Considering the situation described, the classification of the runners is given as follows:
Dan - Ben - Alex - Curtis.
What is the classification of the runners?The oldest came in second place. Ben is older than Alex, and Curtis is older than Dan, hence either Ben or Curtis finished second.
Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis, hence considering the above observation Ben finished second and the classification is:
Dan - Ben - Alex - Curtis.
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A dealer bought digital watches at Rs 5,500 per piece and fixed the price of each watch to make 20% profit. How much should a customer pay for it with 13% VAT?
Answer:
A dealer bought digital watches at Rs 5500 per piece and fixed the price of each watch to make 20 profit. How much should a customer pay for it with 13 VAT? A trader purchased a laptop for Rs 45000 and marked its price to make 24 profit.
Step-by-step explanation:
Select all of the values of x that are solutions to 17-7x> 3(10x-4) + 61.
-2
-4
-1
2
5
0
Answer: -2, -4, -1
Step-by-step explanation:
[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]
So, the values of x are -2, -4, -1.
Find the equation of a line that passes through the points (-2,-3) and (4,1)
The equation of the line from give points is y = 2/3x - 5/3.
According to the statement
We have given that the two points which are (-2,-3) and (4,1)
And we have to find the equation of a line that passes through the given points.
So,For this purpose,
First, we need to determine the slope of the line. The slope can be found by using the formula:
[tex]m = \frac{(y_2) -(y_1)}{(x_2) -(x_1)}[/tex]
Where
m is the slope and
Substituting the values from the points in the problem gives:
m = 1 + 3 /4 + 2
m = 4/6
m = 2/3.
And then
Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:
[tex]y - (y_1) = m(x -x_1)[/tex]
Put the values in it then
y - (-3) = 2/3 (x-(-2))
y +3 = 2/3 (x +2)
3y + 9 = 2x + 4
3y - 2x = 4 -9
3y -2x = -5
3y = 2x - 5
y = 2/3x - 5/3.
So, The equation of the line from give points is y = 2/3x - 5/3.
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Everyone in Sandy's class has to do a science project. Out of 50 students, 56% have completed their projects.
How many students still need to do their projects?
Pls help ASAP
Answer:
22
Step-by-step explanation:
100 - 56 is 44. 44% have still not done the project
.44 x 50 = 22
Answer:
22 coz 56% of 50 which is the total is 28. Then the remaining 44%is22
Step-by-step explanation:
Can I get some help finding the x of the triangle please?
Answer:
61
Step-by-step explanation:
You can see that the sides are both 6. That means that this triangle is an isosceles triangle.
Therefore do this:
180-58=122
122/2= 61
So x= 61 Degrees
Hope This helps! :)
Answer:
x = 61
Step-by-step explanation:
This triangle is an isosceles triangle which means 2 sides are congruent. This also means the 2 angles across from the congruent sides are congruent. So, you would subtract 58 from 180 which equals 122. Then you would divide that in half, which gets you 61. (The angle 58 is the one across from the side that is not congruent to the others. That is why I used it)
Use the graph to find the local minimum and the local maximum for the given function
The local minimum on the interval [-3, 0] is -16, the local maximum on the interval [0, 3] is 4 and the local minimum on the interval [0, 3] is -3
What is a local minimum?In a function, a point located at the local minimum is a point that is at a lower coordinate compared to the other neighboring points
What is a local maximum?In a function, a point located at the local maximum is a point that is at a higher coordinate compared to the other neighboring points
How to determine the local minimum and the local maximum?The complete question is added as an attachment
In the first interval, [-3, 0], the lowest point in the interval is located at (-16, -1.5)
This means that the local minimum on the interval [-3, 0] is -16
In the second interval, [0, 3], the highest maximum in the interval is located at (4, 1)
This means that the local maximum on the interval [0, 3] is 4
In the second interval, [0, 3], the lowest minimum in the interval is located at (0, -3)
This means that the local minimum on the interval [0, 3] is -3
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Which option is the fraction 28/31 closest to? 0, 1/2 or 1?
Answer:
1 is the closest to 28/31
Step-by-step explanation:
0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)
Given: y varies directly with x and has a constant rate of change of 7. when the value of y is 12, then the value of x would be _____.
Answer:X=12/7
Step-by-step explanation:
Y [tex]\alpha[/tex] X
⇒Y=KX
Where K is the constant
From the question,k=7
⇒ When Y=12,
y=KX
12=7X
X=12/7
find the missing numbers in the following equal ratios:
[tex]\frac{?}{3} = \frac{?}{6} = \frac{8}{?} = \frac{16}{24}[/tex]
First blank: Dividing the numerator and denominator of 16/24 by 8 gives the unknown to be 2.
Second blank: Dividing the numerator and denominator of 16/24 by 4 gives the unknown to be 4.
Third blank: Dividing the numerator and denominator of 16/24 by 2 gives the unknown to be 12.
Lee wants to fence off a rectangular area that is 36 feet squared in size for a vegetable garden. He is considering three garden lengths of 6 ft, 9 ft, and 12 ft. He wants to determine which garden would require the least amount of fencing.
Determine the dimensions of the garden that would require the least amount of fencing.
tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.
The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.
The dimensions are the sides of a geometric shape.
The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.
If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:
The width of the garden with a length of 6 ft [tex]= \dfrac{36}{6} = 6\ ft[/tex]
The width of the garden with a length of 9 ft [tex]= \dfrac{36}{9} = 4\ ft[/tex]
The width of the garden with a length of 6 ft [tex]= \dfrac{36}{12} = 3\ ft[/tex]
The parameters are calculated as:
The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft
The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft
The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft
The least of the parameter is of the garden with dimensions (6 ft, 6 ft).
Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.
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Which line of best fit accurately represents the given scatter plot?
PLS HELP IS IT TRUE OR NOT
Answer:
True
Step-by-step explanation:
All faces of a cube are the same.
Help on this math problem!! if there is any work that can be shown it would be great thanks!!!
The sum of 10 consecutive integersstarting with 11, equals the sum of 5 consecutive integers, starting with
(A) 22
(B) 29
(C) 31
(D) 33
Answer: [tex]\large\boxed{29}[/tex]
Step-by-step explanation:
The sum of 10 consecutive integersstarting with 11
= 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
Lets try 29:
29 + 30 + 31 + 32 + 33 = 155
Therefore our answer is:
[tex]\large\boxed{29}[/tex]
6. Encik Azmi bought a locally made car for RM55 000. After 6 years, Encik Azmi wishes to sell the car. Based on the explanation from the used car dealers, the price of Encik Azmi's car will be calculated using the formula RM55 000 (8)". In this situation, n is the number of years after the car is bought. What is the market value of Encik Azmi's car? State your answer correct to the nearest RM. RM55 000
The result is 859,375,000.
What does multiplication mean?The result of two numbers being multiplied is known as the product. The multiplier is the number of such equal groups, and the multiplicand is the number of items in each group.Calculating the outcome of successive additions of two numbers is known as multiplication. The multiplication formula is 4 times 2 equals 8.Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests will be given in addition, subtraction, multiplication, and division. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.Multiplication has the following three characteristics: commutative, associative, and distributive.The market value of Encik Azmi's car:
Get the answer by multiplication.
[tex]=55000*8^{6}[/tex]
=55000*15625
=859,375,000
The market value of Encik Azmi's car is 859,375,000.
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When the dollar price of pounds rises, for example, from $1 = 1 pound to $2 = 1 pound, the dollar has ______ relative to the pound.
The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.
What is Depreciated relative?Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.
A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.
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what is 2^c=8 (please help)
Answer:
c=3.
Step-by-step explanation:
∵2*2*2=8,
∴2^3=8.
∵2^c=8,
∴c=3.
What is the solution to the equation
O x = -3
x = -3 and x=0
O x = 0 and x = 3
O x = 3
X+3
2 ?
2x²
The solution to the equation 1/x = x + 3/2x^2 is x = 0 or x = 3
How to determine the solution to the equation?The equation is given as:
1/x = x + 3/2x^2
Cross multiply in the above equation
2x^2 = x^2 + 3x
Evaluate the like terms
x^2 - 3x = 0
Factor out x
x(x - 3) = 0
Solve for x
x = 0 or x = 3
Hence, the solution to the equation 1/x = x + 3/2x^2 is x = 0 or x = 3
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Answer:
The Answer Is "x=3"
Step-by-step explanation:
I just did it
What is the 7th term of an AP: 50+45+40
Answer:
20
Step-by-step explanation:
using the arithmetic progress formula
tn=a+(n-1)d
from the series given above a which is your first term is 50
the d which is the common difference.. you minus the first term from the second term which is 45-50=-5
so the 7th term which our n=7
we have:
t7=50+(7-1)(-5)
t7=50+(6)(-5)
t7=50-30
t7=20
Answer:
a₇ = 20
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 50 and d = 45 - 50 = - 5 , then
a₇ = 50 + (6 × - 5) = 50 + (- 30) = 50 - 30 = 20
Identify the area of the figure rounded to the nearest tenth.
Answer:
91.5[tex]cm^{2}[/tex]
Step-by-step explanation:
The area of the rectangle:
a = lw
a =(21)(3) = 63
The area of the square:
a = lw
a = (5)(5) = 25
The area of a half circle:
a=[tex]\frac{\pi r^{2} }{2}[/tex]
a= [tex]\frac{3.14(1.5^{2}) }{2}[/tex]
a = [tex]\frac{3.14(2.25)}{2}[/tex]
a = [tex]\frac{7.065}{2}[/tex]
a = 3.5 rounded to the nearest tenth
63 + 25 + 3.5 =91.5
Geometry: Write the theorem or postulate for each of the following, ASAP!!!
The theorems or postulates for the given pair of angles are as follows:
2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;
3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;
4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;
5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;
6. ∠4 ≅ ∠8 → Corresponding angles are congruent;
What are the types of pairs of angles?Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.
So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
Based on their position, they are paired into different categories. Such as:
Interior angles: ∠3, ∠4, ∠5, ∠6
Exterior angles: ∠1, ∠2, ∠7, ∠8
'Alternate interior angles' are the pair of interior angles on the opposite side of the transversal 't'. I.e., (∠3, ∠5), (∠4, ∠6) are congruent.'Alternate exterior angles' are the pair of exterior angles which are on the opposite side of the transversal 't'. I.e., (∠2, ∠8), (∠1, ∠7) are congruent.'Consecutive interior angles' are the pair of interior angles which are on the same side of the transversal 't'. I.e., (∠3, ∠6), (∠4, ∠5). These are also called "Supplementary angles" which mean they add up to 180°.'Consecutive exterior angles' are the pair of exterior angles on the same side of the transversal 't'. I.e., (∠2, ∠7), (∠1, ∠8). These are also called "Supplementary angles" which mean they add up to 180°.'Vertically opposite angles' are the pair of angles that are opposite to each other at the point of intersection. I.e., (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)'Corresponding angles' are the pair of consecutive angles in which one of the angles is exterior and the other is interior. I.e., (∠1, ∠5), (∠2, ∠6), (∠4, ∠8), (∠3, ∠7)Theorems or postulates for the given pair of angles:Classifying the given pair of angles and their corresponding theorems:
2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.
Theorem - "The alternate exterior angles are congruent"
3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.
Theorem - "The verticle angles are congruent"
4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.
Theorem - "The alternate interior angles are congruent"
5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.
Theorem - " The supplementary angles add up to 180°"
6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.
Theorem - " The corresponding angles are congruent".
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]x = -7[/tex]
Step-by-step explanation:
Given the equation:
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],
to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]
⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex] [expand brackets]
⇒ [tex]10x + 96 = -44 - 10x[/tex]
⇒ [tex]10x + 10x + 96 = -44[/tex] [add [tex]10x[/tex] to both sides]
⇒ [tex]20x + 96 = -44[/tex]
⇒ [tex]20x = -44 - 96[/tex] [subtract 96 from both sides]
⇒ [tex]20x = -140[/tex]
⇒ [tex]x = \frac{-140}{20}[/tex] [divide both sides by 20]
⇒ [tex]x = \bf-7[/tex]
Answer:
B) x = -7
Step-by-step explanation:
Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]
Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.
[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]
[tex]\implies 10x+100-4=11-10x-55[/tex]
Step 2: Simplify (combine like terms).
[tex]\implies 10x+100-4=11-10x-55[/tex]
[tex]\implies 10x+96=-44-10x[/tex]
Step 3: Add [tex]10x[/tex] to both sides.
[tex]\implies 10x+10x+96=-44-10x+10x[/tex]
[tex]\implies 20x+96=-44[/tex]
Step 4: Subtract [tex]96[/tex] from both sides.
[tex]\implies 20x+96-96=-44-96[/tex]
[tex]\implies 20x=-140[/tex]
Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].
[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]
[tex]\implies \boxed{x=-7}[/tex]
HEY PLS HELP IM STUCK
The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?
The possible base and height of a second triangle are:
B = 5 H = 12What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To find the base and height of the triangle:
First, we must find the constant of variation (k).
The problem indicates that the base of each triangle varies inversely with the height.
So, this can be represented as below:
B = k/H
B is the base of the triangle (B=10). H is the height of the triangle (H=6). k is the constant of variation.When we clear "k", we obtain:
B = k/H k = BxH k = 10x6 k = 60Now, we have:
B = 60/HWe can give any value to "H" and you will obtain the base of the second triangle.
If H = 12, then:
B = 60/H B = 60/12 B = 5Therefore, the possible base and height of a second triangle are:
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QPS=
Help me please! Thankss
Answer:
44°
Step-by-step explanation:
[tex]\frac{134-46}{2}=44[/tex]
.
Write down the equation for the following
i,Grade 7 students received a total of 88 books from world vision.they received 63 books on Monday and g books on Tuesday
ii,Solve the equation above
A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Kelvin has enough money to buy only 19 sweets. What is the biggest number of sweets that he can get from the shop?
Answer:
Kelvin can get 6 free sweets
When you send out a resume, the probability of being called for an interview is 0. 40. what is the probability that the first interview occurs on the fifth resume that you send out?
The probability that the first interview occurs on the fifth resume that you sent is 0.2592.
According to the given question.
The probability of being called for an interview, p = 0.40.
So, the probability of not being called for an interview, q = 1 - 0.40 = 0.60
As we know that binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.
Therefore, the probability that the first interview occurs on the fifth resume that you send out
= [tex]^{5} C_{1} (0.40)^{1} (0.60)^{4}[/tex]
= 5(0.40)(0.1296)
= 0.2592
Hence, the probability that the first interview occurs on the fifth resume that you sent is 0.2592.
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What is the product of –3 and 5?
Using f(x), what is the equation that represents g(x)?
Og(x) = log5 (x) - 3
O
g(x) = log5 (x) +3
Og(x) = log5 (x-3)
Og(x) = logs(x + 3)
The equation that represents the function g(x) is g(x) = log₅(x - 3)
How to determine the equation that represents g(x)?The equation of the function f(x) is given as:
f(x) = log₅(x)
From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)
This means that
g(x) = f(x - 3)
The function f(x - 3) is calculated as follows
f(x - 3) = log₅(x - 3)
Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)
g(x) = log₅(x - 3)
Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)
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