Answer:
A. 4.33 minutes
B. it will be about 11% less than the initial time (4.85 -0.54)
Step-by-step explanation:
You want to know the team's final time if it decreases by 5 1/2% on each of two runs after their initial run time of 4.85 minutes. And you want to know how to check the answer for reasonableness.
A. Final runIf the time decreases by 5.5% on each run, it is multiplied by (1 -5.5%) = 0.945 on each run. The time after 2 more runs will be ...
(4.85 min)(0.945)(0.945) ≈ 4.33 min
The team's time on the final run was about 4.33 minutes.
B. Reasonableness checkFor small percentages, the product of small percentage changes is nearly the same as the sum of the percentage changes. That is, two changes by -5.5% will be about the same as a change of 2 × (-5.5%) = -11%.
Of course a decrease of 11% is a decrease of 10% and another decrease of 1%. This makes the estimated time be ...
4.85 -0.485 -0.0485 ≈ 4.85 -0.54 = 4.31
The estimate is a larger change than the actual change, so the computed value of 4.33 is judged to be reasonable. (The actual effect of two -5.5% changes is about a -10.7% change.)
__
Additional comment
This "add the percentages" is a suitable way to check the reasonableness of all sorts of problems involving percent changes, including problems involving investments or loan interest.
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HELP SOLVE FOR 24 points
Answer:
Slope = -1/6
Step-by-step explanation:
Answer:
the correct one is Slope = -1/6
Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of Sprite to make 12 cups. He pays $3.00 for a 2-liter container of Sprite and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.
The $3.00 for 2 liters of Sprite and $16 for 1 gallon of raspberry sorbet indicates that the minimum amount Rafael should sell a cup of punch.
The minimum price at which Rafael should sell a cup of punch to make a profit of $10 is approximately $2.42 What is a profit?A profit is a financial gain from the revenue that exceeds the sum of expenses and the taxes.
The ingredients required to make 12 cups of punch are;
1 gallon of raspberry and 2 liters of Sprite
Amount he pays for 2-liter of Sprite = $3.00
Amount paid for a quart of sorbet = $4.00
The minimum amount to be charged so as to make a $10 profit is found as follows;
4 quarts is equivalent to one gallon
Therefore;
1 quart of sorbet costs $4
4 quart of sorbet = 1 gallon of sorbet costs 4 × $4 = $16
The cost of 2-liters of Sprite = $3.00
The cost of 12 cups of punch is therefore;
$3 + $16 = $19
The revenue when a profit of $10 is made is therefore;
Revenue = $19 + $10 = $29
The selling price per cup, p, is therefore;
p = $29 ÷ 12 $2.42
The price per cup to make a profit of $10 is approximately $2.42≈
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A small pizza has a diameter of 8 inches.
(a) What is the size of the outer ring of the pizza?
(b) What is the amount of cheese covering the entire top of the pizza?
The size of the outer ring of the pizza = 25.12 inches
The amount of cheese covering the entire top of the pizza = 50.24 sq inches.
A small pizza has a diameter of 8 inches.
A Pizza has a circular base structure whose diameter, d = 8 inches.
Radius of the pizza, r = d/2 = 8/2 = 4 inches.
The size of the outer ring of the pizza means we talk about the circumference of the pizza.
The size of the outer ring of the pizza = 2πr
If we take the value π = 3.14 ( round off figure)
Then the size of the outer ring of the pizza = 2×3.14×4=25.12 inches.
The amount of cheese covering the entire top of the pizza means we talk about entire top area of the pizza.
The amount of cheese covering the entire top of the pizza = π × r^2
= 3.14 ×4×4
The amount of cheese covering the entire top of the pizza = 50.24 sq inches.
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You estimate that there are 42 marbles in a jar. The actual amount is 67 marbles. Find the percent error. Round to the nearest tenth of a percent if necessary.
If the actual amount is 67 marbles. the percent error is 37%.
How to find the percent error?Using this formula to find the percent error
Percent error = Actual value -Estimated value/ Estimated value
Where:
Actual value = 67
Estimated value = 42
Let plug in the formula
Percent error = 67 - 42 /67
Percent error = 25/67 × 100
Percent error = 37%
Therefore the percent error is 37%.
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Your restaurant has a gross profit of $274,232, administrative expenses of $29,147 and marketing expenses of 32,645. What is the income from operations of your business?.
The income from operations of your business is $2,12,440.
Given:
Your restaurant has a gross profit of $274,232, administrative expenses of $29,147 and marketing expenses of 32,645.
Total expenses = administrative + marketing expenses
= $29,147 + $32,645
= $61792
Income = gross profit - total expenses
= 274232 - 61792
= $2,12,440
Therefore the income from operations of your business is $2,12,440.
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in 2020 summer camp registration was $15 more than it was in 2021. in 2020, registration was $285 by what percentage did the summer camp registration decrease in 2021
If in 2020, registration was $285.The percentage that the summer camp registration decrease in 2021 is 5.26%%.
How to calculate the decrease in percentageUsing this formula to find the decrease in percentage
Decrease in percentage = [2020 registration cost - (2020 registration cost - 2020 summer registration)] / 2020 registration cost
Let plug in the formula
Decrease in percentage = [285 - (285 -15)] /285
Decrease in percentage =285 - 270 / 285
Decrease in percentage = 15 /285
Decrease in percentage =0.0526× 100
Decrease in percentage =5.26%
Therefore 5.26% is the decrease in percentage .
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a deck of cards has only red cards and black cards. the probability of a randomly chosen card being red is 1 3 . when 4 black cards are added to the deck, the probability of choosing red becomes 1 4 . how many cards were in the deck originally?
Answer: The answer is (264)×(261)(525), because (264)×(261) are the possibilities for choosing 4 red cards and 1 black card from a deck of 52 cards, while (525) are the possibilities for choosing 5 cards from a deck of 52 cards.
So, your first solution is almost correct. On why your second solution is wrong, you'll have to explain your thought process.
Step-by-step explanation:
Consider the expression 1/3bwh
Complete 2 of the description parts of the expression:
1. The entire expression is the product of ____.
2. In this context, 1/3 is a ____.
1. The entire expression is the product of 4 factors.
2. In this context, 1/3 is a coefficient.
What are factors?Factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors simply refers to numbers which can be multiplied together to get another number.
What is a coefficient?In Mathematics, a coefficient can be defined as a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
Based on the given expression 1/3bwh, we can logically deduce that there are four (4) factors and these include the following:
1/3bwhIn conclusion, 1/3 is considered as a coefficient of bwh.
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I need assistance of Geometry, please help. (Transformation, Triangles, and Quadrilaterals.)
Answer: oh ok
Step-by-step explanation:
well you know just ask your mom
At an electronics store, a $165 television is marked up 110%. Trevor purchases the tv and must pay 6. 5% sales tax. What is the total cost of this television at the store? a. $193. 30 b. $299. 48 c. $369. 02 d. $571. 73.
The total cost of this television at the store is $193.30
Given,
A $165 television has indeed been increased 110% in price at an electronics store. When Trevor buys the TV, he is bound to pay 6.5% in sales tax.
A $165 television has been increased 110% in price at an electronics store.
When Trevor buys the TV, a 6.5% sales tax is due.
Consequently, this television will cost in the store a total of
The total cost of the TV is equal to 165 dollars multiplied by 1.10 and 1.065.
⇒ $165*1.10*1.065
= $193.30
TVs cost a total of $193.30.
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find the annual salary of a person who is paid $3,800.00 per month and show working for the this question
Answer:
$45600.00
Step-by-step explanation:
Year is synonm to annual
As there is 12 months in a year
we times $3,800 by 12 which is $45600.00
Pls give me brainliest
pls:(
What is the answer to the equation:
2x+10=3x-5
Answer:
x=15
Step-by-step explanation:
Answer:
x=15
Step-by-step explanation:
See image below
there are 200 sixth graders and 170 of them want to take geometry and 175 want to take algebra what is the least number of people who want to take both geomtry and algebra
The least number of people who want to take both geometry and algebra is 145
How to find the least number of people that would like to take geometry and algebraThe inclusion-exclusion principle is a counting method that generalizes the well-known approach to determining the number of members in the union of two
The inclusion - exclusion principle is used here
let the number that will take both algebra and geometry be x
200 = 170 - x + 175 - x + x
200 = 345 - x
x = 354 - 200
x = 145
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The least number of people who want to take both geometry and algebra is 145 graders
What is intersection of set?The intersection of sets can be denoted using the symbol '∩'. the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.
The number of graders that want to take geometry is 170
The number of graders that want to take algebra is 175
A ∩ G= n(A) + n(G) -( AUB)
=175+170-200
= 345-200
= 145
Therefore the least number of people that will want to do both geometry and algebra is 145
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A scientist uses a submarine to study ocean life. . She begins 198 feet below sea level. After traveling down for 15 seconds, she's 316 feet below sea level. 0 Find the rate of change in the submarine's elevation in feet per second. If necessary, round your answer to the nearest tenth.
The rate of change in the submarine's elevation is given by 7.87 feet per second approximately.
Given that the initial depth of the submarine = 198 feet
The final depth of the submarine = 316 feet.
The submarine takes 15 seconds to reach the final depth to initial depth.
The elevation of the submarine = (316-198) = 118 feet
So the rate of change = 118/15 = 7.87 feet/second (approximately)
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Let us consider the points with an integer y-coordinate from (-1) to 1 and with an integer x-coordinate from (-20) to 20. How many lines are there parallel to the line y=2x and passing through any of these points? PLEASE HELP I NEED THE ANSWER!!!!
There are infinite linear functions that are parallel to y = 2x passing through these two points.
What is a linear function?The slope-intercept representation of a linear function is presented by the equation shown as follows:
y = mx + b
The coefficients of the the linear function, along with their meaning, are described as follows:
m is the slope of the function, representing the unit rate of change of the output y in relation to the input x.b is the y-intercept of the function, which is value of y at which the linear function crosses the y-axis.What defines two parallel linear functions is that they have the same slope.
The slope of the line y = 2x is of 2, hence we will have an infinity number of linear functions in the following format:
y = 2x + b.
In which b is the y-intercept of the function.
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Find the cross-sectional area
Answer:
at middle of a,b,c
Step-by-step explanation:
........
Write the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 1.
The quadratic equation whose roots are -3 and -1, and whose leading coefficient is 1 is x^2 + 4x + 3 = 0.
We know that the standard form of a quadratic equation is given by;
y = f(x) = ax² + bx + c = 0
We are given:
The roots of the quadratic equation are -3 and -1.
The leading coefficient of the quadratic equation is 1.
We need to find the quadratic equation.
The roots of the quadratic equation are -3 and -1.
So, (x + 3) and (x + 1) will be the factors.
Since the leading coefficient of the quadratic equation is 1.
So, the quadratic equation is given by;
1 * (x + 3) * (x + 1) = 0
x (x + 1) + 3 (x + 1) = 0
x^2 + x + 3x + 3 = 0
x^2 + 4x + 3 = 0
So, the required quadratic equation is x^2 + 4x + 3 = 0.
Thus, the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 1 is x^2 + 4x + 3 = 0.
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Lesson Performance Task
The image shows the angles formed by a pair of scissors. When the
scissors are closed, m<1= 0°. As the scissors are opened, the measures
of all four angles change in relation to each other. Describe how the
measures change as m<1 increases from 0° to 180°.
Answer: Angle 3 is a vertical angle of angle 1 and will always be identical to what angle 1 is.
Angle 2 and angle 4 are supplementary angles to angle 1 and will always be the difference between 180 and what angle 1 is.
For example, if angle 1 were 45 degrees, angle 3 would also be 45 degrees, and angles 2 and 4 would be 180-45 = 135 degrees.
Step-by-step explanation:
question is in the pic
The ordered pair that shows the dilation of the square ABCD, located at A(-10, -2), B(-5, -2), C(-5, -7), and D(-10, -7), by a scale factor of 5 about the origin is option B
B. A'(-50, -10), B'(-25, -10), C'(-25, -35), and D'(-50, -35)
What is a dilation transformation?A dilation transformation is in which the sizes of the sides of the pre image or original figure is changes proportionately to get the image.
The vertex of the preimage ABCD are; A(-10, -2), B(-5, -2), C(-5, -7), and D(-10, -7)
A dilation by a scale factor of 5 is found using the formula;
(x, y) Dilation by scale factor of 5 about the origin ⇒ (5·x, 5·y)
Therefore, the coordinates of the square ABCD following a dilation by a scale factor of 5 is therefore;
A'(5 × -10, 5 × -2), B'(5 × -5, 5 × -2), C'(5 × -5, 5 × -7), and D'(5 × -10, 5 × -7)
Which gives;
A'(-50, -10), B'(-25, -10), C'(-25, -35), and D'(-50, -35)
Checking the lengths of the sides gives;
AB = 5
A'B' = -25 - (-50) = 25
BC = 5
B'C' = -10 - (-30) = 25
CD = 5
C'D' = -25 - (-50) = 25
AD = 5
A'D' = -10 - (-35) = 25
Therefore, the lengths of the sides of A'B'C'D' are 5 times the lengths of the sides of the square ABCD
The correct option is therefore option B
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Which expressions are equivalent to g16? Check all that apply.
Answer:
I think you mean 6^16
if so, the right answers are
the 3rd one (6^-4)^-4
the 4th one (6^-2)^-8
last answer (6^8)^2
Step-by-step explanation:
you have to apply the Powers of a Powers Property:
(a^n)^m=a^(nm), basically you're multiplying the exponents (the powers)
Hope this helps.
Look at the picture and answer the four questions
Answer:
First Picture is a rotation
Second Picture is a rotation
Third Picture is a vertical translation
The last Picture is a reflection
Step-by-step explanation:
Answer:
First is rotation
Second is rotation
Third is translation
Fourth is reflection
PLS HELP
Find the missing term
b) 3:7= : __ 42
The missing term is 18.
How to find denominator ?The lower number in a fraction is known as the denominator. It demonstrates the equal division of something into portions. Four would be the denominator, for instance, if the fraction was 3/4.Making ensuring your denominators are the same is always the first step when adding or subtracting fractions. This implies that you must identify the common factor. The numerators may then be easily added or subtracted after you have determined the common denominator.Equations with identical denominators are simple to solve because you don't need to identify their shared denominator. The lowest common denominator is known. For instance: 1/4 + 2/4 = 3/4The common denominator in this equation is 4, thus. As a result, you may add the numerators together and place 4 at the bottom of the fraction. You now have 3/4.From given details : 3:7= : __ 42
Here's a little tip for you. Any numbercan be converted to fraction if you
use 1 as the denominator: = 3 / 7 = 42 / 1
= 3 x 42 / 7 x 1 = 126 / 7
= 18
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Determine if 0. 7653765376537653. 0. 7653765376537653. Is rational or irrational and give a reason for your answer.
The number 0. 7653765376537653 is rational number.
What is rational and irrational number?
Perfect squares like 4, 9, 16, 25, and other integers are included in the category of rational numbers. Surds like 2, 3, 5, 7, and so forth are examples of irrational numbers. Rational numbers have whole integers for both their numerator and their denominator, meaning that their denominator is not equal to zero. All whole numbers, fractions, and decimal numbers that finish or repeat are considered rational numbers. Any number that is not rational—that is, any number that cannot be divided by a fraction—is considered to be irrational.
Here the given number is
=>0.7653765376537653
It consists repeated numbers and we can also convert into fraction value.
Hence it is a rational number.
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pls help me with annoying sparx maths questions
and ill mark u as brainiest
An elephant can’t drink up to 6400 fluid ounces of water a day how many gallons of water can an elephant drink per day
The number of gallons of water can an elephant drink per day is 50 gallons.
Given that, an elephant can’t drink up to 6400 fluid ounces of water a day.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, there are 128 fluid ounces in 1 gallon.
Now, 6400/128
= 50 gallons
Hence, the number of gallons of water can an elephant drink per day is 50 gallons.
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A cuboid has sides xcm, 5cm and 7 cm. The total surface area of the cuboid is 142 cm². Form an equation in terms of x. Solve the equation to find x.
We know that the surface area of cuboid with sides L, B and H is given by,
S = 2 (LB + BH + LH)
Given that the sides of cuboid are x cm, 5 cm and 7 cm.
So L = x cm and B = 5 cm and H = 7 cm.
Given that the surface area of the cuboid is 142 square cm.
According to information the suitable equation for this is:
2(5x+7*5+7x) = 142
Now solving the equation we get,
5x+35+7x = 142/2 = 71
12x+35 = 71
12x = 71-35
12x = 36
x = 36/12
x = 3
Hence the value of x is 3 cm.
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Please help me with this question
Answer:
1.5 cm
Step-by-step explanation:
Triangles WTY and UTV are similar. Segment WT corresponds to UT and segment YT corresponds to VT. Thus we can create an equation knowing that the ratio of WT to UT must equal to the ratio of YT to VT.
WT = 7.5 cm
UT = ?
YT = 15 cm
VT = 12 cm
WT / UT = YT / VT
7.5 / UT = 15 / 12
UT = 6
WT = WU + UT
7.5 = WU + 6
WU = 1.5
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is.
The number of degree of freedom for reading the t values is 60 , the correct option is (c) .
In the question ,
it is given that ,
number of items in the sample = 61 items
the mean of the sample is given as 23 ,
we have to find the degree of freedom(df) ,
the degree of freedom(df) can be solved using the formula
degree of freedom(df) [tex]=[/tex] (number of observations) - 1
Substituting the values in the formula ,
we get ,
degree of freedom = 61 - 1
= 60
Therefore , The number of degree of freedom for reading the t values is 60 , the correct option is (c) .
The given question is incomplete , the complete question is
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is ?
(a) 22
(b) 23
(c) 60
(d) 61
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a bag contains 11 counters.
5 of the counters are white.
a counter is taken at random from the bag and is not replaced.
a 2nd counter is taken out of the bag by random.
calc probability that only one of the counters is white.
The probability that only one of the counters is white is the fraction 6/11 or 0.55 considering that the first take is without replacement
Probability of an event without replacementThe probability for an event without replacement implies that once an item is taken, then we do not replace it back to the sample space before taking a second item.
Given that there are 11 counters in the bag, with 5 of them being white;
The probability of taking a white counter = 5/11
The probability of not taking a white counter = 6/11
The probability of taking a white counter first without replacement and not taking it the second time = (6/11) × (5/10)
The probability of not taking a white counter first without replacement and taking it the second time = (5/11) × (6/10)
The probability that only one of the counters is white = (6/11) × (5/10) + (5/11) × (6/10)
The probability that only one of the counters is white = (30/110) + (30/110)
Therefore, probability that only one of the counters is white = 6/11 [by simplification]
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4 times the sum of a number and -6 equals 20
Answer:
The number is 11.
Step-by-step explanation:
Step one: Convert to algebraic equation
4 x ( a -6 ) = 20
Step two: Simplify both sides of the equation.
4 (a −6) = 20
(4)(a) +(4)(−6) = 20 (Distribute)
4a +−24 = 20
4a −24 = 20
Step three: Add 24 to both sides.
4a −24 +24 = 20 +24
4a = 44
Step four: Divide both sides by 4.
(4a /4) = (44 /4)
a = 11