Mr. Giordano's drove 4.5 miles in 5 minutes. Mr. Baras drove 6.3 miles in 8 minutes. Who drove faster? Explain using unit rates for both teachers.
If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras
The distance traveled by Mr. Giordano = 4.5 miles
The time taken = 5 minutes
Speed = Distance / Time
Substitute the values in the equation
Speed = 4.5/5
= 0.9 miles per minutes
The distance traveled by Mr. Baras = 6.3 miles
The time taken = 8 minutes
Speed = Distance / Time
Substitute the values in the equation
Speed = 6.3/8
= 0.78 miles per minutes
Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras
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A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof
Given
A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof
Solution
The final answer
Option C
There are 8 batteries in a package of AA batteries, and 12 batteries in
a package of AAA batteries. If you buy 10 packages of AA batteries and
6 packages of AAA batteries, how many batteries would you have?
A- 156 batteries
B- 36 batteries
C- 152 batteries
Answer:
C. 152
Step-by-step explanation:
8 × 10 + 6 × 12 = 80 + 72 = 152
Find the values of the ratios
(red to blue) of the
perimeters and areas of the
similar figures. Write the
ratios as fractions in
simplest form.
5
8
The ratio of the perimeters is
The ratio of the areas is
Answer:
perimeter: 5/8area: 25/64Step-by-step explanation:
You want the ratios (red to blue), of perimeter and area, given that corresponding sides have the ratio red to blue = 5 to 8.
Perimeter ratioThe ratio of perimeters is the ratio of corresponding side lengths:
red to blue = 5 / 8
Area ratioThe ratio of areas is the square of the ratio of corresponding side lengths:
red to blue = (5 to 8)² = 25 / 64
__
Additional comment
Ratios are customarily expressed in any of three equivalent forms:
5 to 85:85/8 "fraction" formThe amount of gas that a helicopter uses is directly
proportional to the number of hours spent flying. The
helicopter flies for 2 hours and Uses 26 gallons of fuel.
Find the number of gallons of fuel that the helicopter uses
to fly for 5 hours.
Answer:
65
Step-by-step explanation:
2:26
1:x
26/2 = x = 13
The heli uses 13 gallons per hour.
5:y
13x5 = y = 65
Hope that helps
RUNNING Stella ran her first half marathon in 2.7 hours. By how many hours must Stella reduce her time to run her next half marathon in fewer than 2.3 hours? Enter an inequality to represent the situation.
Answer:
2.7 - h < 2.3
Step-by-step explanation:
You want an inequality to represent the relationship described by "Stella wants to know the number of hours (h) by which she must reduce her 2.7 hour half-marathon time to run in under 2.3 hours."
InequalityIf h is the number of hours by which the time is reduced, Stella wants ...
2.7 -h < 2.3 . . . . . . . . . representative inequality
__
Additional comment
The solution would be h > 0.4. Stella must reduce her time by more than 0.4 hours.
<95141404393>
A right cylinder has a radius of 5 and a height of 9. What is its surface area? O A. 72 units O B. 90 units O c. 45rt units O D. 108r units
The formula to find the surface area of a cylinder is:
[tex]\begin{gathered} SA=2\pi r^2+2\pi rh\text{ } \\ \text{ Where} \\ SA\text{ is the surface area} \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} r=5 \\ h=9 \end{gathered}[/tex][tex]\begin{gathered} SA=2\pi r^2+2\pi rh \\ SA=2\pi(5^2)+2\pi(5)(9) \\ SA=2\pi(25)+90\pi \\ SA=50\pi+90\pi \\ SA=140\pi \end{gathered}[/tex]AnswerB. 140π units²
difference between a number and its positive square root is 12.find the number
Answer:16
Step-by-step explanation:
x-[tex]\sqrt{x}[/tex]=12
x=16
Mr Tan had 2 kg of sugar
He usedkg of sugar to make dessert and kg of sugar to ooke
some cakes.
(a) What was the total mass of sugar used?
(b) How much sugar did he have left?
a) The total mass of sugar used is 1.7 kg.
b)The mass of sugar he has left is 0.3 kg.
What are fractions?A fraction is a numerical value that represents a piece of a total in mathematics. The total can be any number, a specific value, or a single item. Fractions are denoted by the symbol p/q.
Given:
Total mass of sugar Mr tan has = 2 kg
Fraction of sugar used to make dessert = 1/4 kg
Fraction of sugar used to bake some cakes = 3/5 kg
The total mass of sugar used is determined as,
= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes
Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg
Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg
Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg
Mass of sugar left with him = Total mass of sugar - Total mass of sugar used
= 2 kg - 1.7 kg = 0.3 kg
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The complete question is: "Mr tan had 2 kg of sugar. He used 1/4 kg of sugar to make dessert and 3/5 kg of sugar to bake some cakes.
(a) What was the total mass of sugar used?
(b) How much sugar did he have left?"
Members of a lacrosse team raised $2863.50 to go to a tournament. They rented a
bus for $1087.50 and budgeted $74 per player for meals. Which equation or tape
diagram could be used to represent the context if a represents the number of players
the team can bring to the tournament?
Linear equations - The team can bring its 24 players
What do you mean by linear equations with one variable?
A linear equation with one variable is one that can be written as ax+b = 0, where a and b are two integers, and x is a variable. This type of problem only has one solution. For instance, the linear equation 4x+4=8 only has one variable.
We are given that,
the total money raised by the lacrosse team is given to be $2863.50
bus rented at a cost of $1087.50
meal budget per person is calculated to be $74
let us assume the number of players the team can bring to the tournament to be "x".
bus rent + (meal budget * number of players) = total money raised
= 1087.50 + (74*x) = 2863.50
= 1087.50 + 74x = 2863.50
= 74x = 2863.50 - 1087.50
= 74x = 1776
= x = 1776 ÷ 74
= x = 24
Thus the team can bring its 24 players.
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John and Nelly are cleaning their house, Nelly takes 3 hours longer than John if she cleans alone, If they can do the cleaning together in 2 hours, how long can John clean all b yh himself
Answer: 3 hours
Let john take x hours to finish the work
Let nelly take y hours to finish the work
given, y =x+3
Portion of work done by john alone in one hour = 1/x
Portion of work done by Nelly alone in one hour = 1/y
∴Portion of work done by both john and nelly in one hour = 1/x + 1/y
[tex]= \frac{1}{x} + \frac{1}{x+3}\\=\frac{x+3+x}{x*(x+3)}\\=\frac{2x+3}{x^2+3x}[/tex]
Total time taken by John and nelly to finish the work = 2 hours
[tex]\therefore [2(2x+3)]/[x^2 + 3x] = 1\\= > 4x + 6 = x^2 + 3x\\= > x^2 -x -6 =0\\= > x^2 - 3x + 2x -6 =0\\= > x(x-3) + 2(x-3)=0\\= > (x+2)(x-3)=0[/tex]
Hence either x = -2 or x = 3
Since x is time taken, it cannot be negative, hence x = 3
∴Time taken by john to finish the work = 3 hours
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Question ♀️ 2The function p(t) = 2(3)^t represents the population of a certain type of bacteria after t days. What is the population of the bacteria after 7 days?
Explanation
Given the function;
[tex]p(t)=2(3)^t[/tex]We are asked to find the population of the bacteria after 7 days.
Given that t represents the number of days, we can find the population by substituting 7 into the formula. This can be seen below.
[tex]\begin{gathered} p(t)=2(3)^7 \\ =2\times2187=4374 \end{gathered}[/tex]Answer: 4374
A car’s velocity increases from 4.2m/s to 14.8 m/s, E, in 2.5 sec. What is its acceleration?
Answer:
4.24ms-²
Step-by-step explanation:
S: x. write suvat and sub in values
u:4.2
v:14.8
a:?
t:2.5
use correct equation
v=u+at
sub values in
14.8=4.2+2.5a
rearrange to get a
10.6/2.5= a
a=4.24
As the x-value increases by 20, the y-value increases by 10. Which of the following equations represents the relationship between the x and y-values
An equation which represents the proportional relationship between the x and y-values is: C. y = 2x.
What is direct variation?A direct variation represents two variables that are directly proportional to each other, which simply means as one variable increases, the other variable also increases and vice-versa.
How to determine the equation?Mathematically, a proportional relationship can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) based on the data points given:
k = y/x
k = 20/10
k = 2
Therefore, the required equation is as follows:
y = 2x
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Complete Question:
As the x-value increases by 20, the y-value increases by 10. Which of the following equations represents the relationship between the x and y-values?
A. y = 2 + x
B. y = 2 - x
C. y = 2x
URGENT!!! PLEASE HELP ME!!!
Which ratios have the unit rate less than 1?choose all the apply
2 feet : 12/5 minutes
1/8 foot: 1 2/3 minutes
3 feet : 4 2/3 minutes
1 5/8 feet :2 minutes
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, whereas the ratio of lemons to oranges is 6:8. Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
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Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
After four years, the investment is worth £8934.34.
How does compound interest work?The interest you earn on interest is known as compound interest. For instance, if you start with $100 and it generates 5% interest annually, you will conclude the first year with $105 in your account. You'll have $110.25 after the second year is over.
We employ the formula approach to determine the entire amount,
A = P(1+r)^n
The amount invested, or principal(P), is £8,000.
Interest rate r is 2.8%, or 0.028.
n = 4 years have passed.
Now, immediately enter these values into the formula, A = P(1+r)n.
A = 8000 * (1 + 0.028) ^ 4
= 8000 * 1.028 ^ 4
= 8934.34
Consequently, the investment's value after four years is £8934.34.
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after cynthia microwaves her bowl of morning porridge, it is either too cold, just right, or too hot. she estimates that there is a 35\55, percent chance that it will be too cold and a 50\pp, percent chance that it will be too hot. what is the probability that cynthia's morning porridge will be just right?
The probability that Cynthia's morning porridge will be just right is 15%.
Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.
The sum of the probabilities in a probability distribution is always 1.
If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.
P(too cold) + P(just right) + P(too hot) = 100%
35% + P(just right) + 50% = 100%
P(just right) = 100 - (35 + 50)
P(just right) = 100 - 85
P(just right) = 15%
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Toby’s Tiny Toys have fixed expenses of $53,900 for the production of their tiny toys.
Toby’s has a variable expense of $12.50 a piece for each toy they produce, and they
sell their toys for $16.50 a piece. How many tiny toys do they have to sell to reach
their breakeven point?
The number of tiny toys that Toby's Tiny Toys need to sell to reach its break-even point is 13,475.
What is the break-even point?The break-even point is the production and sales units that will ensure that Toby's Tiny Toys does not incur a loss or generate a profit.
At the break-even point, the total revenues are equal to the total costs (fixed and variable).
Selling price per unit = $16.50
Variable expenses per unit = $12.50
Contribution margin per unit = $4 ($16.50 - $12.50)
Fixed expenses = $53,900
Break-even point in units = Fixed costs/Contribution margin per unit
= 13,475 ($53,900/$4)
Thus, we can conclude that Toby’s Tiny Toys needs to sell 13,475 to break even.
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The number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.
The overall revenues and entire costs are equal at the break-even point (fixed and variable).
The production and sales units that will verify that Toby's Tiny Toys does not suffer a loss or make a profit are the break-even point.
$16.50 is the selling price per unit.
Variable costs amount to $12.50 per unit.
The contribution margin = $16.50 - $12.50 = $4 per unit equals
Fixed costs is $53,900.
Break-even point = Fixed costs / Contribution margin
Break-even point = $53,900/$4
Apply division operation to get
Break-even point = 13,475
Thus, the number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.
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PLS HELP!!!!!
31 POINTS
Lilly has a bag only containing blue beads and purple beads.
3/8 of the beads are blue.
If there are 9 blue beads in the bag, how many beads are purple?
Answer:
15 purple beads
Step-by-step explanation:
Calculate total beads
[tex]\frac{9}{\frac{3}{8} } =\frac{72}{3} =24[/tex]
Calculate how many beads are purple
[tex]24-9=15[/tex]
Hope this helps
There are total 15 purple beads.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
Fraction of blue beads = 3/8
Total blue beads = 9
let the total number of beads be x.
So, 3/8x = 9
x= 9. 8/3
x= 72/3
x= 24
So, number of purple beads = 24 -9= 15 beads
Hence, there total 15 purple beads.
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AThe formula for the circumference of a circle is C = 2tr. Find the circumference of acircle with a diameter of 4 ft.
Given the formula for the circumference of a circle:
C = 2πr
Let's find the circumference of a circle with a diameter of 4 ft.
Where r is the radius.
To find the radius, we have:
[tex]\text{radius}=\frac{\text{diameter}}{2}=\frac{4}{2}=2ft[/tex]The radius of the circle is 2 ft.
Take π = 3.14
Hence, to find the circumference of the circle, C, substitute 2 for r, 3.14 for π, and evaluate.
Thus, we have:
[tex]\begin{gathered} C=2\pi r \\ \\ C=2\ast3.14\ast2 \\ \\ C=12.56\text{ ft} \end{gathered}[/tex]Therefore, the circumference of the circle is 12.56 ft
ANSWER:
C. 12.56 ft
Simplify to a single power of 3:
3^{6}\cdot 3^{5}
3
6
⋅3
5 this isnt an abc choice you have to find the small number????
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
Given,
The exponents; 3^6 and 3^5.
We have to simplify this into a single power of 3.
In multiplication;
For exponents with same base, simply add the exponents.That is,
aᵇ . aⁿ = a^(b + n)
For exponents with different base, multiply the base and add the exponents.a^b . c^d = a x c ^ (b + d) = ac^bd
So,
3⁶ . 3⁵ = 3^(6 + 5) = 3¹¹
That is,
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
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Help me with this please
Answer:
first plot the positive 2 on the y axis
plot (0,2)
Then from (0,2) go up 2 and right 2.
Answer in attached image
Danny measured a house and its lot and made a scale drawing. The scale of the drawing was 1 inch : 5 feet. The houses driveway is 20 feet widein real life. How wide is the driveway in the drawing?
The width of the house driveway in the scale drawing is 4 inches.
What is scale drawing?Scale drawing is drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale).
Therefore, he measured a house and its lot and made a scale drawing.
The scale of the drawing was 1 inch : 5 feet.
The houses driveway is 20 feet wide in real life.
Therefore,
5 feet = 1 inch
20 feet = ?
cross multiply
Therefore,
width of the driveway on the scale drawing = 20 × 1 / 5
width of the driveway on the scale drawing = 20 / 5
width of the driveway on the scale drawing = 4 inches.
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ms. Torres has a box of scraps of wood. She measures the length of each scrap of wood to the nearest half inch results are represented on the line plot below.
The length of the scraps of wood when placed side by side is 53 inches.
What is the length of the scraps of wood?A line plot is a graph that is made up of a number line and check marks above the numbers on the number line. The check marks above the number line represents the frequency of the data. For example, there are two checkmarks above 7. This means that there are two scraps of woods that measure 7 inches.
In order to determine the approximate length of the scraps of wood if they are placed side by side, add the length of each scrap of wood together.
Addition is a mathematical operation that is used to determine the sum of two or more numbers. The sign that is used to denote addition is +.
[tex]5\frac{1}{2} + 6 + (6\frac{1}{2}. 3) + (7. 2) + 8[/tex] =
[tex]5\frac{1}{2} + 6 + 19\frac{1}{2} + 14 + 8[/tex] = 53 inches
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A committee of 3 members is selected from a club made up of junior members and senior members. What is the expected number of juniors in the committee?.
The expected number of juniors in the committee is 1.3
The question is incomplete, the complete question is given below:
A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the committee?
The expected number of juniors in the committee is computed here as:
Juniors in the committee=13
Seniors in the committee=17
Total number of members=(13+17)=30
Fraction of juniors in total members=13/30
So expected number of juniors in the committee:
=Fraction of juniors in total members*Total number of members to be selected
=(13/30)*3
=1.3
Therefore 1.30 is the expected number of juniors in the committee
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What is the slope of the line that passes through the points (-4, 2)(−4,2) and (-5, 0)(−5,0)? Write your answer in simplest form.
Answer: 2
Step-by-step explanation:
We will use the slope formula to find the slope of the line going through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{0-2}{-5--4} =\frac{-2}{-5+4} =\frac{-2}{-1} =2[/tex]
The slope of this line is 2.
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a rectangular plot of ground is 30 meters longer than it is wide. Its area is 20,000 square meters. which equation will help you find the detentions?
The equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0
How to find the dimensions of the plot of land?Let
L = length of rectangular plot of land, W = width of plot of rectangular plot landSince the rectangular plot of ground is 30 meters longer than it is wide, we have that
L = W + 30
Since the area of the rectangular plot is A = LW where
L = length of rectangular plot of land, W = width of plot of landSince A = 20,000 m², we have that
LW = 20,000
(W + 30)W = 20,000
W² + 30W = 20,000
W² + 30W - 20,000 = 0
Using the quadratic formula, we have that
[tex]W = \frac{-30 +/- \sqrt{30^{2} - 4 X (-20000)} }{2 X 1} \\W = \frac{-30 +/- \sqrt{900 + 80000} }{2} \\W = \frac{-30 +/- \sqrt{80900} }{2} \\W = \frac{-30 +/- 284.43}{2} \\W = \frac{-30 +/- 284.43}{2}\\W = \frac{-30 - 284.43}{2} or \frac{-30 + 284.43}{2}\\W = \frac{-314.43}{2} or \frac{254.43}{2}\\W = -157.22 or 127.23\\[/tex]
Since W cannot be negative, we have W = 127.23
Since L = W + 30
L = 127.23 + 30
L = 157.23
So, the dimensions are
Length = 157.23 mWidth = 127.23 mSo, the equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0
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Tammy’s take-home pay is $800 a month. She spends 7% on her take-home pay on her cell phone bill. How much is Tammy’s monthly cell phone bill?
Answer:744
Step-by-step explanation:
800-7%=744
Answer:
$56
Step-by-step explanation: