The straight line distance between the northbound and eastbound cars is 5.7 kilometres.
The movement of cars and straight line connecting them forms a right angled triangle. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.
Distance between the two cars = ✓4² + 4²
Taking square of the numbers
Distance between the two cars = ✓16 + 16
Performing addition
Distance between the two cars = ✓32
Taking square root
Distance between the two cars = 5.66
Round to nearest tenth = 5.7
Thus, the distance is 5.7 kilometres.
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how many 10-element subsets of {1, 2, 3, . . . , 20} contain at least one odd element? (hint: we are selecting a subset of the previous set, so {1,2,3,4,5,6,7,8,9,10} is the same as {1,2,3,5,4,6,7,8,9,10}.)
The no. of subsets with at least one odd number is ²⁰C₁₀ - 1
We have the sample set to be {1, 2, 3, 4, ... 20}
Now we need to make subsets of 10 from these 20 elements.
Hence, the number of possible subsets of 10 elements will be
²⁰C₁₀
Now, there are 10 odd elements in the given sample set.
Hence the number of sets that contain at least 1 odd element
= Total no. of possible sets - no. of possible sets with no odd no.
Now since there are only 10 even numbers, there can be only one such set possible.
Hence no. of the subsets with at least one odd number is
²⁰C₁₀ - 1
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A water sample shows 0. 097 grams of some trace element for every cubic centimeter
of water. Ayden uses a container in the shape of a right cylinder with a diameter of
16. 8 cm and a height of 10. 8 cm to collect a second sample, filling the container all
the way. Assuming the sample contains the same proportion of the trace element,
approximately how much trace element has Ayden collected? Round your answer to
the nearest tenth.
Adam has gathered 232.32 g of trace elements, which are contained in a cylindrical container with a radius of 8.4 cm and a height of 10.8 cm.
Radius of the cylinder 8.4 cm
Height of the cylinder = 10.8 cm
Volume of the cylinder = π r² h
When we change the values in the formula, we obtain:
V = π (8.4 cm)² (10.8 cm)
V = 22 / 7 (70.56 cm²) ( 10.8 cm)
V = 2395.008 cm³
Presence of particle = 0.097 g for every cm³
The element's trace for 2395.008 cm3 will be:
= 2395.008 × 0.097 g
= 232.315776 g
As a result, Adam has gathered 232.32 g of trace elements in the cylindrical container with a radius of 8.8 cm and a height of 15.9 cm.
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The set of natural numbers between 11 and 155
Choose the correct answer below.
OA. {12, 154}
B. {12, 13, 14, 15, ..., 154}
C. {11, 155}
D. 11, 12, 13, 14, ..., 155}
OE. {..., 11, 12, 13, 14, ..., 155, ...}
F. {..., 12, 13, 14, 15, ..., 154, ...}
G. Ø
The set of natural numbers between 11 and 155 is {12, 13, 14, 15, ..., 154}.
A natural number is a positive integer, also known as a counting number. The set of natural numbers is represented by the symbol {1, 2, 3, 4, ...}.
The set of natural numbers between 11 and 155 includes all the natural numbers that are greater than or equal to 12 and less than or equal to 154.
This set is represented by {12, 13, 14, 15, ..., 154}. This set is infinite, meaning it contains an infinite number of elements. The dots indicate that the set goes on infinitely in both directions, but in this case, we are only concerned with the numbers between 11 and 155.
It is important to note that the answer "A" is incorrect because it only contains 2 elements, while the correct answer B is infinite set of numbers between 11 and 155 inclusive.
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How many solutions does the system have?
x = 5y + 4
- 2x+10y = -8
A one solution
B infinitely many solutions
no solution
D) two solutions
Answer:
D) two solutions
Step-by-step explanation:
because the first one is: x = 5y + 4
and the second one is: -2x+10y=8
and the equals in the first one is just how to get the value of x and it doesn't count as a third solution
Use the box method to distribute and
simplify (-5x - 2) (5x + 4). Drag and
drop the terms to the correct locations of
the table.
( − 5x − 2)(5x+4)
You must answer all questions above
in order to submit.
Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.
What is the box method?
Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.
Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.
Here's how you can use the box method to distribute and simplify the expression:
( -5x - 2 ) ( 5x + 4 )
⇒-5x -2
⇒5x 4
⇒-25x^2 -10x + 20x - 8
⇒-25x^2 + 10x - 8
So the simplified expression is:
-25x^2 + 10x - 8.
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Examine the following scales.
The correct reading to all possible significant figures is:
The sum of the two given is 7.867.
When expressed in scientific notation, the number of significant figures equals the number of digits. Significant figures are the numbers that give any measurement meaning.
The decimal point is marked by leading zeros. They don't matter much. After the decimal point, a trailing zero is reliably known. It is important. In a whole number, every non-zero number has importance.
You must keep in mind these three guidelines in order to ascertain how many significant figures are present in a number.
Digits that are not zero are always important.Any zeros in the range of two significant digits are noteworthy.ONLY the following zeros in the decimal part matter.If you add 4.667 g and 3.2 g,
the answer has 4 significant figures.
The sum of the two given is 7.867.
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The full question:
If you add 4.667 g and 3.2 g how many significant figures does the answer have
suppose a number is chosen at random from the set {0,1,2,3,...,501}. what is the probability that the number is a perfect cube? the probability of choosing a perfect cube is
The probability of choosing a perfect cube is [tex]\frac{7}{502}[/tex] .
According to the question,
Suppose a number is chosen at random from the set {0,1,2,3,...,501}.
Cube of 1=1
Cube of 2=8
Cube of 3=27
Cube of 4=64
Cube of 5=125
Cube of 6 = 216
Cube of 7 = 343
Cube of 8 = 512
So in a set of members {0,1,2,3,... 501}, only 7 numbers are a cube of a natural number: 1,8,27,64,125,216,343.
The probability of selecting cubes in a set of members {0,1,2,3,... 501} is
= [tex]\frac{7}{502}[/tex]
So, the probability is [tex]\frac{7}{502}[/tex] .
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A florist wants to determine if a new additive helps
extend the life of cut flowers longer than the original
additive does. The florist selects 20 flowers of different
types and puts each flower in its own vase with the
same amount of water. She positions the vases so they
also receive the same exposure to light. She numbers
the flowers 1-20, and places these numbers on equal-
sized slips of paper. The slips are placed in a hat and
mixed thoroughly. A slip is chosen and the
corresponding flower receives the new additive. After
the hat is shaken, another slip is chosen and the
corresponding flower also receives the new additive.
This procedure continues until 10 flowers have been
assigned to receive the new additive. The remaining 10
flowers receive the original additive.
"No, the flowers were not put into groups first and then randomly assigned the two additives.
Now, According to the question:
Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a random experiment. To avoid any ambiguity or surprise, a random experiment must be properly defined.
"Information available from the question"
The florist selects 20 flowers of different
And puts in each vase with same amount of water.
10 flowers have been assigned to receive the new additive.
The remaining 10 flowers receive the original additive.
Based on the data, this is not a randomized block design for the experiment because the flowers were not put into groups first and then randomly assigned the two additives.
Therefore, "No, the flowers were not put into groups first and then randomly assigned the two additives.
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Solve the system by substitution.
-2x-10y=
−2x−10y=
\,\,-2
−2
-4y=
−4y=
\,\,x
x
The solution of the system of equations:
-2x - 10y = -2
-4y = x
is the point (-4, 1).
How to solve the system of equations?Here we want to solve the system of equations below:
-2x - 10y = -2
-4y = x
By the substitution method, to do so, we need to isolate one of the variables in one of the equations and then replace that in the other equation.
We can see that x = -4y is already isolated on the second equation, then we can replace this on the first one to get:
-2*(-4y) - 10y = -2
We can solve this for y.
8y - 10y = -2
-2y = -2
y = -2/-2 = 1
And thus, the value of x is:
x = -4y
x = -4*1 = -4
The solution of the system is (-4, 1).
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A manager at a theater needs to order 267 new seats if the seats are sold only in groups of 10 what is the least number of seats that the manager should order
The least number of seats the manger could order to 270 seats
How to find the least number of seats the manger could orderThe information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.
The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.
This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.
Hence the manager will order 270 and heave 3 extra seats
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A sari-sari store sells two types of detergent powder. One type(a) cost php 9. 00 and the other type(b) cost php 7. 0. They want to raise at least php 180. 00 for detergents. How many pieces of each detergent must be sold to achieve her goal?
Sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.
Determine the number of pieces of type (a) detergent.
9.00 x x = 180.00
Divide both sides by 9.00:
x = 20 pieces
Determine the number of pieces of type (b) detergent.
7.00 x y = 180.00
Divide both sides by 7.00:
y = 25.71
Since we cannot sell partial pieces, the number of pieces of type (b) detergent must be rounded up to 26 pieces.
Therefore, the sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.
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You invest $300 in an account that has a annual interest rate of 6%, compounded quarterly for four years. What is the equivalent interest rate, and how many times will the money be compounded?
A) 6. 7% and 16 times
B) 1. 5% and 1 time
C) 1. 5% and 16 times
D) 6. 7% and 4 times
Please Answer!
The correct answer for equivalent interest rate and no. of times will the money be compounded is C) 1.5% and 16 times respectively.
The annual interest rate of 6% is equivalent to a quarterly interest rate of 6% / 4 = 1.5%. The money will be compounded quarterly, so it will be compounded 16 times in total over 4 years.
Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
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Identify bias based on a survey of 2718 people the national opinion research center concluded that 30% 32% of americans always make a special effort to sort and recycle glass cans plastic or papers 24% americans often make such an effort
Based on a survey of 2718 people, a research center concluded that 32% of Americans "always" make a special effort to sort and recycle glass, cans, plastic, or papers. Participation bias is there in this case.
The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.
When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.
1. Participation bias is inherent in studies that involve participant enrollment.
2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.
Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.
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5 units right and 2 units up pre image, and image
The translation rule that defines a translation 5 units right and 2 units up is given as follows:
(x,y) -> (x + 5, y + 2).
What is a translation?A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.More can be learned about translations at brainly.com/question/28174785
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researchers collect data about juuling by asking users to keep track of the number of times per day they turn their device on and the number of inhalations each time they turn the device on. what type of data are these? group of answer choices interval nominal ratio ordinal
The given data is ordinal data.
This type of data is ordinal data, as the variables are collected on an ordered scale (the number of times per day the device is turned on and the number of inhalations per activation). Although the actual numerical values may not have equal distances, they can still be ordered and compared based on the magnitude of the numbers.
Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. These statistics are presented on an ordinal scale, one of the four measurement levels that S. S. Stevens described in 1946.
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Evaluate. Write your answer as a whole number or as a simplified fraction. 5/2–2 =
Answer: 1.25 or 1, 1/4
solve 3x≤-5/4 as a inequality
Answer:
Inequality Form:
x ≤ −5/12
Interval Notation:
(−∞, −5/12]
Step-by-step explanation:
Find MP.
J
M,
K
DO
3x + 14
O 9x-34
L
The length of the segment MP is 38 units
How to determine the length MPFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have
9x - 34 = 3x + 14
Evaluate the like terms
6x = 48
Divide by 6
x = 8
Given that
MP = 9x - 34
We have
MP = 9 * 8 - 34
Evaluate
MP = 38
Hence, the length of MP is 38 units
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At a local play, student tickets cost $5 each and adult tickets cost $11 each. if ticket sales were $3,000 for 300 tickets, how many students attended the play? a. 50 b. 150 c. 250d. 300
This problem can be solved used linear equations. Here there are two variables, number of students and number of adults. After calculations we get the number of students attended the play is 50.
Lets consider the number of students is x and number of adults is y.
Total tickets sold = 300
x + y = 300 ------------ equation 1
The amount of total tickets sold is 3000.
Amount sold to students = 5x
Amount sold to adults = 11y
So, 5x+11y =3000 ----------- equation 2
Equating the x term for equation 1
Multiplying both sides with 5
5 (x+y) = 5 × 300
5x + 5y = 1500 ---------- equation 3
Subtracting equation 3 from equation 2
5x + 11y = 3000
- ( 5x + 5y = 1500)
6y = 1500
y = 1500/6 = 250
Number of adult attended = 250
From equation 1, x+y = 300
Substituting the value of y
x + 250 = 300
x = 300-250 = 50
So number of students attended is 50
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Answer: 50
Step-by-step explanation: i got it right on my quiz
Take care to properly set up your equations. The $3,000 is the sum of total money from student tickets and total money from the adult tickets.
Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's. If there is no visible coefficient, then enter for the coefficient. If a specific variable is not present in the equation, then enter for the coefficient. Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165. Total amount invested: + + = Total amount earned from investements: + + = Relation of bonds and CDs: + + =
The system of equations is:
a + b + c = 2000000.109a + 0.029b + 0.05c = 11165b = c + 20000How to determine the system of equationsFrom the question, we have the following parameters that can be used in our computation:
Total amount invested = $110000
Using the fiollowing variable representations:
Amount invested in stocks = a Amount invested in bonds = bAmount invested in CD's = cWe have
a + b + c = 200000
Using the total interest earned of 7145, we have:
10.9% * a + 2.9% * b + 5% * c = 11165
So, we have
0.109a + 0.029b + 0.05%c = 11165
Country day invests $20000 more in bonds than in CDs.
So, we have
b = c + 20000
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8 of the tables at Joy's Italian Restaurant are full and the other 13 tables are empty. What is the ratio of the number of empty tables to the total number of tables?
The ratio of the number of empty tables to the total number of tables 13:21.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that 8 of the tables at Joy's Italian Restaurant are full
13 tables are empty
The total number of tables in the restaurant are 8+13=21
We have to find ratio of the number of empty tables to the total number of tables
Empty tables = 13
Total number of tables=21
Ratio of the number of empty tables to the total number of tables 13:21
Hence, the ratio of the number of empty tables to the total number of tables 13:21.
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which is the equation of the line with slope 3 and y-intercept 5
Answer:
y=3x+5
Step-by-step explanation:
an equation is always
y= slope*x + intercept so y=3x+5
Mr. Ramirez is always trying to clean up his garage. He has 1/5 liter of oil in one can and 2 5 liter of oil in another can. How much will he have if he pours them both into one can URGENT PLEASE ANSWER
The total amount of oil he would have if he pours them both in a can is 2.7 liters.
How much oil would he have?In order to determine the amount of oil he would have, add both numbers together. In order to add the numbers, both numbers have to be in the same form. One of the numbers is a decimal and the other is a fraction.
In order to convert the fraction to a decimal, divide the numerator by the denominator.
1/5 = 0.2
Total number of oil = 0.2 + 2.5 = 2.7 liters
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Select all the expressions which are equivalent to -5/2z-5/6
All the expressions which are equivalent to -5/2z-5/6 are given below.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression,
-(5/2)z - 5/6
Simplifying,
-(5/2)z - 5/6,
= -5(z/2 + 1/6) is an equivalent expression.
= -5/2 (z + 1/3) is an equivalent expression.
Therefore, -5(z/2 + 1/6) and -5/2 (z + 1/3) are the equivalent expressions
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In △FGH, ∠F≅∠H, HF=13 and GH=11. Find FG.
To find the value of FG, FG is 11.
Properties of isosceles triangle.When there exist a triangle which has two of its sides to be equal in length, then it can be referred to as an isosceles triangle. Such that its two angles opposite the equal sides have equal measure.
Considering the given question, to find the value of FG;
since it has been given that <F ≅ <H, then;
GH ≅ FG (properties of sides of an isosceles triangle)
Such that;
GH = 11, then
GH ≅ FG = 11
Thus the value of FG is 11.
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a light post casts a shadow on a small boy. the boy, who is 4 feet 6 inches tall, notices that his shadow is 3 feet 4 inches long. he decided that if he measures how far he is from the light post, he can determine how tall the post is from the ground. explain how he can figure out the height of the light post. use mathematical reasoning.
The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.
Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -
(boy's height) / (boy's shadow) = (light post height) / (light post shadow)
i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)
Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.
The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)
This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)
In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
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a) Divide 260 in the ratio 1:3
Answer:
Step-by-step explanation:
Total number = 260
Ratio would be 1 : 3
So, the first part is given by
[tex]\frac{1}{4}[/tex] x 260
=[tex]\frac{260}{4}[/tex]
=65
And the second part is given by
[tex]\frac{3}{4}[/tex] x 260
=[tex]\frac{780}{4}[/tex]
=195
Hence, the first and second part are 65 and 195 respectively.
Help me pls it’s due tomorrow and pls have a explanation!!
Answer:
Okay so the answer would be 8 cups
Step-by-step explanation:
the reason this is is because if you combine the cups its 2 2/3 so then all you have to do is multiply it by 3 and then your answer is 8 cups of sugar
Think about what you know about breaking apart numbers with addition. Fill in each box. Use words,numbers. and picture. Show as many ideas as you can.
The breaking apart numbers with addition help us to solve an addition more efficient than left-to-right addition.
What is addition?Addition in math is a process of combining two or more numbers.
Given that, think about what you know about breaking apart numbers with addition.
What is it?Breaking apart an addend is a mental math strategy for addition. Some students may find this method more efficient than left-to-right addition.
What I know about it?This strategy involves breaking up one addend in an equation into more manageable parts.
Examples :-1) 32 + 46 =
Breaking the second term 46 in 40 + 6
32 + 40 + 6
= 72 + 6
= 78
2) 89 + 73 =
Breaking the second term 73 into 70 + 3
89 + 70 + 3
= 159 + 3
= 162
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8x +x2/3 what is that answer
The solution to the expression when x = 3 is 26
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
8x + x * 2/3
Also, we have
x = 3
substitute the known values in the above equation, so, we have the following representation
8 * 3 + 3 * 2/3
Evaluate the product
24 + 2
Evaluate the sum
26
Hence, the solution is 26
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Complete question
Given that 8x + x * 2/3, calculate the expression when x = 3
The algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3
How to simply the algebraic expressionWe shall first find the lowest common multiple (LCM) of the denominators of both terms to have a single fraction and then we simplify as follows;
The denominator of 8x is 1 and 2x/3 is 3
LCM of 1 and 3 is 3
we simplify to a single fraction;
multiply the term 8x by the LCM 3
(3 × 8x + 2x)/3
multiply the term 8x by the LCM 3
(24x + 2x)/3
add the algebraic terms 24x and 2x together
26x/3
Therefore, the algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3.
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