The average time in two races must be less than 7 minutes.
Given,
Runner's times in three races = 6.9 minutes, 6.6 minutes, 6.5 minutes.
Runner will run two more races.
The average time of all five races = less than 6.8 minutes
We have to find the average time needed in the two races:
Now,
(6.9 + 6.6 + 6.5 + x + y) / 5 < 6.8
Here, x and y are the time in two races.
Let's assume the average as 6.5 which is less than 6.8.
Then,
(6.9 + 6.6 + 6.5 + x + y) / 5 = 6.5
(6.9 + 6.6 + 6.5 + x + y) = (6.5 × 5)
x + y = (6.5 × 5) - (6.9 + 6.6 + 6.5)
x + y = 32.5 - 20
x + y = 12.5
Now, we have to find the average of two races:
That is, (x + y) / 2 = 12.5 / 2 = 6.25.
Above is a solution required by an assumption. By this solution we came to know that the average of two races must be less than 7 minutes.
So, let's conclude like:
The average time in the two races must be less than 7 minutes.
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Suppose that 11 inches of wire costs 44 cents. At the same rate, how many inches of wire can be bought for 32 cents?
Answer:
8 inches
Step-by-step explanation:
So if 11 in. cost 44 cents, then each inch cost 4 cents.
32/4=8
63.5+2.25÷0.75−6 • 1881 Heeeeeeeeeeeeeelp please
Answer: 750,519
Step-by-step explanation:
1st: multiply terms
2nd: divide terms
3rd: add terms
4th: subtract your last two terms
I hope this helps!
Samantha is a farmer and the other day she was on her way to sell eggs at the
market she got into an accident and all her eggs broke. In order for her to collect
money from the insurance company, she had to give the exact amount of eggs she
had. She doesn't remember how many eggs there were but when she was packing
them she remembered when she put them in groups of 2, 3, 4, 5, or 6, one egg was
left over. But in groups of 7 no eggs were left over.
How many eggs did she have?
Answer: 6
Step-by-step explanation: 6+1 Is 7 and there are no eggs left in the group of 7 so if they need one egg left and 7-1 is 6 the answer is 6.
ointwise characterization of angle bisector. a point p lies on the bisector of ! †bac if and only if p is in the interior of †bac and the distance from p to ab !
According to the given information the Pointwise Characterization of Perpendicular Bisectors.
What are Perpendicular Bisectors?A line known as a perpendicular bisector divides a specified line segment precisely in half, creating a 90° angle at the intersection. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.
The perpendicular bisector seems to be a mathematical construct that is being explored along with its creation in this article. We'll also look at the perpendicular bisector of a triangle and its properties. We will solve some few cases at the end to help you understand the subject better.
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12.
2
-
Do not write
Mrs Chandra bought as many pears as apples and as many in this spac
5
mangoes as apples. She paid a total of $150 for all the fruits. The
ratio of the amount of money she spent on the apples to the amount
she spent on the pears was 3:2. The ratio of the amount of money
she spent on the pears to the amount of money she spent on the
mangoes was 1:5. The cost of each apple was $0.60. Find the total
number of fruits Mrs Chandra bought.
50 is the total number of fruits Mrs Chandra bought in ratio .
What does a math ratio mean?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.a total of $150 for all the fruits.
ratio of apple and pears = 3: 2
ratio of pears and mangoes = 1 : 5
5 units = 50
11 units = 110
15 units = $150
3 units = $30
number of apple = $30 ÷ $0.60 = 50
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to provide a baseline against which they can evaluate the effects of a specific treatment, experimenters make use of a(n)
To provide a baseline against which they can evaluate the effects of a specific treatment, experimenters make use of a(n) Control condition (Option D).
What is a control problem and optimal control?A cost functional that depends on state and control variables is a part of a control problem. A collection of differential equations describing the movements of the control variables in a way that minimizes the cost function is referred to as an optimal control.Now,
When conducting an experiment, a control condition is established to serve as a reference point for evaluating the outcome. For instance, a control group is typically established and given a placebo when evaluating the effects of a new treatment. This serves as a tool to gauge the medication's actual effects because it will not include any of the active ingredients.Hence, to provide a baseline against which they can evaluate the effects of a specific treatment, experimenters make use of a(n) Control condition (Option D).
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If 2000 pizzas were split between 4 people, how long would they last?
Answer:
It depends, each person gets 500 pizzas, and since there is no info on how long it takes for each of them to eat one pizza, there is no possible answer,
Step-by-step explanation:
Answer:
Each person would have 500 pizzas but how long they last would depend how fast they eat 'em lol
Step-by-step explanation:
2000 / 4 is 500
State a) whether each graph is a function, b) whether the relation is
continuous, discrete, or neither, and c) the domain and range in the notation
indicated.
For the given graph, we have that:
a) It is not a function.
b) The function is discrete.
c) The domain is {-5,2} and the range is all real values.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we can see that it is not a function, as the values of x = -5 and x = 2 are mapped to multiple values of y.
When a function is discrete and when it is continuous?A function is discrete when it is defined for only integer values of x.A function is continuous when it is defined for real values of x.For this problem, the function is defined only for x = -5 and x = 2, which are integer values, hence it is a discrete function.
What are the domain and the range of a function?The domain of a function is the set that contains all possible input values for the function. Hence, in a graph, it is the set that contains the values of x.The range of a function is the set that contains all possible output values for the function. Hence, in a graph, it is the set that contains the values of y.Thus, the domain is {-5,2} and the range is all real values.
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Solve inequality.
-n/7 ≥ 3
To solve the inequality, multiply both sides by -7 and flip the inequality direction. The solution is n ≤ -21 or (∞, -21]
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
-n/7 ≥ 3
Multiply both sides by -7. Since we multiply it by a negative number, flip the inequality.
-n/7 . (-7) ≤ 3 . (-7)
n ≤ -21
Using the interval notation, the solution is (∞, -21]
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the following are amounts of total snow falls (in inches) in different midwestern cities in the united states in a certain year: 20 40 31 7 15 29 25 20 17 32 28 12 34 29 20 17 33 23 find the sample mean.
The sample mean of snowfalls in the 18 midwestern cities of the United States is 24. This is calculated by applying the formula of arithmetic mean or average to the given sample of data.
What is arithmetic mean?
An arithmetic mean is examined as very similar to an average. Mathematically, it is obtained by dividing the sum of all objects by the total number of objects.
Calculation of the sample mean for given data
Given the total number of cities = 18
The total amount of snow falls = 20 + 40 + 31 + 7 + 15 + 29 + 25 + 20 + 17 + 32 + 28 + 12 + 34 + 29 + 20 + 17 + 33 + 23
The sample mean = total amount of snowfalls / total number of cities
= 432 / 18
= 24
Hence, the sample mean of the given data is 24.
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Tammy received
5
of the 49 votes cast for class vice-president. How many votes did she receive?
7
Write your answer in simplest form.
Answer:
Step-by-step explanation:
you will do 5+49 if u gain something u are adding the answer would be 98
When calculating a loan’s effective interest rate, if the nominal rate is 8.5%, what value of i do you plug into your equation? a. 8.5 b. 0.85 c. 0.085 d. 1.85 please select the best answer from the choices provided a b c d
The nominal interest rate to plug in will be 0.085.
What is interest rate?
An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.Given to us, the nominal rate is 8.5%,
The value to plug into your equation,
The equation can be simple interest or compound interest in both cases the value of the nominal rate to the plugin will be the same.
Thus, the nominal rate is 8.5% can be written as
Nominal rate = 8.5%
= 85/100 = 0.085
Hence, the nominal rate to plug in will be 0.085.
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Can someone please help with this? And if you do answer, can you please include an explanation on how to do it? I am very confused.
Answer:
Step-by-step explanation: 16. | 2x - 8| = 6
| 2x -8| = 6
+8 +8
____________
2x = 14 divide by 2
x = 7 , 16 will macth section a
Second equation : 19. | 8 - x | = 2
-8 -8
_____________
x=-6 , section c
If the surface area of a cube is 125 square inches what is the length of a slide
The length of a side of cube is 4.56 Inches whose surface area is 125 square inches .
The definition of the surface area of a given cube is that the total surface area is equal to the sum of the areas of all the sides of the cube. Since a cube has 6 faces The formula for surface area is equal to 6 times the square of the side of a cube. If the side length of the cube is a, area of the cube is given by [tex]AREA=6a^2[/tex] ...(1)
It is given that surface area of a cube is 125 square inches
Putting area = 125 in equation (1) , we get
[tex]125=6a^2\\a^2=20.33\\a=4.56 \ in[/tex]
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please help with problem 22
I am writing this because the app says the answer is to short :)))
Answer:
Step-by-step explanation:
-2x+3y
A continuous probability distribution is characterized by:_____.a. a continuum of possible values. b. an array of individual values. c. counts. d. a list of possible values.
Option (b), “a continuum of possible values” is the correct option.
The concepts of continuous probability distribution and normal distribution are used here to solve this problem.
The continuous probability distribution can be defined as the probability distribution of a continuous random variable. Normal distribution is used for finding the probability of a continuous variable when the data is more or less symmetric. The probability of being less than or more than some value can be calculated by calculating the area of the curve to the left of that value.
The probability of a continuous random variable will assume a particular value is zero. Consider a continuous random variable, which follows normal distribution with a mean, and a standard deviation, which can be represented as to calculate the probability for a random variable, convert the variable into a standard normal variable by the transformation:
Option (a), “an array of individual values” is incorrect because the continuous probability distribution does not contain an array of individual values. Option (c), “a list of possible values” is incorrect because it is not just a list of possible values. Option (d), “counts” is incorrect because the counts is not a characterized by the continuous probability.
Probability is defined as a task that cannot be completed.True or FalseFalse
Probability can be defined as the likelihood or chance of an event occuring. Probability is a branch of Mathematics that deals with the calculation on the chances of happening of a particular event.
For instance, the probability that a student will pass an exam is 1/2.
The students has a total of two possible outcomes, pass or fail.So, the probability of one outcome = 1/total outcome which is 1/2
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a student receives test scores of 62, 83, and 91. the student's term project score is 88 and her homework score is 76. each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework grade is 15% of the final grade. what is the student's mean score in the class?
Student's mean score of the class is 80.6.
Mean:
Mean or the average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Given,
A student receives test scores of 62, 83, and 91. the student's term project score is 88 and her homework score is 76. each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework grade is 15% of the final grade.
Here we need to find the student's mean score in the class.
First, we have to convert the percentage into decimal,
Then
=> 20% = 0.20
=> 25% = 0.25
=> 15% = 0.15
Then we have to find the scores from it,
Test A is 0.20 of the total and scores 62.
Test B is 0.20 of the total and scores 83.
Test C is 0.20 of the total and scores 91.
Project F is 0.25 of the total and scores 88.
Work H is 0.15 of the total and scores 76.
Multiply across:
=> A = (0.2 * 62) = 12.4
=> B = (0.2 * 83) = 16.6
=> C = (0.2 * 91) = 18.2
=> F = (0.25 * 88) = 22
=> H = (0.15 * 76) = 11.4
Now we have to add all these values to find the mean,
=> A + B + C + F + H
=> 12.4 + 16.6 + 18.2 + 22 + 11.4
=> 80.6
Therefore, the mean of that student is 80.6
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You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
Subtracting the maximum sodium intake from the intake of the cereal bar, you can eat amounts of sodium less than 2,175 mg of sodium the rest of the day.
How to find the amount of sodium you can eat during the rest of the day?From the text, the intake has to be less than 2300 mg. From the table, each cereal bar has 125 mg of sodium.
You eat one cereal bar, hence:
2300 - 125 = 2,175.
You can eat amounts of sodium less than 2,175 mg of sodium the rest of the day.
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make an equation for a line that goes through (-1,-2) (-2,-5)
Answer: y=3x+1
Step-by-step explanation:
Slope formula: m=(y2-y1)/(x2-x1)
m=(-5-(-2))/(-2-(-1))
m=(-5+2)/(-2+1)
m=(-3)/(-1)
m=3/1
m=3
y=mx+b
-2=3(-1)+b
-2=-3+b
b=1
y=3x+1
2x² + 5x – 6 when x = 3 I need help
Answer:
27
Step-by-step explanation:
[tex]3^2 = 9\\2\cdot \:9+5\left(3\right)-6\\2 \cdot 9 = 18\\18+5\left(3\right)-6\\5 \cdot 3 = 15\\18+15-6\\18 + 15 = 33\\33 - 6 = 27\\= 27[/tex]
[tex] \bf \implies27[/tex]
Step-by-step explanation:[tex] \bf \leadsto{2x }^{2} + 5x - 6 \\ \bf \leadsto 2 {(3)}^{2} + 5(3) - 6 \\ \bf \leadsto 2(9) + 15 - 6 \\ \bf \leadsto18 + 15 - 6 \\ \bf \leadsto18 + 9 \\ \bf \leadsto27[/tex]
13. (-3,-1), (5, -1)
15. (0, 0), (3, 4)
17. (-2, 0), (5,0)
14. (-4,-3), (1, 1)
16. (-1, 2), (2, -3)
18. (0, -8), (0, -1)
Find the distance between each pair of points.
We need to know about distance between two points to solve the problem. The distance between each pair of points are: 13. 8, 14. 6.40, 15. 5, 16. 5.83 , 17. 7 , 18. 7
The distance between two points is the length of the line that will join these two points. The distance can be calculated by taking the square of the difference of the x-coordinates and y-coordinates of the two points, adding them up and taking their square root. In order to understand the formula we have to draw a right angled triangle using these two points, where the line joining the points is the hypotenuse, the difference in the x-coordinates is the base and the difference between the y-coordinates is the height. We use Pythagoras' theorem to find the hypotenuse which gives us the formula of distance between two points
d=[tex]\sqrt{(x-a)^{2} +(y-b)^{2} }[/tex] where (x,y) and (a,b) are the two points
13. (-3,-1) (5,-1)
d=[tex]\sqrt{(-3-5)^{2}+(-1+1)^{2} } =\sqrt{64} =8[/tex]
14. (-4,-3), (1, 1)
d=[tex]\sqrt{(-4-1)^{2}+(-3-1)^{2} } =\sqrt{25+16} =\sqrt{41} =6.40[/tex]
15.(0, 0), (3, 4)
d=[tex]\sqrt{(0-3)^{2}+(0-4)^{2} } =\sqrt{9+16} =\sqrt{25} =5[/tex]
16. (-1,2) ,(2,-3)
d=[tex]\sqrt{(-1-2)^{2}+(2+3)^{2} } =\sqrt{9+25} =\sqrt{34} =5.83[/tex]
17.(-2,0) , (5,0)
d=[tex]\sqrt{(-2-5)^{2}+(0-0)^{2} } =\sqrt{49} =7[/tex]
18.(0,-8), (0,-1)
d=[tex]\sqrt{(0-0)^{2}+(-8+1)^{2} } =\sqrt{49} =7[/tex]
Therefore we found the distance between each pair of points using the formula to find distance between two points, 13) 8, (14) 6.40, (15) 5, (16) 5.83, (17) 7, (18) 7
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The path of an aeroplane is given by the equation 3x – 4y = 1 2: Represent the path
graphically. Also, show that the point (-4,-6) lies on the graph. Just give the full steps also pls
Answer:
Graph is attached
Step-by-step explanation:
The equation of the line is 3x - 4y = 12
If the point(-4, -6) is to lie on this line then the values x = -4 and y = -6 must satisfy this equation
Plug in these values on the left side
3(-4) - 4(-6) = -12 - (-24) = -12 + 24 = 12
So indeed this point satisfies this equation and therefore it must lie on this line
Can someone help me with this?
Answer:
x = 6
Step-by-step explanation:
21 : 28
27 : 6x
Cross multiply
21*6x = 27*28
126x = 756
756/126 = x
x = 6
Which expression is equivalent to (2^7⋅3^−5⋅9)^4?
The expression (2⁷ · 3⁻⁵ · 9)⁴ is equivalent to the power expression 2²⁸ / 3¹² = 505.109.
How to simplify an expression involving power expressions
In this problem we find an expression involving several numbers in power form and we must simplify into a single real number by using algebra properties:
(2⁷ · 3⁻⁵ · 9)⁴ Given(2⁷)⁴ · (3⁻⁵)⁴ · (3²)⁴ Power of a product of numbers / Definition of power2²⁸ · 3⁻²⁰ · 3⁸ Power of a power2²⁸ · 3⁻¹² Multiplication of powers with equal base2²⁸ / 3¹² Power of a power / Definition of division / ResultTo learn more on power properties: https://brainly.com/question/26480839
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there are six members on a student council. three of these members will serve on a spring formal committee. how many possible spring formal committees are there?
There are 20 possible combinations are there for spring formal committees.
Combination:
The process of determining the number of ways in which r objects can be selected from n distinct objects without regard to the order in which they are selected. Such selections are called combinations.
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]
Where
n refers the total number of ways
r refers the selected one
Given,
There are six members on a student council.
Three of these members will serve on a spring formal committee.
Here we need to find the possible number of members in spring formal committees.
We know that the value of,
n = 6
and r = 3
So, apply the values on the formula,
Then we get,
[tex]^6C_3=\frac{6!}{(6-3)!3!}[/tex]
[tex]^6C_3=\frac{6!}{3!3!}[/tex]
⁶C₃ = 720/36
⁶C₃ = 20
Therefore, the resulting value is 20.
Therefore, there are 20 possible combinations are there for spring formal committees.
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isabelle is mixing red paint with blue paint to make purple paint. She 3/10 adds of 1 1/10 a fluid ounce of red to of a fluid ounce of blue to make 1 1/30 fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
27/31 ounce of red paint should she really have to make 3 fluid ounces of purple paint.
common denominator in math's:Any arithmetic operation involving two or more fractions, such as addition or subtraction, is achievable if the denominators of both fractions are equal. This is referred to as the common denominator. A common denominator is an integer that has at least one element in common with both denominators other than 1.
According to the given data:Given:
3 /10 red + 11 /15 blue makes 1 1/30 purple
Get a common denominator of 30
3/10 * 3/3 = 9/30 red
11/15 *2/2 = 22/ 30 blue
1 1/30 = 31/30 purple
the amount of paint required to make 3 fluid ounce of purple color of paints:
So,
((3/10) * (31/30)) * 3
= (3/10 * 30/31) * 3
= 27/31 ounce.
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-1/9 + (-5/7) =
will give brainiest
Answer:-0.825 or 52/63
which expression uses the greatest common factor and the distributive property to rewrite the sum 75 45?
The expression uses the greatest common factor and the distributive property to rewrite the sum 75+45 is 15(5+3)
The greatest common factor is the greatest factor that divides both numbers.
The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation
Given,
75=3×5×5
45=3×3×5
The greatest common factor = 3×5=15
Then,
(75+45)=15(5+3)
Hence, the expression uses the greatest common factor and the distributive property to rewrite the sum 75+45 is 15(5+3)
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A company orders 11 boxed lunches from a deli for $108.90. If each boxed lunch costs
the same amount, how much do 17 boxed lunches cost?
Answer:
$7.95
Step-by-step explanation:
The equation c = 7.95b represents the total cost of the boxed lunches
c represents the total cost
b represents the number of boxed lunches
To find the total cost of multiple items, you generally multiply the cost of a single item by the number of items there are.
Using this, we can find the cost per item is 7.95 dollars, or 7 dollars and 95 cents.
The sum of three consecutive integers is 108. What are the integers?
smallest integer
middle integer
largest integer
Answer: 58,60,62
Step-by-step explanation:
1. find the numbers; since our middle term is 2n, our other two terms are 2n-2 and 2n+2.
2.Write the equation for the problem.
Therefore, the three consecutive integers are 58,60,62