Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the personal best time of Dean be = A
Now , the value of A = 3 hours 14 minutes 45 seconds
And ,
The time taken by Dean to complete 1 km = 9 minutes 30 seconds
Now , the total distance of the race lap = 20 km
So , the equation will be
Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km
Substituting the values in the equation , we get
Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds
Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds
Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds
1 hour = 60 minutes
1 minute = 60 seconds
180 minutes = 3 hours
600 seconds = 10 minutes
So , the equation is
Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes
So , the value of B < value of A
Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes
Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
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a boat leave a dock and sails 8 km north and then 13 km east how far is the boat from the dock
The equation c = 6.99p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store.
Which description is true, based on the equation of the proportional relationship?
For $1, you can buy 6.99 pounds of shrimp.
For $6.99, you can buy 6.99 pounds of shrimp.
For $6.99, you can buy 1 pound of shrimp.
For $0.01, you can buy 1 pound of shrimp.
For $6.99, you can buy 1 pound of shrimp, therefore, the third option is correct
What is a Ratio?A ratio indicates the number of times one number contains another.
The given equation is c = 6.99p, where c is the cost and p is the weight in pounds.
c = 6.99p
substitute p = 1:
c = 6.99
Hence, for $6.99, you can buy 1 pound of shrimp, therefore, the third option is correct.
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omar had 5/7 acres of land. He planted 5/6 of this land with corn. How many acres did he plant with corn
Answer: He planted 5/42 acres
Step-by-step explanation:
First, find the common of 7 and 6, which is 42
5/7 - 5/6
= 30/42 - 35/42
= -5/42
Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded quarterly until
April 1 of the fillowing year.
The amount of money in the account by April 1st of the following year is $4372.78.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount =3620(1+6.5/100)³
= 3620(1+0.065)³
= 3620(1.065)³
= $4372.78
Therefore, amount of money in the account by April 1st of the following year is $4372.78.
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The average speed of a ship for the first hour of a journey is 32 km/hr.Its average speed for the next 2 hours is 41 km/hr.Find its average speed for the whole journey.
The average speed for the whole journey is 24.3 km per hour.
What is the average speed for the whole journey?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
It should be noted that:
Speed = Distance / Time
Distance = 32km + 41km
= 73km
Time = 1 hour + 2 hours
Time = 3 hours
Speed = Distance / Time
Speed = 73 / 3
Speed = 24.3 km per hour.
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What is the slope-intercept form of the equation of a line the line passing through point (6, -1)
that is parallel to y = 2x - 3?
Answer:
baba perksssssssssssssss
Step-by-step explanation:
Answer: y=2x-13
Step-by-step explanation:
When lines are parallel to each other they have the same slope so the slope of the line we are trying to find is 2.
To find the y-intercept we can turn the equation into point-slope form using our point (6,-1) and slope (2).
Point-Slope Form: y-y1=m(x-x1)
y+1=2(x-6)
Then solve for y to find the y-intercept
y+1=2x-12
y=2x-13 is your answer in Slope-intercept form
Please help me with this question in the picture
Answer:c
Step-by-step explanation: decreasing
A new video game has been released. The table shows the proportional relationship between the number of levels completed and the time it should take to complete them.
Number of Levels 2 7
Time (hours) ? 3.5
How many minutes should it take to complete 2 levels?
60 minutes
120 minutes
180 minutes
210 minutes
The number of minutes it takes to complete 2 levels is (a) 60 minutes
How many minutes should it take to complete 2 levels?From the question, we have the following parameters that can be used in our computation:
Number of Levels 2 7
Time (hours) ? 3.5
This table can be represented as follows:
Ratio = Level : Time
So, we have the following representation
Level : Time = 7 : 3.5
At level 2, we have
2 : Time = 7 : 3.5
Express as fraction
Time/2 = 3.5/7
So, we have
Time = 2 * 3.5/7
Evaluate
Time = 1
Express as minutes
Time = 60 minutes
Hence. the time is 60 minutes
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Hurricanes are large storms that form over warm waters out in the ocean. hurricanes are associated with low-pressure regions in the atmosphere. how does the low pressure associated with a hurricane help them to grow big and powerful?
A hurricane is a big rotating storm system that develops over warm ocean waters and usually travels westward toward the American mainland.
An Atlantic Ocean hurricane or a northern Pacific Ocean hurricane is a tropical storm. In most years, hurricanes develop between June 1 and November 30. The Taino Indian word "hurakan," which means "god of wind," is where the word "hurricane" originates.
A hurricane is a big rotating storm system that develops over warm ocean waters and usually travels westward toward the American mainland. Depending on the maximum sustained wind speeds, hurricanes are either classed as tropical storms or hurricanes. Hurricanes have winds of 74 mph or more, whereas tropical storms have winds of 39 to 73 mph.
The hurricane's eye, which is a calm, clear region encircled by powerful winds, is the most hazardous component of the storm. The hurricane's eye, which can be up to 30 miles across, frequently experiences the storm's greatest rains and highest winds.
A hurricane's landfall can result in flooding from storm surges, strong winds, and heavy rains. The increase in sea level that happens as a cyclone nears land is known as a storm surge. Along with coastal locations, this increase in water level has the potential to inflict significant harm and flooding.
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Name the corresponding part if polygon WXYZ polygon PQRS.
X =
The corresponding angle of X is angle Q
What are corresponding shapes?Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure.
For two congruent shapes, the corresponding are equal.
if polygons WXYZ and PQRS are congruent, then, line XY= line QS
Therefore angle X= angle Q
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Need help on b please
Answer:
As the age of your car increases the value of that car decreases
Step-by-step explanation:
hope this helps
What’s the square root of 9 ? Explanation
Answer:
The square root of 9 is equal to 3.
Step-by-step explanation:
Square roots are essentially x squared = y. In this case, y is 9. x squared makes x = 3 because 3 * 3 * 3 = 9
what is 7 8/11 rounded to the nearest tenth
The provided mixed fraction (7 8/11) will have a decimal value of 7.7.
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
Here,
7 8/11=(7*11+8)/11
=85/11
=7.7
The value of the given mixed fraction 7 8/11 will be 7.7 in the decimal format.
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if my annual fee is $37,000 a year and i get a 5% raise every year what would be my annual salary in 14 years
Answer: $62900
Step-by-step explanation:
Find 5% of 37000 by taking 37000 timed 0.05 = $1850
Then find the total rise after 14 years by taking 1850 timed 14 = $25900
Then we add the original 37000 with 25900 = $62900
If you can, please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Answer: around 62900 Dollars in 14 years
Step-by-step explanation:
find the percentage of the raise per year
1850
Multiply by 14
25900
add the starting amount of salary per year
25900+37000
73257
9. a travel agency will plan tours for groups of 25 or larger. if the group contains exactly 25 people, the price is $300 per person. however, the price per person is reduced by $10 for each additional person above 25. you want to find what size group will produce the largest revenue for the agency. when x is the number of people added to the 25, the total revenue will be r(x)
If more than 25 people are added, the total revenue will be r(x) = $ 50, with the x = 5 size group producing the highest revenue for the agency.
what is marginal revenue ?The law of diminishing returns dictates that marginal revenue will eventually begin to decline as output level rises, even though it can remain constant above a certain threshold of output.
calculation
If a group of 25 people or more, a travel agency will organize the excursion.
The cost is $300 per person, if the group has exactly 25 participants. However, the cost per person drops by $10 for each additional person beyond the calculated maximum of 25.
R(X) = ( 25 + x ) ( 300 - 10x ) ( 300 - 10x )
evaluate in relation to x = R'(X) = 300 - 10x - 250 - 10x = 50 - 20x
We now have 30 people, which means that there are 5 more persons than 25.
Marginal revenue equals $50 when x = 5 and R'(X) = 50 - 20(5).
The revenue will drop by $50 for the following individual (31st ).
If more than 25 people are added, the total revenue will be r(x) = $ 50, with the x = 5 size group producing the highest revenue for the agency.
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(PICTURE INCLUDED) What are the missing parts that correctly complete the proof?
It is proved that Point A is situated equal distance from Triangle PQA and RQA.
What is bisector?
It is a line that divide an angle or a line in two equal parts. In the given figure, QA is a bisector as it divides the angle PQR.
what is congruent triangle?Triangles are called congruent when they have equal corresponding sides and equal corresponding angles. As shown in figure, the bisector QA creates two congruent triangle PQA and RQA.
it is given, QA is bisector of angle Q, so point A lies equal distance from P and R. According to the figure, APQ and ARQ are right angle.
As per the rules of congruence theorem, triangle PQA and Triangle RQA are two congruent triangles.
hence, A is the same distance from P and R
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Statement Reason
1. QA is the bisector of ∠PQR Given
2. ∠PQA ≅ ∠RQA Definition of bisector
4. ∠QXA ≅ ∠QYA All right angles are congruent
5. QA ≅ QA Given
6.△PQA ≅ △RQA AAS Postulate
8. Point A is equidistance Definition equidistance
from the side of ∠PQR
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given that point A is lie on the bisector of ∠PQR.
When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.
Therefore QA is the bisector of ∠PQR
Then ∠PQA ≅ ∠RQA
Since ∠QXA and ∠QYA are right angle, therefore they are congruent.
∠QXA ≅ ∠QYA
QA ≅ QA
AAS postulate: The triangles are congruent if two angles and the excluded side of one triangle match two angles and the excluded side of another triangle.
According to AAS postulate,
△PQA ≅ △RQA
Point A is equidistance from ∠PQR.
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Use fundamental identities to solve the equation.
csc^3 (x) - csc^2 (x) - csc (x) + 1
x = ± π/2 + 2kπ with k ∈ Z is the solution of fundamental identities
What is fundamental identities?
An equation is referred to as an identity if it has one or more variables and holds true for any replacement value of each variable that is specified on both sides of the equation.
y = cscx
y³ - y² - y + 1 = 0 has a root for y = 1
= y³ - y² - y + 1
= ( y² - 1 ) ( y - 1 )
= ( y + 1 ) ( y - 1 )²
cscx = ± 1
sinx = ± 1
or
x = ± π/2 + 2kπ with k ∈ Z
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2(log 2x − log y) − (log 3 + 2 log 5)
Answer:
.................=/
Step-by-step explanation:
to use a binomial distribution to approximate the count of successes in an srs, why do we require that the sample size n be no more than 10% of the population size n?
When the 10% criterion is met, we can use a binomial distribution to approximate the number of successes in a simple random sample (SRS) (as a simple random sample selects the trials without replacement).
The sample must be less than 10% of the population in order to satisfy the 10% requirement. It is fair to presume that the trials are independent because the sample is so much smaller than the population (even though the sampling occurred without replacement).
This suggests that the sample size n in this situation must be less than 10% of the population size NN.
This is the reason why 10% condition should be met.
In a binomial probability distribution, the number of successes in a series of n experiments is represented as either success or failure (probability q = 1 p), depending on the outcome's boolean value. A Bernoulli trial or experiment is another name for a single success or failure test, while a Bernoulli process is another name for a sequence of results.
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the estimated regression equation is . a. what is the value of the standard error of the estimate (to decimals)?
The value of the standard error of the estimate is 6.5141.
Given :
the estimated regression equation is y = 7.6 + 0.9x
we need to find the value of the standard error of the estimate.
Regression equation ;
A regression equation is used in stats to find out what relationship, if any, exists between sets of data.
Standard error :
The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.
here n = 5 and k = 2
σ = [tex]\sqrt{127.3/3}[/tex]
= 6.5141.
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Full question:
the estimated regression equation is y = 7.6 + 0.9x . a. what is the value of the standard error of the estimate (to decimals)?
if m, p, and t are distinct positive prime numbers, then m3pt has how many different positive divisors greater than 1 ?
There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.
How to find the number of positive factors for a number?The following are the steps to find the number of positive factors of a number:
Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:
24 = 2 × 2 × 2 × 3
Step 2: Same bases should be added in powers. So, the factors we can write as
24 = 2³ × 3¹
Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.
I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.
So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.
Calculation:It is given that, m, p, and t are distinct positive prime numbers.
Then, the number of positive divisors greater than 1 for the number m³pt are
m³× p × t
Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,
N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16
So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.
Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.
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A houe on the market wa valued at 376,000. After everal year, the value decreaed by 9%. By how much did the houe value decreae in dollar. What i the current value of the houe?
The house value is decreased by $33840 and the current value of the house is $342160
Here, we have been given a house on the market was valued at $376,000.
The value decreased by 9% .
We need to find the amount by which the house value decreased in dollar and the current value of the house.
The 9 percent of $376,000
376,000 * (9/100) = 33840
This means, the house value is decreased by $33840
So, the current value would be,
376,000 - 33840 = 342160
Therefore, the house value is decreased by $33840.
The current value = $342160
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Jason spent $25.50 on movie tickets. Each movie ticket (m) cost $8.50 . Which equation could be used to represent how many tickets Jason bought?
Answer:
8.50m = 25.50
Step-by-step explanation:
Total movie ticket spent = 25.50
Movie ticket unitary price = 8.50
Then an equation to represent that is:
8.50m = 25.50
m = 25.50/8.50
m = 3
Answer:
He bought 3 tickets
Step-by-step explanation:
Add $8.50 3 times to get how much he spent
I dont know which comes first
Answer:
Step-by-step explanation:
Distribute 3
Subtract 3x
Divide 9
-4/3 = x
Check
A model is drawn with a scale of 1:200.
a) The model is 17.5cm long. Find the actual length, in metres of the boat.
b) The actual length of the boat is 6.2m. Find the height, in centimeters, of the model.
Answer:
3500
Step-by-step explanation:
1 : 200 = 17.5 : x
x = 200 × 17.5
x = 3500
Write a story or situation that can be represented by the given equation.
4a + 5=12a − 11
story that represented equation, Maria, who liked cookie packages, did the arithmetic and discovered that the price of 4 cookie packages plus $5 is equivalent to the price of 12 cookie packages less $11.
What is a equation?A mathematical equation is a formula that connects two expressions with the equal sign = to express equality.
As a fan of cookie packages, Maria did the math and found that the cost of 4 packages of cookies + $5 is equal to the cost of 12 packages of cookies less $11.
[tex]'a'[/tex] represents the expense of a box of cookies,
On one side of the equation, we have the 4 packages of cookies plus $5.
[tex]4a + 5[/tex]
additionally, the 12 packages of cookies less 11 dollars on the other side of the equation.
[tex]12a - 11[/tex]
Now,
[tex]4a + 5 = 12a - 11[/tex]
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set up an equation and solve: the length of a rectangle is 4 feet more than three times the width. the perimeter is 48 feet. find the length and the width of the rectangle.
solving the equation, the width of the rectangle was found to be 6.67 feet and the length was found to be 22.67 feet.
Let x = the width of the rectangle
Then, the length = 3x + 4
Perimeter = 2(3x + 4) + 2x = 48
2(3x + 4) + 2x = 48
6x + 8 = 48
6x = 40
x = 40/6
x = 6.67 feet
The width of the rectangle = 6.67 feet
The length of the rectangle = 3(6.67) + 4 = 22.67 feet
To solve for the length and width of the rectangle, an equation was set up using the perimeter of 48 feet. The length was represented by 3x + 4, where x is the width. After solving the equation, the width of the rectangle was found to be 6.67 feet and the length was found to be 22.67 feet.
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An arithmetic sequence is given below.
7, 13, 19, 25,
the
Write an explicit formula for the n'th term
a’n
Hello,
I hope you and your family are doing well!
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the difference between consecutive terms is 6, so the common difference is 6.
The explicit formula for the nth term of an arithmetic sequence with first term a1 and common difference d is:
a_n = a1 + (n-1)d
Plugging in the values from the given sequence, we have:
a_n = 7 + (n-1)6
This is the explicit formula for the nth term of the arithmetic sequence.
For example, if you want to find the fifth term of the sequence, you would plug in n = 5:
a_5 = 7 + (5-1)6 = 7 + 4*6 = 7 + 24 = 31
So the fifth term of the sequence is 31.
---
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Triangle ABC has vertices A(-4,1), B(-2,1), and C(-1,-2) on a coordinate grid. If it is rotated 180 degrees about the origin, what are the coordinates of A'B'C'?
Answer: A' (-4,-1) B' (-2,-1) C' (-1,2)
Step-by-step explanation: The reasons these are the correct answers because if you look at the rule of a rotation, it states that: The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
Deanna and lulu are playing games at the arcade. Deanna starts with $15, and the machine she is playing costs $0. 75 per game. Lulu starts with $13, and her machine costs $0. 50 per game. Choose the correct expressions to write an equation that could be used to find after how many games the two friends will have the same amount of money remaining. Let g represent the number of games.
After 8 number of games both has equal amount of money.
Deana starts with $15 and the machine she is playing costs $0.75 per game
lulu starts with $13 and the machine she is playing costs $0.50 per game
Let us after x number of games both has same money
Deana spends 0.75*x amount of money after playing x number of games.
Deana has remaining amount of money 15 - 0.75*x.
lulu spends 0.50*x amount of money after playing x number of games.
lulu has remaining amount of money 13 - 0.50*x.
We have assumes that after x number of games both has same amount of money.
[tex]15-0.75*x = 13 - 0.50*x[/tex] --- this is the correct expression to write an equation that could be used to find after how many games the two friends will have the same amount of money.
15 - 13 = 0.75*x - 0.50*x
2 = 0.25*x
x = 2/0.25
x = 8.
So After 8 number of games both has equal amount of money.
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