Harry is trying to complete his hill walking scouts badge. He is using a map with a scale of 1 cm : 2 km. To earn the badge he needs to walk 14 km. What is the distance he needs to walk on the map?
Answer:
7 cm
Step-by-step explanation:
14 / 2 = 7 cm
7cm is the distance Harry needs to walk on the map?
What is Distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
Given that,
Harry is trying to complete his hill walking scouts badge.
He is using a map with a scale of 1 cm : 2 km.
To earn the badge he needs to walk 14 km.
Let the distance he needs to walk on the map is x.
By given data we write an equation
1/2=x/14
Apply Cross Multiplication
14/2=x
7=x
Hence, 7cm is the distance he needs to walk on the map.
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Solve x is less than or equal to 0 and x is greater than or equal to -4
Answer:
x = {-3, -2, -1, 0}
Step-by-step explanation:
x ≤ 0
x > -4
then
x {-3, -2, -1, 0}
The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds
Answer:
0.8390
Step-by-step explanation:
From the question,
Z score = (Value-mean)/standard deviation
Z score = (150.2-160.5)/10.4
Z score = -0.9904.
P(x>Z) = 1- P(x<Z)
From the Z table,
P(x<Z) = 0.16099
Therefore,
P(x>Z) = 1-0.16099
P(x>Z) = 0.8390
Hence the probability that a person weighs more than 150.2 pounds = 0.8390
The total cost of a sweater and a jacket was $71.55 If the price of the sweater was $3.19 less than the jacket, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer: $34.18
Step-by-step explanation:
Let the cost of the Jacket = $x and
The cost of the sweater. = $y
Now total price. = $71.55.
So, $x + $y. = $71.55 -- 1
From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation
y = ( x - $3.19 )
Now substitute for y in the equation (1) above.
x + ( x - 3.19 ) = 71.55
Now solve the equation
x + x - 3.19 = 71.55
2x - 3.19. = 71.55
2x = 71.55 + 3.19
2x. = 74.74
x = 74.74/2
= $37.37. cost of the jacket
Now to determine the cost of the sweater,
$71.55 - $37.37 = $34.18
The cost of the sweater = $34.18.
what is the solution to the system of equations?
y = 4x-10
y=2
A) (3,2)
B) (2,3)
C) (-2,2)
D) (2,-2)
Answer:
A) (3, 2)
Step-by-step explanation:
y = 4x - 10
y = 2
Substitute y with 2 in the first equation and solve for x.
y = 4x - 10
2 = 4x - 10
12 = 4x
3 = x
Solution: x = 3, y = 2
Answer: A) (3, 2)
Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The negative root of ex = 4 − x2
Answer:
x = -1.964636
Step-by-step explanation:
Given equation;
eˣ = 4 - x²
This can be re-written as;
eˣ - 4 + x² = 0
Let
f(x) = eˣ - 4 + x² -----------(i)
To use Newton's method, we need to get the first derivative of the above equation as follows;
f¹(x) = eˣ - 0 + 2x
f¹(x) = eˣ + 2x -----------(ii)
The graph of f(x) has been attached to this response.
As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.
Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0
From Newton's method,
[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]
=> When n=0, the equation becomes;
[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]
[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]
Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;
f(-2) = e⁻² - 4 + (-2)²
f(-2) = e⁻² = 0.13533528323
And;
f¹(2) = e⁻² + 2(-2)
f¹(2) = e⁻² - 4 = -3.8646647167
Therefore
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - -0.03501863503[/tex]
[tex]x_{1} = -2 + 0.03501863503[/tex]
[tex]x_{1} = -1.9649813649[/tex]
[tex]x_{1} = -1.96498136[/tex] [to 8 decimal places]
=> When n=1, the equation becomes;
[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]
[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]
Following the same procedure as above we have
[tex]x_{2} = -1.96463563[/tex]
=> When n=2, the equation becomes;
[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]
[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]
Following the same procedure as above we have
[tex]x_{3} = -1.96463560[/tex]
From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately -1.964636 to 6 decimal places.
Newton's method of approximation is one of the several ways of estimating values.
The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
The equation is given as:
[tex]\mathbf{e^x = 4 - x^2}[/tex]
Equate to 0
[tex]\mathbf{4 - x^2 = 0}[/tex]
So, we have:
[tex]\mathbf{x^2 = 4}[/tex]
Take square roots of both sides
[tex]\mathbf{ x= \pm 2}[/tex]
So, the negative root is:
[tex]\mathbf{x = -2}[/tex]
[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]
Differentiate
[tex]\mathbf{f'(x) = e^x +2x }[/tex]
Using Newton's method of approximation, we have:
[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]
When x = -2, we have:
[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]
[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]
So, we have:
[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -1.96498136}[/tex]
Repeat the above process for repeated x values.
We have:
[tex]\mathbf{x_{2} = -1.96463563}[/tex]
[tex]\mathbf{x_{3} = -1.96463560}[/tex]
Up till the 6th decimal places,
[tex]\mathbf{x_2 = x_3}[/tex]
Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
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A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
Answer:
a) percentage of the employees that will experience lost-time accidents in both years = 1.2%
b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%
Step-by-step explanation:
given
percentage of lost time accident last year
P(L) = 8% = 0.08 of the employees
percentage of lost time accident current year
P(C) = 4% = 0.04 of the employees
P(C/L) = 15% = 0.15
using the probability
P(L ∩ C) = P(C/L) × P(L)
= 0.08 × 0.15 = 0.012 = 1.2%
percentage of the employees will experience lost-time accidents in both years = 1.2%
b) Using the probability of the event
P(L ∪ C) = P(L) + P(C) - P(L ∩ C)
= 0.08 + 0.04 -0.012 = 0.108 = 10.8%
percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%
WILL MARK BRAINLIST----- A particular map shows a scale of 1 cm:5 km. What would the map distance be (in cm) if the actual distance to be represented is 14 km?
Answer:
2.8 cm
Step-by-step explanation:
The map scale is 1 cm : 5 km. That means that 1 cm is equal to 5 km.
To find the map distance (in cm), we have to set up a ratio.
[tex]\frac{1 cm}{5 km} = \frac{x}{14 km}[/tex]
X (the map distance in cm) is over the actual distance of 14 km.
Now cross multiply and divide.
[tex]5x = 14[/tex]
[tex]\frac{5x}{5} = \frac{14}{5}[/tex]
[tex]x = 2.8 cm[/tex]
If the actual distance to be represented is 14 km, the map distance (in cm) will be 2.8 cm.
Hope that helps.
A recipe for 1 batch of muffins used 2/3 of blueberries. Amir made 2 1/2 batches of muffins. How many cups of blueberries did he use? A. 1 4/6 B. 1 5/6 C. 2 2/6 D. 3 1/6. Please show your work.
Answer:
A. 1 4/6 cups of blueberries
Step-by-step explanation:
1 -- 2/3
Proportion, Batches to Blueberries
1*(2 1/2) -- (2/3)( 2 1/2)
Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion
2 1/2 -- (2/3)( 5/2 )
2 1/2 -- 5/3
2 1/2 -- 1 2/3
Simplify
On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6
Hope that helps! Tell me if you need more info
A 6 foot person casts a 26 foot shadow. What is the angle of elevation of the sun? (nearest whole degree)
Answer:
13°
Step-by-step explanation:
The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.
The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft
Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:
[tex] tan x = \frac{opposite}{adjacent} [/tex]
[tex] tan x = \frac{6}{26} [/tex]
[tex] tan x = 0.2308 [/tex]
x = tan-¹(0.2308)
x = 12.996
x ≈ 13° (to the nearest whole degree)
The angle of elevation of the sun = 13°
Need Assistance With This
*Please Show Work*
Answer:
a =7.5
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + 10 ^2 = 12.5^2
a^2 + 100 =156.25
Subtract 100 from each side
a^2 = 56.25
Take the square root of each side
sqrt(a^2) = sqrt( 56.25)
a =7.5
Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses 3 cups of chex. He wants to make 12 cups of party mix.
Answer:
36 cups of Chex total.
Step-by-step explanation:
Well, he will obviously be using 12 cups of pretzels, so let's set that aside. For every cup of pretzels, there are 3 cups of chex. So, multiply 3x12. That will give you how much chex you will need.
i give you brailenst
Answer:
The answer is #3 which is 24%.
Step-by-step explanation:
6 × 100
25
25 into 100 is 4, then 6×4 = 24%
I really hope this helps :)
Six identical coins are tossed. How many possible arrangements of the coins include three heads and three tails?
Answer:
The possible arrangement= 18 ways
Step-by-step explanation:
Six identical coin are tossed.
Coin has only a tail and a head.
In how many possible ways can the arrangement be 3 head and 3 tail.
The possible arrangement= (3! * 3!)/2
The reason for dividing by two because coin has two face.
The possible arrangement= (3! * 3!)/2
The possible arrangement=( 6*6)/2
The possible arrangement= 36/2
The possible arrangement= 18 ways
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:b
Step-by-step explanation:
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
Which of the following statement is incorrect?
4
A.3/4<4/5
B.5/6>0.83
C.2/3>0.66
D.1/3>0.3
درا
Answer:
None,
they are all correct.
Step-by-step explanation:
A)
3/4 - 75%
4/5 - 80%
3/4 < 4/5
B)
5 ÷ 6 = .83333333333
5/6 > .83
C)
2 ÷ 3 = .666666666
2/3 > .66
D)
1 ÷ 3 = .33333333333
1/3 > .3
Thus,
all of the given statements are correct.
Hope this helps :)
write and equation to represent the following statement 28 is 12 less thank K. solve for K K =
Answer:
K = 40
Step-by-step explanation:
As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"
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Answer:
Equation : 28 = k - 12K = 40Step-by-step explanation:
28 is 12 less than k
Let's create an equation:
[tex]28 = k - 12[/tex]
Now, let's solve:
[tex]28 = k - 12[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - k = - 12 - 28[/tex]
Calculate the difference
[tex] - k = - 40[/tex]
Change the signs on both sides of the equation
[tex]k = 40[/tex]
Hope this helps...
Best regards!!
check whether -2 and 2 are zeroes of the polynomial x+2
Answer:
-2 is a zero of the polynomial. 2 is not a zero of the polynomial.
Step-by-step explanation:
A value of x is a zero of a polynomial if when it is substituted for x in the polynomial, it makes the polynomial evaluate to zero.
The polynomial is x + 2
Let x = -2:
x + 2 = -2 + 2 = 0
-2 is a zero of the polynomial.
Let x = 2:
x + 2 = 2 + 2 = 4
2 is not a zero of the polynomial.
Cell phone bills for residents of have a mean of $47/line with a standard deviation of $9/line. Find the probability that the average cost/line for the Math
Help please!!!!!!! Thxxxxx
Answer:
x= 155°
straight line equals 180°
since you have a side that equals to 25°
you subtract
180°-25° = 155°
The triangles in the diagram are congruent. If mF = 40°, mA = 80°, and mG = 60°, what is mB?
Answer:
40
Step-by-step explanation:
The measure of m∠B in the triangle is 40°.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
Since the triangles are congruent, we know that their corresponding angles are congruent as well.
Therefore, we have:
m∠B = m∠F = 40°.
Note that we also have:
m∠C = m∠A = 80° (by corresponding angles)
m∠H = m∠G = 60° (by corresponding angles)
Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle D:
m∠D = 180° - m∠B - m∠C = 180° - 40° - 80° = 60°.
Therefore,
m∠B = 40°.
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Question 10 of 10
Which set of polar coordinates are plotted in the graph below?
Answer:
(-2, -(2pi)/3)
Step-by-step explanation:
a p ex
In da pic :)))))))))
Please help. I’ll mark you as brainliest if correct!
Answer:
CDs: $30,000bonds: $90,000stocks: $50,000Step-by-step explanation:
You can let c, b, s represent the investments in CDs, bonds, and stocks, respectively.
c + b + s = 170000 . . . . . . total invested
0.0325c +0.038b +0.067s = 7745 . . . . . . . annual income
-c + b = 60000
You can solve this set of equations using any of a number of methods, including on-line calculators, graphing calculators, scientific calculators, Cramer's Rule, substitution, elimination, and more. The solution is ...
c = 30,000
b = 90,000
s = 50,000
Maricopa's Success invested $30,000 in CDs, $90,000 in bonds, and $50,000 in stocks.
Please answer this correctly without making mistakes.Please simplify the correct answer
Answer:
19/70 of NASA shuttle missions were carried out by Discovery.
9/140 of NASA shuttle missions were carried out by Challenger.
17/70 of NASA shuttle missions were carried out by Endeavour.
Step-by-step explanation:
Adding the number of missions carried out by NASA gives us 140 in total.
Discovery's total amount of missions simplified is 19/70.
Challenger's total amount of missions is already in the simplest form.
Endeavour's total amount of missions simplified is 17/70.
Answer:
81/140
Step-by-step explanation:
Well to find the fraction we first need to total amount of NASA missions.
38 + 32 = 70
70 + 34 = 104
104 + 27 = 131
131 + 9 = 140
Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.
38 + 9 + 34 = 81
Now we can make the following fraction,
81/140
This is already in simplest form.
Thus,
the answer is 81/140.
Hope this helps :)
the sum of two consecutive multiples of 5 is 55.what are the multiples
Answer:
25 and 30
Step-by-step explanation:
Let the smaller consecutive multiples of 5 be x. Therefore, other consecutive multiples will be x + 5.
Now as per statement the sum of two consecutive multiples of 5 is 55. To find the multiples. Thus
x + x + 5 = 55
2x + 5 = 55
2x = 55 - 5
2x = 50
x = 50/2
x = 25
This the smaller consecutive multiples of 5 is 25, the other consecutuve multiple is x+ 5, 25 + 5 = 30.
The consecutive multiple numbers of 5 are 25 and 30
Answer the two consecutive multiples of 5 are 25 and 30
Answer:
25 and 30.
Step-by-step explanation:
Let the smaller consecutive multiple of 5 be 'x'. So, the other multiple will be x + 5.
Now, the statement is the sum of two consecutive multiples of 5 is 55. To find the multiples, we must simplify as below.
x + x + 5 = 55
2x + 5 = 55
2x = 55 - 5
2x = 50
x = 50/2
x = 25
We observe that the smaller consecutive is 25, so the other multiple is x+ 5, 25 + 5 = 30.
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Letters a, b, c, and d are angles measures. Lines m and n are cut by transversal p. At the intersection of lines p and m, labeled clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°
Answer:
b, c, e
Step-by-step explanation:
the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right
Answer:
B. a=d
C. c=d
E. b + d=180°
Step-by-step explanation:
Got Correct On MyPath.
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠CAB ≅ ∠SAB ∠CAS ≅ ∠BAS
Answer:
∠CAB ≅ ∠SAB is not true
Step-by-step explanation:
CPCTC means id ABC = XYZ, than A=X, AB=XY, C=Z and so on. Basically the number numbers that come in the same order as the other one is equal.
So ∠CAS ≅ ∠BAS is true but ∠CAB ≅ ∠SAB is not.
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Answer:
sap
Step-by-step explanation:
What are the solutions to the system of equations graphed below?
Answer:
Its B and D
Step-by-step explanation:
Because thats where the points intersects/meet.
PLEASE HELP The probability distribution for a
random variable x is given in the table.
1
Step-by-step explanation:
p(x≤20)=p(x=-10) +p(x=-5)+p(X=0) +p(x=5) +p(x=10)+ p(X=15)+p(X=20)
This, p(X≤20)=0.20+0.15+0.05+0.1+0.25+0.1+0.15
=1
Draw the straight line y = x + 2
Answer:
Graph is attached below
Step-by-step explanation:
You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.
The plotted straight line is as shown in below graph.
Given straight line equation is y = x + 2
To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.
After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.
Example, take x = 1 and x = 2 for straight line y = x + 2
Then we get:
For x = 1, y = 1 + 2 = 3
For x = 2, y = 2 + 2 = 4
The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.
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