to find the value of x.
ANSWER:
Angle x is 103 degrees
EXPLANATION
The sum of all the angles in a triangle is 180 degrees
Hence, Let angle A = 27 degrees
Angle B = 50 degrees
Angle C = x degrees
Triangle sum theorem state that
50 + 27 + x = 180
77 + x = 180
x = 180 - 77
x = 103 degrees
Please Help! An eight foot ladder leans against a building. if the ladder makes an angle of 60 degrees with the ground, haw far from the building is the base of the ladder. Round you answer to the nearest tenth.
The base of the ladder is 4 ft away from the buliding
Here, we want to calculate the distance from the building to the base of the ladder
To properly answer this, an image of the question is needed
We have this as follows;
From the diagram, what we want to calculate is the distance d
To calculate this, we need the appropriate trigonometric identity
Firstly, we need to identify the parts of the triangle present
As we can see, we have the hypotenuse which is the side that faces the right angle and also is the longest side
The side we want to get is the adjacent
Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine
Thus, we have it that;
[tex]\begin{gathered} \cos \text{ 60 = }\frac{d}{8} \\ \\ d\text{ = 8 cos 60} \\ d\text{ = }4.0\text{ ft} \end{gathered}[/tex]Solve the system of two linear inequalities graphically,2y <&- 1618v 2 - 7x+56Step 1 of 3: Graph the solution set of the festlinear InequallyAnswerThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawEnable ZoonpanChoose the type of boundary linesSolid (-) Dashed)Enter two points on the boundarytine:10Select the region you wish to be shaded:
Given
[tex]\begin{gathered} 2y<8x-16 \\ 8y\ge7x+56 \end{gathered}[/tex]The graph
Two boundary points
(0,7) (2,0)
Multiply. Write the result in standard form.(2 + 1)(3^4 + 7 + 2)
To multiply polynomials, we use the distributive law
[tex]\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}[/tex]The last part follows by the laws of exponentials, finally we combine like terms
[tex]\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}[/tex]5) Given the following matrices, find the products of LN and MN
Answer:
The products MN and LN are not possible.
Explanation:
Matrix multiplication is only possible when the column number of the first matrix equals the row number of the second matrix.
Now, matrix L is a 2 x 2 matrix and N is a 5 x 2 matrix. Now L has 2 columns and N has 5 rows. Meaning, that columns of L are not equal to the rows of N. Therefore, matrix multiplication is not possible.
Matrix M is 2 x 4 and matrix N is 2 x 2. Since columns of matrix M equal the rows of matrix N, matrix multiplication is possible.
Therefore,
[tex][/tex]Find the standard deviation for the following wroup of data Hems, Round your answer to the nearest tenth for one decimal place), 7,9,11,14,15,16
The standard deviation of the groups of data is 3.3 .
The standard deviation is calculated using the formula [tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
Where σ is the standard deviation.
x denotes the data of the population.
N is the size of the population.
μ is the mean of the population.
The given population is 7,9,11,14,15,16
Here N= 6
Mean (μ) = (7+9+11+14+15+16)÷6 = 72/6=12
Now we will put the values in the above equation to calculate the sd.
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{6}}\sum _{i=1}^{6}\left(x_{i}-{12 }\right)^{2}}}}[/tex]
Simplifying we get:
σ = √(64/6)
σ = 3.2659..
σ = 3.3
The standard deviation is a statistic that indicates the degree of volatility or dispersion in a set of numerical values.
A low standard deviation shows that possibly the values tend toward being close to the mean, sometimes referred to as the expected value of the set, whereas a large standard deviation suggests that the values are distributed over a wider range.
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To solve the inequality -7x<24, the inequality sign must be reversed.A. TrueB. False
ANSWER
True
EXPLANATION
To solve the inequality given:
-7x < 24
we have to divide both sides of the inequality by -7.
Dividing both sides of an inequality causes the sign to change direction (or be reversed) and so we will have:
x > -24 / 7
Therefore, it is true that the sign will be reversed.
solution of the system of equations.2. (3, 0) 2x+y=-63x + 2y = 94. (-2,3) y =2x+75x+y=-76. (0,-7) 2x -2y = 14X-Y=-7
We can solve these systems of equations as follows:
First CaseWe have:
[tex]\begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases}[/tex]And we can solve this system by substitution as follows:
[tex]\begin{gathered} 2x+y=-6 \\ 2x-2x+y=-6-2x \\ y=-6-2x \end{gathered}[/tex]Now, we can substitute the corresponding value of y into the second equation as follows:
[tex]\begin{gathered} y=-6-2x \\ 3x+2y=9 \\ 3x+2(-6-2x)=9 \\ 3x+(2)(-6)+(2)(-2x)=9 \\ 3x-12-4x=9 \\ 3x-4x-12=9 \\ -x-12=9 \\ -x-12+12=9+12 \\ -x=21\Rightarrow x=-21 \end{gathered}[/tex]Now, we can substitute the value x = -21 into either of the original equations to find the value of y. We will use the first equation:
[tex]\begin{gathered} 2x+y=-6 \\ 2(-21)+y=-6 \\ -42+y=-6 \\ -42+42+y=-6+42 \\ y=36 \end{gathered}[/tex]Therefore, the solution to this first system is (-21, 36).
We can check this result if we substitute both values into the original equations:
[tex]\begin{gathered} \begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases} \\ x=-21,y=36 \\ \begin{cases}2(-21)+36=-6 \\ 3(-21)+2(36)=9\end{cases} \\ \begin{cases}-42+36=-6 \\ -63+72=9\end{cases} \\ \begin{cases}-6=-6\Rightarrow This\text{ is true.} \\ 9=9\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]Therefore, the solution to the first system of equations is (-21, 36).
Second Case
[tex]\begin{cases}y=2x+7 \\ 5x+y=-7\end{cases}[/tex]We can rewrite the system as follows:
[tex]\begin{cases}-2x+y=7 \\ 5x+y=-7\end{cases}[/tex]And we can solve this system by the elimination method: We have to multiply one of the equations by -1 and then add them algebraically as follows:
[tex]\begin{gathered} \begin{cases}-2x+y=7 \\ -1(5x+y=-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ (-1)(5x)+(-1)(y)=(-1)(-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ -5x-y=7\end{cases} \end{gathered}[/tex]If we add both equations, then we have:
[tex]\begin{gathered} \frac{\begin{cases}-2x+y=7 \\ -5x-y=7\end{cases}}{-7x=14} \\ -\frac{7x}{-7}=\frac{14}{-7} \\ x=-2 \end{gathered}[/tex]And now we can substitute this value in either equation to find y:
[tex]\begin{gathered} y=2x+7 \\ y=2(-2)+7 \\ y=-4+7 \\ y=3 \end{gathered}[/tex]And we got y = 3.
Therefore, the solution to this system is equal to (-2, 3), and we can also check the solutions using the original equations:
[tex]\begin{gathered} \begin{cases}y=2x+7 \\ 5x+y=-7\end{cases} \\ \begin{cases}3=2(-2)+7 \\ 5(-2)+3=-7\end{cases} \\ \begin{cases}3=-4+7 \\ -10+3=-7\end{cases} \\ \begin{cases}3=3\Rightarrow This\text{ is true.} \\ -7=-7\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]In summary, we have that:
The solution to the first system ---> (-21, 36).
The solution to the second system ---> (-2, 3).
Maggie graphed a scatter plot of the numberof hours she drove, t, and the number of milesshe traveled, d. She then found a trend line ofher data to be d = 45.5t + 8. What is thepredicted distance Maggie will travel # shedrives for 4 hours?A 182 milesB 372 milesC 364 milesD 190 milesWhat’s the answer ?
WE have the following:
[tex]d=45.5t+8[/tex]When t = 4
[tex]undefined[/tex]I need help on 4 please it says find the value of x round each answer to the nearest tenth
The pythagorean theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse
a and b are the legs of the triangle.
From the problem, a = x, b = 19.1 and c = 30.5
Using the formula :
[tex]\begin{gathered} 30.5^2=x^2+19.1^2 \\ 930.25=x^2+364.81 \\ x^2=930.25-364.81 \\ x^2=565.44 \\ x=\sqrt[]{565.44} \\ x=23.779 \end{gathered}[/tex]The answer rounded to the nearest tenth is x = 23.8
a teacher performing a demonstration find that a piece of court displaces 23.5 ml of water . the piece of cork had a density of 5.7 grams. what is the density of the cork
We are asked to determine the density of the cork. To do that we will use the following formula:
[tex]D=\frac{m}{V}[/tex]Where:
[tex]\begin{gathered} D=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}[/tex]The volume of the cork is the same as the volume that it displaced of water, therefore, we have:
[tex]V=23.5ml[/tex]Now, we substitute the values and we get:
[tex]D=\frac{5.7g}{23.5ml}[/tex]Solving the operations:
[tex]D=0.24\frac{g}{ml}[/tex]Therefore, the density of the cork is 0.24 g/ml.
The graph of g consists of two straight lines and a semi circle. Evaluate each
Given:
a)
[tex]\int ^1_0g(x)dx[/tex]Consider the shape included in the region from 0 to 1 of g(x).
The area is,
[tex]\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2[/tex]b) From x = to x = 6 includes the semi-circle. Its area is calculated as,
[tex]\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28[/tex]#1) Write the ratio of 60 km in 28 minutes in simplest form.#2) Is this ratio a rate? Explain your answer using words. [C
1. Expressing 60km per 28 minutes in its simplest form requires us to get it per 1 minute. This, we can easily obtain by:
[tex]\frac{60\operatorname{km}}{28\min}=\frac{15\operatorname{km}}{7\min}=2\frac{1}{7}\frac{km}{\min }[/tex]2.143 km per minute
2. The ratio is a rate. A rate is a measure of a quantity with respect to another, especially with respect to time.
As can be seen, this ratio is speed. Speed is a measure of distance covered per time.
Multiply the following polynomials. Once simplified, name the resulting polynomial. (x + 2) (4x^2 - 3x - 2)name:
The resulting polynomial consists of four terms , it is called a quadrinomial.
Samuel is 10 years old. He moaned the neighbors lawn on Saturday and I and $40. It took him 2 hours come on the lawn in 2 hours to clean his room. How much money did Samuel earn an hour? A) $4.00B) $6.67C) $10.00D) 20.00
If he earned $40 in total and it took 4 hours to finish everything, he earns in an hour:
[tex]\frac{40}{4}=10[/tex]Answer: Samuel earns $10.00. Letter C.
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room. Step-by-step explanation:10 x 4 = 40$
Step-by-step explanation:
Helpppppppp I can’t answer because I am bad at math
The magnitude of a number is the absoulute value of the number. Recall, the absolute value of a number is always positive. The absolute value of a is written as IaI
Hence,
magnitude of - 7.5 is 7.5
The correct option is D
Which two ratios are equivalent to 11/12?A. 4/5 and 12/13B. 22/24 and 33/36C. 22/33 and 33/34D. 23/24 and 35/36
Two ratios are equivalent if the division between them is equal to one. We need to look at the options to check for which these are true.
For A:
[tex]\frac{\frac{11}{12}}{\frac{4}{5}}=\frac{11}{12}\cdot\frac{5}{4}=\frac{55}{48}[/tex]Since the answer is different than one, this is not the correct option.
For B:
[tex]\frac{\frac{11}{12}}{\frac{22}{24}}=\frac{11}{12}\cdot\frac{24}{22}=\frac{264}{264}=1[/tex][tex]\frac{\frac{11}{12}}{\frac{33}{36}}=\frac{11}{12}\cdot\frac{36}{33}=\frac{396}{396}=1[/tex]Since the result of the division is one for both ratios, the correct option is "B".
Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in thissituation?O a bag containing 12 chips in three different colors, with four of each coloro a six-sided number cubea full standard deck of cardsa spinner divided evenly into four sections, with each section a different colorO two coins
the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Explanation:
number of groups of student = 3
We need to select one out of the three.
The option that can be used to simulate this choice is having 12 chips in three different colours. Each colour will have 4 each.
The 3 different colours represent the 3 different groups. While each 4 number of a colour represent the number of students in each group.
Hence, the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
If a bow requires 3/4 yards of lace how many bows can u make with 12 yards of lace
3/4 yards of a lace for each bow
for 12 yards of lace:?
Simply divide the 12 yards of lace by the lace required by each bow (3/4)
12 / (3/4) = 16 bows
A bag of numbered lottery balls contains the numbers 1 through 50. What is the probability that a randomly selected ball will be a number that is not a multiple of 8? Give your answer as a simplified fraction.
A bag of numbered lottery balls contains he numbers 1 through 50.
One ball is selected at random.
From 50 balls, one ball can be selected in 50 different ways.
So, the total number of points in sample space is 50.
Let us consider the event that the number is a multiple of 8 be A.
There are six numbers between 1 o 50 which are multiple of 8.
Therefore, one ball can be selected from 6 balls in 6 different ways.
So, the number of points in sample space in favour of the event A is 6.
Therefore, by the classical definition of probability,
[tex]\begin{gathered} P(A)=\frac{6}{50} \\ =\frac{3}{25} \end{gathered}[/tex]Then, the probability that the selected number is not a multiple of 8 is
[tex]\begin{gathered} P(A^C)=1-P(A) \\ =1-\frac{3}{25} \\ =\frac{22}{25} \end{gathered}[/tex]So, the required probability is 22/25.
Translate this sentence into an equation 43 is the difference of Chrissy’s age and 14 Use the variable c to represent Chrissy’s age
When translating into mathematical equations, "is" uses the equal sign and "difference" means that the operation to be used is subtraction.
So, "43 is the difference of Chrissy's age and 14" is written as:
43 = C - 14
Select all of the constraints that apply to this situation $1.25x when x <12$12.00 + $0.75(x-12) when X_>12$1.25x when x _>120.75x when x >12$12.00 + $0.75x when x >12
We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be
[tex]1.25x,x<12[/tex]Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be
[tex]0.75\cdot(x\text{ -12)}[/tex]as this is an additional cost to the 12, we add 12 to this expression. THen we get
[tex]12+0.75\cdot(x\text{ -12)}[/tex]Note that for this expression, when x=12, we get that the expression becomes
[tex]12+0.75\cdot(12\text{ -12)=12}[/tex]THis means that the expression applies from 12 and on, so we have the followin inequality12
[tex]12+0.75\cdot(x\text{ -12), x}\ge12[/tex]CAN SOMEONE HELP WITH THIS QUESTION?✨
The coterminal angle is 943° .
What is a coterminal angle?Coterminal angles are angles with the starting side on the positive x-axis and a shared terminal side. They are in standard position. Examples include the coterminal nature of the angles 30, -330, and 390. The phrase "coterminal angle" refers to angles with the same starting side and terminal side. If the specified angle is given in radians or degrees, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. It is possible to find all possible coterminal angles. The coterminal angle is described in mathematics as the angle formed by two angles drawn side by side in the same plane. Furthermore, both of them share the same location for their terminal sides. As an illustration, 405 and -315 are the coterminal angles of 45.
1294° = 360° + 934°
So the coterminal angle for 1294° is 934° .
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Which of the following transformations shows a rotation 270 degrees counterclockwise? *
Explanation:
A rotation 270 degrees counterclockwise happens when the y and x axis value are interchanged and the interchanged y value becomes negative.
When we look at the options given, we look for the image whose rotation is in the positive x axis and negative y axis.
Also the movement will be thrice while moving anticlockwise.
From the options, the one which fits into the description above is B.
There is a movement of counterclockwise
I inserted a picture of the question answer choices E. 15 F.x
Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.
Answer: 8 and 12, 1, and 15 are like terms.
Victor took a survey of high school students to see how many had part-time jobs last summer. The results of the survey are shown in the table. Compare theprobability that a student in the sophomore class had a part-time job to the probability that a student in the junior class had a part-time job.
Answer:
A sophomore is less likely than a Junior to have a job.
Explanation:
Given the table in the attached image.
The total number of sophomores is
[tex]35[/tex]The number of sophomores with a job is;
[tex]12[/tex]The probability that a sophomore had a job is;
[tex]P_S=\frac{12}{35}[/tex]The total number of Juniors is
[tex]37[/tex]The number of Juniors with a job is;
[tex]27[/tex]The probability that a Junior had a job is;
[tex]P_J=\frac{27}{37}[/tex]From the derived Probability, we can observe that the probability that a Junior had a job is greater than the probability that a Sophomore had a job.
[tex]P_J>P_S[/tex]Therefore, A sophomore is less likely than a Junior to have a job.
1. Solve -4x < -3(6x - 2) and sketch the solution set on a number line.
We need to solve the inequality:
[tex]-4x<-3\mleft(6x-2\mright)[/tex]Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:
[tex]\begin{gathered} -4x<-3\mleft(6x-2\mright) \\ -4x<-18x+6 \\ -4x+18x<6 \\ 14x<6 \\ x<\frac{6}{14} \\ x<\frac{3}{7} \end{gathered}[/tex]The solution set is:
[tex]\begin{gathered} x<\frac{3}{7} \\ or \\ x<0.4286 \end{gathered}[/tex]This means that x is less than 3/7, or
x is less than 0.4286
On the number line it looks:
Express - 345 asin simplest form, where m and n are integers.Enter the correct answer in the box.-345 =
As -345 is an integer, the simplest fraction form is:
[tex]\frac{-345}{1}[/tex]or -345/1 (m=-345, n=1).