The solution to the question is given below.
[tex]\begin{gathered} The\text{ 2.6km is some fraction of the entire Circumference which is: C= 2}\pi r\text{ = 2}\times\text{ }\pi\text{ }\times2.9 \\ \text{ = 5.8}\pi cm \\ \text{ The fraction becomes: }\frac{2.61}{5.8\pi}\text{ = }\frac{0.45}{\pi} \\ \text{The entire circle is: 2 }\pi\text{ radian} \\ \text{ = }\frac{0.45}{\pi}\text{ }\times2\text{ }\times\pi\text{ = 0.9} \\ The\text{ skier has gone 0.9 radian from (-.1.464, 2.503)} \\ \text{The x- cordinate become: =-1.}464\text{ cos}(0.9)\text{ = -1.4625} \\ while\text{ the Y-cordinate becomes: =-1.}464\text{ sin}(0.9)\text{ = -}0.0229 \\ \text{The skier rested at: (-1.4625, -0.0229)} \\ \end{gathered}[/tex]Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answer:
45.1
Step-by-step explanation:
96 x .47 = 45.12
Rounded to the nearest tenth is 45.1
Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.
The speedometer on Leona's car shows the speed in both miles per hour and kilometers per hour. Using 1.6 km as the equivalent for 1 mi, find the mile per hour rate that is equivalent to 40 kilometers per hour.
To find the mile per hour rate equivalent to 40 km per hour, let's convert 40km to miles using the given equivalence in the question.
[tex]\begin{gathered} 1.6\operatorname{km}=1mi \\ 40\operatorname{km}\times\frac{1mi}{1.6\operatorname{km}}=\frac{40\operatorname{km}mi}{1.6\operatorname{km}}=25mi \end{gathered}[/tex]Therefore, 40 km = 25 miles.
The mile per hour rate equivalent to 40km per hour is 25 miles per hour.
The Hornet's soccer team scored 5 goals in their last match.The other team, the Panthers, won by 3 goals. Which integerrepresents the number of goals that the Panthers won by?
The match was Hornet's vs Panthers
Hornets's scored 5 goals
Panthers won by 3 goals, this means that the panters scored 3 more goals than the Hornets.
That would be +3 goals.
Given that DE is the midsegment of the scalene AABC, answer theprompts to the right.
Answers:
Part A.
C. AD = AE
Part B.
BC = 26
Explanation:
Part A.
If DE is a midsegment of triangle ABC, D is a point that divides AB into two equal segments, so option A. 1/2 AB = AD is true.
Additionally, if DE is a midsegment of triangle ABC, its length is equal to half the length of the side that the segment doesn't cross. So:
[tex]\begin{gathered} DE=\frac{1}{2}BC \\ 2DE=2\times\frac{1}{2}BC \\ 2DE=BC \end{gathered}[/tex]Therefore, option B is also true.
Triangle ABC is scalene, it means that all their sides have different length, it means that AD is not equal to AE and option C is not true.
Finally, segments AE and EC form AB, so:
AC = AE + EC
AC - AE = AE + EC - AE
AC - AE = EC
So, option D is also true.
Therefore, the answer for part A is C. AD = AE
Part B.
We know that 2DE = BC, so replacing the expression for each segment, we get:
[tex]\begin{gathered} 2DE=BC \\ 2(2x+1)=5x-4 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 2(2x)+2(1)=5x-4 \\ 4x+2=5x-4 \\ 4x+2-4x=5x-4-4x \\ 2=x-4 \\ 2+4=x-4+4 \\ x=6 \end{gathered}[/tex]Now, with the value of x, we get that BC is equal to:
BC = 5x - 4
BC = 5(6) - 4
BC = 30 - 4
BC = 26
So, the answer for part B is 26.
Translate the sentence into an equation,The sum of 5 times a number and 4 is 3.Use the variable b for the unknown number.
Given the sentence, the sum of 5 times a number and 4 is 3.
The information would translate to;
[tex]\begin{gathered} (5\times b)+4=3 \\ 5b+4=3 \end{gathered}[/tex]ANSWER:
[tex]5b+4=3[/tex]Convert 253 inches to yards using dimensional analysis.
As given by the question
There are given that the 253 inches
Now,
To convert the inches to yards, multiply the value in inches by the conversion factor 0.0277777787.
So,
[tex]253\times0.0277777787=7.0277778.[/tex]Hence, the value of the given inches is 7.0278 yards.
A true-false test contains 10 questions. In how many different ways can this test be completed?(Assume we don't care about our scores.)This test can be completed indifferent ways.
Explanation:
The test contains 10 questions, each one can be answered either with 'true' or with 'false' which means that for each question there are only 2 options.
We need to find the number of ways in which the test can be completed.
To answer the question we use the fundamental counting principle:
In this case, there are 2 ways to complete each question, therefore, we multiply that by the 10 questions that we have:
[tex]2\times2\times2\times2\times2\times2\times2\times2\times2\times2[/tex]This can be simplified to
[tex]2^{10}[/tex]which is equal to:
[tex]2^{10}=\boxed{1024}[/tex]Answer:
1024
I need help with this question... it's about special triangles and I need to find y and z.. it should also not be a decimal.
To find z, consider the right-angled triangle at the botton in the diagram showm
[tex]\begin{gathered} \sin 45\text{ = }\frac{z}{20} \\ z\text{ = 20 }\sin 45 \\ z\text{ = }20\text{ }\times\frac{1}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ z\text{ = }\frac{20\sqrt[]{2}}{2} \\ z\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]Let the common base of both triangles be m
[tex]\begin{gathered} \cos 45\text{ = }\frac{m}{20} \\ m\text{ = 20 }\cos 45 \\ m\text{ = }\frac{20}{\sqrt[]{2}} \\ m\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ m\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]To find y:
[tex]\begin{gathered} \tan 30\text{ = }\frac{y}{m} \\ \tan 30\text{ = }\frac{y}{10\sqrt[]{2}} \\ \frac{1}{\sqrt[]{3}}=\text{ }\frac{y}{10\sqrt[]{2}} \\ y\text{ = }\frac{10\sqrt[]{2}}{\sqrt[]{3}} \\ y\text{ = }\frac{10\sqrt[]{6}}{3} \end{gathered}[/tex]To find x:
[tex]\begin{gathered} \sin 30=\frac{y}{x} \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\div x \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\times\frac{1}{x} \\ x\text{ = }\frac{20\sqrt[]{6}}{3} \end{gathered}[/tex]need help with math
are natural numbers closed under theoperation of subtraction? why or why not?
Firstly, let us define natural numbers.
Natural numbers are simply positive intergers, that is integers that are greater than zero e.g 1,2,3,4...
Secondly, when is a set said to be closed under a particular operation?
A set is said to be closed under an operation if and only if the operation on any two elements of the set produces another element of the same set. for example when you perform an operation (like addition) on a set of number (like natural numbers) it must give you a number from that same set.
E.g
let's check whether natural numbers are closed under the operation of adddition.
taking two numbers 3 and 5.
[tex]3+5=8[/tex]since the operation gives us 8, which is a natural number, it means natural numbers are closed under the operation of addition.
Back to the main question, which is to check whether natural numbers are closed under the operation of subtraction.
taking two cases.
case 1; taking numbers 3 and 5
[tex]3-5=-2[/tex]case 2: taking numbers 7 and 2
[tex]7-2=5[/tex]From the two cases, case 2 gave us a natural number while case 1 does not give us a natural number.
This means that Natural numbers are not Closed under subtraction.
Because subtraction operation on natural numbers does not necessarily produce another natural number.
On a general note;
Natural numbers are closed under Addition and Multiplication operations
while They are not closed under subtraction and division operation
2. When is it important to use a strict inequality vs a non-strict inequality?
A strict inequality is one which involves the use of
[tex]>\text{, }<\text{ or }\ne[/tex]A non-strict inequality is one which involves the use of
[tex]\ge\text{ or }\leq[/tex]A strict inequality is used in a case when the two values being compared or related to one another cannot be equal to one another. That is, they are different.
A non-strict inequality is used in case when there is a possibility that the two values being compared can be equal to one another.
Question 13 (3 points)
Intel's microprocessors have a 1.8% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.
EXPLANATION
The probability that Event A happening is the following:
[tex]P(A)[/tex]
The probability of Event A not happening is the following:
[tex]100-P(A)[/tex]Therefore, we have:
[tex]P(Malfunctioning)+P(Non\text{ Malfunctioning\rparen=100\%}[/tex]Plugging in the terms into the expression:
1.8 + P(Not malfunctioning) = 100%
Subtracting -1.8 to both sides:
[tex]P(Not\text{ malfunctioning\rparen=100-1.8}[/tex]Subtracting numbers:
[tex]P(Not\text{ malfunctioning\rparen=98.2}[/tex]In conclusion, the probability of not malfunctioning is 0.982
Find the equation of a line parallel to y=x+6 that passes through the point (8,7)(8,7).
The equation of the line which is parallel to the line y = x + 6, and which passes through the point (8, 7) is; y = x - 1
What are parallel lines in geometry?Parallel lines are lines do not intersect and which while on the same plane, have the same slope.
The given line to which the required line is parallel to is y = x + 6
The point through which the required line passes = (8, 7)
The slope of the given line, y = x + 6, is 1,
The slope of parallel lines are equal, which gives;
The slope of the required line is 1
The equation of the required line in point and slope form is therefore;
y - 7 = 1×(x - 8) = x - 8
y = x - 8 + 7 = x - 1
The equation of the required line in slope–intercept form is; y = x - 1
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This relation map is the musician to the instrument they play. is this relation a function?
Find the horizontal and vertical components for a vector round to the nearest tenth
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The horizontal component of a vector having:
[tex]\text{ a magnitude of v and a direction of }\theta\text{ = v cos }\theta[/tex]The vertical component of a vector having:
[tex]a\text{ magnitude of v and direction of }\theta\text{ = v sin}\theta[/tex]
Then, with the information above, the horizontal component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} \text{Horizontal component = 15 x cos 210}^{\text{ 0}}=\text{ 15 x -0.8860 = -12.99}\approx\text{ -13.0 } \\ \text{Taking the absolute value, we have } \\ \text{Horizontal component = 13.0 units ( to the nearest tenth)} \end{gathered}[/tex]The vertical component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} vertical\text{ component = 15 x sin 210}^{\text{ 0}}=\text{ 15 x -0.5 = -7.5 } \\ \text{Taking the absolute value, we have } \\ Vertical\text{component = 7.5 units ( to the nearest tenth)} \\ \\ \text{Hence the horizontal and vertical component of the vector =} \\ (\text{ 13. 0 , 7. 5 ) ( to the nearest tenth)} \end{gathered}[/tex]I have to find cars a speed in miles per hour
The graph in the picture shows the relationship between the distance traveled (y-axis) and the time (x-axis) that car A traveled.
The slope of the line represents the speed at which the car traveled. To determine the said speed you have to calculate the slope of the line.
-The first step is to determine two points of the line:
(x₁,y₁) → (2,80)
(x₂,y₂) → (0,30)
-The second step is to calculate the slope using the following formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) represent the coordinates of one point of the line
(x₂,y₂) represents the coordinates of a second point of the line
Replace the formula with the coordinates of the points and calculate the slope:
[tex]\begin{gathered} m=\frac{(80-30)mi}{(2-0)hr} \\ m=\frac{50mi}{2hr} \\ m=25\frac{mi}{hr} \end{gathered}[/tex]The slope of the line, which represents the speed of the car, is 25 miles per hour
a wood cutter measures a piece of wood to be 830 grams.There are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pounds.Whats is the mass of the wood in pounds
The mass of the wood in pounds is 1.826 pounds.
How to calculate the value?From the information, the wood cutter measures a piece of wood to be 830 grams and there are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pound.
Therefore,the mass will be represented as x
This will be:
830 grams = 0.83 kilograms
0.83/1 = x/2.2
Cross multiply
x = 2.2 × 0.83
x = 1.826 pounds.
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ABCD is a parallelogram
BE= 6x+44
ED= -6x-16
Find the length of BD
The line segment BD has a length of 18 units
How to calculate the length of BD?The possible figure is added as an attachment
From the question, we have the following parameters:
Name of shape = ABCDShape type = ParallelogramBE = 6x + 44ED = -6x - 16The lengths BE and ED implies that the point E is between the endpoints B and D
Since the shape is a parallelogram, then the point E is halfway between the endpoints B and D
So, we have
BE = ED
Substitute the known values in the above equation
6x + 44 = -6x - 16
Evaluate the like terms
So, we have
12x = -60
Divide both sides by 12
x = -5
Substitute x = -5 in BE = 6x + 44
So, we have
BE = 6 x -5 + 44
Evaluate
BE = 14
The length is then calculated as
BD = 2 x BE
So, we have
BD = 2 x 14
Evaluate
BD = 18 units
Hence, the length of BD is 18 units
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The sum of 3 and r is less than 7.What number sentence represents the statement?
The sum of 3 and r can be represented by "3 + r"
If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:
[tex]3+r<7[/tex]Solve the inequality 8y- 5 < 3
Solve the inequality as you do with equations.
[tex]\begin{gathered} 8y-5<3 \\ 8y<3+5 \\ y<\frac{8}{8} \\ y<1 \end{gathered}[/tex]y is less than 1.
The graph of the solution is:
Find the Standard form of the line that has a slope of -6 and y intercept of 10.
We have to write the standard form, Ax+By=C, of the line that has a slope m = -6 and y-intercept b = 10.
To do that we use that information to write the slope-intercept form of the equation and then rearrange it into standard form.
The slope-intercept for the line is:
[tex]\begin{gathered} y=mx+b \\ y=-6x+10 \end{gathered}[/tex]We can then rearrange it as:
[tex]\begin{gathered} y=-6x+10 \\ 6x+y=10 \end{gathered}[/tex]Answer: 6x + y = 10
The function P(x) is mapped to I(x) by a dilation in the following graph. Line p of x passes through (negative 2, 4) & (2, negative 2). Line I of X passes through (negative 4, 4) & (4, negative 2).© 2018 StrongMind. Created using GeoGebra. Which answer gives the correct transformation of P(x) to get to I(x)?
When we're dilating a line, we can either multiply the function value by a constant
[tex]f(x)\to kf(x)[/tex]or the argument of the function
[tex]f(x)\to f(kx)[/tex]Since the y-intercept of both functions is the same, then the multiplied quantity was the argument of the function.
We want to know the constant associated to the transformation
[tex]I(x)\to I(kx)=P(x)[/tex]We have the following values for both functions
[tex]\begin{gathered} I(-4)=4,\:I(4)=-2 \\ P(-2)=4,\:P(2)=-2 \end{gathered}[/tex]For the same y-value, we have the following correlations
[tex]\begin{gathered} I(-4)=P(-2)=P(\frac{1}{2}\cdot-4) \\ I(4)=P(2)=P(\frac{1}{2}\cdot4) \\ \implies I(x)=P(\frac{1}{2}x) \end{gathered}[/tex]and this is our answer.
[tex]I(x)=P(\frac{1}{2}x)[/tex]Three students that share a townhouse find that their electric bill for October is $2.65 less than the September bill. The total of both bills is $174.65, and eachbill is split evenly among the roommates. How much did each owe in September?
SOLUTION
Let the electric bill for September be x.
October's bill is $2.65 less than the September bill
This means that October's bill = x - 2.65
September + october bill = $174.65
That means that x + x - 2.65 = 174.65
Now let's find x which is september's bill
[tex]\begin{gathered} x+x-2.65=174.65 \\ 2x-2.65=174.65 \\ 2x=174.65+2.65 \\ 2x=177.3 \\ x=\frac{177.3}{2} \\ \\ x=88.65 \end{gathered}[/tex]So September's bill is $88.65, now each student pays
[tex]\begin{gathered} \frac{88.65}{3} \\ \\ =\text{ 29.55} \end{gathered}[/tex]So each student owe $29.55 for the month of September
For each of the following scenarios state the domain (starting set) show and state the mapping, and decide if it is a function. Be sure to label your set and indicate the direction of the relation.
Domain: Number of pages
Range:Number of books
Mapping: Number of pages to the number of books.
Explaination: The number of pages is the independent variable and the number of books is the dependent variable.
The given mapping is a function as total number of pages can not have more than two output (number of books).
8 O 6 4. N Which function is graphed? 2. 4 6 8 -8 -6 -4 -2 0 -2 -6 O A. Y- (x² + 4, x=2 1-x+4,452 (x² + 4, x2 OD. V- x + 4, x32 1-x+4,4
The given curve is parabola and its last point is on the x axis at x = 2
So, the equation of curve is :
[tex]x^2+4,x<2[/tex]In the equation of line,
The line start from x = 2 so, x ≥ 2
So, Equation of line is : -x + 4, x ≥ 2
Answer : B)
[tex]y=\begin{cases}x^2+4,x<2 \\ \square \\ -x+4,\text{ x}\ge2\end{cases}[/tex]Which measurement is closest to the shortest distance in miles from Natasha's house to the library?
Given:
The objective is to find the shortest distance between house and library.
Consider the given triangle as,
Here, A represents the house, B the grocery and C the library.
Since it is a right angled triangle, the distance between the house and the library can be calculated using Pythagoras theorem.
[tex]\text{Hypotenuse}^2=Opposite^2+Adjacent^2[/tex]Apply the given values in the above formula,
[tex]\begin{gathered} AC^2=17^2+0.9^2 \\ AC^2=289+8.1 \\ AC^2=297.1 \\ AC=\sqrt[]{297.1} \\ AC=17.237\text{ miles} \end{gathered}[/tex]If Natasha walks through Grocery store,
[tex]\begin{gathered} AC^{\prime}=AB+BC \\ AC^{\prime}=0.9+17 \\ AC^{\prime}=17.9\text{ miles} \end{gathered}[/tex]By comparing the two ways, ACHence, the hypotenuse distance AC, between house and library is the closest distance.
In the diagram below, GD = 10.1,EF 28.1, and EG 16.9. Find the length==of FC. Round your answer to the nearest tenthif necessary.
Solution:
In the figure;
[tex]\begin{gathered} \frac{EG}{EF}=\frac{ED}{EC} \\ \\ EG=16.9,ED=27,EF=28.1 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} \frac{16.9}{28.1}=\frac{27}{EC} \\ \\ EC=44.9 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} FC=EC-EF \\ \\ FC=44.9-28.1 \\ \\ FC=16.8 \end{gathered}[/tex]Good morning, I need help on this questions. Thanks :)
The observed values are given in the table shown in the question. The line of best fit is given to be:
[tex]y=-1.1x+90.31[/tex]where x is the average monthly temperature and y is the heating cost.
A residual is a difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). The formula will be:
[tex]Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value[/tex]QUESTION A
The average monthly temperature is 24.9:
[tex]x=24.9[/tex]Observed cost:
[tex]y=51.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(24.9)+90.31=-27.39+90.31 \\ y=62.92 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=51.00-62.92 \\ R=-11.92 \end{gathered}[/tex]QUESTION B
The average monthly temperature is 35.9:
[tex]x=35.9[/tex]Observed cost:
[tex]y=67.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(35.9)+90.31=-39.49+90.31 \\ y=50.82 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=67.00-50.82 \\ R=16.18 \end{gathered}[/tex]Answer: Hl
Step-by-step explanation:
A can contains 24 fluid ounces of fruit juice. How many pints of fruit juice does the can contain?A 12 ptB 3 pt C 1 1/2 ptD 1/3 pt
In order to convert from fluid ounce to pint, we need to know that 16 fluid ounces is equivalent to 1 pint.
Then, to find how many pints is 24 fluid ounces, we can use a rule of three:
[tex]\begin{gathered} 16\text{ fluid ounces}\to1\text{ pint} \\ 24\text{ fluid ounces}\to x\text{ pints} \\ \\ \frac{16}{24}=\frac{1}{x} \\ x=\frac{24}{16}=\frac{3}{2}=1\frac{1}{2} \end{gathered}[/tex]So 24 fluid ounces is equivalent to 1 1/2 pints, therefore the correct answer is C.
raymond bought 5 rolls of toilet paper towels he got 99 4/3 inches of paper towels in all. how many meters of paper towels were on each roll? please help my grades go in tomorrow and i have a lot today that i dont know how and if i dont make a passing grade on my report card i have to quit band
The length of 5 rolls of toilet papers is 99 4/3
So, the length of one roll will be = 99 4/3 ÷ 5 = 20 1/15 inches
