Answer:
Therefore both Ken and Billy ran the same amount of the training course.
Step-by-step explanation:
i) Billy was going to [tex]\frac{3}{4}[/tex] th of the training course.
ii) Ken was going to run [tex]\dfrac{1}{2}[/tex] of the training course.
iii) Billy finished [tex]\frac{1}{3}[/tex] of his run Therefore Billy finished only [tex]\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}[/tex] of the training course.
iv) Ken finished [tex]\dfrac{1}{2}[/tex] of his run Therefore Billy finished only [tex]\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex] of the training course.
v) Therefore both Ken and Billy ran the same amount of the training course.
The temperature has been going down at a constant rate.In 4 hours it went down 12 degrees.Which expression best shows the temperature change each hour? )
Answer:
t = t₀ - 3n
Step-by-step explanation:
Let t be the temperature and t₀ be the initial temperature of the day
Let n be the number of hours after the initial temperature ( t₀) was registered
Let -3 be the constant of change of temperature ( In 4 hours it went down 12 degrees)
Now, let's write down the expression that shows the temperature change each hour, this way:
t = t₀ - 3n
After 2 hours
t = t₀ - 3 * 2 = t₀ - 6
After 5 hours
t = t₀ - 3 * 5 = t₀ - 15
After 3 hours and 30 minutes
t = t₀ - 3 * 3.5 = t₀ - 10.5
it costs $50 plus $28 per month to join the gym.How much would it cost to join for 7 months?
Answer:
$546
Step-by-step explanation:
50 + 28 = 78 x 7 = 546
Which is the same function as -2x – 3 = y?
Answer: f(x)= -2x - 3
Step-by-step explanation
Simplify 8y + 4x - 2y + 5x
Answer:
6y+9x
Step-by-step explanation:
Combine like terms.
8y-2y=6y
4x+5x=9x
6y+9x
Answer:9x+6y
Step-by-step explanation:
8y +4y-2y+5x
=8y+4x+-2y+5x
(4x+5x)+(8y+-2y)
Yes I’m very aware of my dumbness but can someone please help with A and B plzzzzz
a wooden dowel has a diameter of 1.20 cm it floats in water with 0.400 cm its diameter above water determine the density of the dowel?
Final answer:
The density of the wooden dowel can be determined using the principle of buoyancy to calculate the volume of the submerged part and the total volume of the dowel which, when combined with the mass of the displaced water, provides the density of the dowel.
Explanation:
To determine the density of the wooden dowel based on its flotation characteristics, you can use the principle of buoyancy, which states that the buoyant force exerted on a submerged object equals the weight of the fluid displaced by that object. Since the dowel floats in water, the weight of the displaced water equals the weight of the dowel.
First, calculate the volume of the submerged part of the dowel: The dowel has a diameter of 1.20 cm, and the submerged height is the total diameter minus the portion above water, which is 1.20 cm - 0.400 cm = 0.800 cm. The volume (V) of the submerged cylinder is V = πr^2h, where r is the radius (half the diameter) and h is the submerged height. Plugging in values, V = π(0.6 cm)^2(0.8 cm).
Second, calculate the mass (m) of the dowel using the density (ρ) of water (1 g/cm^3) and the volume of water displaced which equals the volume of the submerged part of the dowel: m = ρ_water * V_submerged.
Finally, to find the density of the dowel, divide the mass of the dowel by the total volume of the dowel. The total volume is the same formula V = πr^2h, but with h being the full diameter of the dowel since it's cylindrical. The density of the dowel is ρ_dowel = m / V_total.
Using these steps, you can calculate the density of the dowel.
find the value of x and the measure of the exterior angle
The measure of the angle x is 70 degrees because the sum of the two interior angles is equal to the exterior angle.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
As we know,
The sum of the two interior angles is equal to the exterior angle.
15 + 35 = x
x = 70 degrees
Thus, the measure of the angle x is 70 degrees because the sum of the two interior angles is equal to the exterior angle.
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Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (4,-6) and perpendicular to the line whose equation is y=1/4x+4
Write an equation for the line in point-slope form.
The line passing through the point (4, -6) and perpendicular to the line y=1/4x+4 has an equation in point-slope form of y + 6 = -4(x - 4) and in slope-intercept form, it is y = -4x + 10.
Explanation:In Mathematics, lines that are perpendicular have slopes that are negative reciprocals of each other. This means if one line has a slope of m, the line perpendicular to it will have a slope of -1/m. The given line has a slope of 1/4, so the line perpendicular to it will have a slope of -4 (negative reciprocal of 1/4).
The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Thus, the equation of a line passing through the point (4, -6) with a slope of -4 can be expressed as y - (-6) = -4(x - 4), which simplifies to y + 6 = -4x + 16 or y = -4x + 10.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Therefore, based on our previous findings, the equation of the line in slope-intercept form is y = -4x + 10.
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R+2r=105 what is answer
Answer:
If you're trying to solve for r. r=35
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
r+2r=105
(r+2r)=105(Combine Like Terms)
3r=105
3r=105
Step 2: Divide both sides by 3.
3r/3 = 105/3
r=35
factor 9f²-12f plus 4
Good morning ☕️
Answer:
9f² - 12f + 4 = (3f - 2)²Step-by-step explanation:
9f²-12f+4 = (3f)²-2×(3f)×(2)+2² = (3f-2)²
:)
In the piece-wise function graphed below, which is the correct equation for when − 2 ≤ x ≤ 2
y=-2x+2
y=-1/2x+2
y=-2x+4
y=-1/2x+4
Answer:
[tex]y=-\frac{1}{2}x+2[/tex]
Step-by-step explanation:
Looking at the graph
For x=-2 ---> f(x)=3
For x=2 ---> f(x)=1
so
we have the points
(-2,3) and (2,1)
Find the slope
[tex]m=(1-3)/(2+2)=-\frac{1}{2}[/tex]
The equation of the line in slope-intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{1}{2}[/tex]
[tex]b=2[/tex] ---> see the graph
substitute
[tex]y=-\frac{1}{2}x+2[/tex]
How much will a person pay for 1.1 pounds of bananas at a price of $1.86 per pound?
Answer:
$2.046
Step-by-step explanation: I think..don't take my word.
Daniel spent $40 on eating utensils. Spoons cost $5 and forks cost $6. If he bought a total of 7, then how many of each kind did he buy?
Daniel bought 2 spoons and 5 forks.
Step-by-step explanation:
Given,
Amount spent on utensils = $40
Cost of each spoon = $5
Cost of each fork = $6
Total items bought = 7
Let,
x be the number of spoons bought
y be the number of forks bought
x+y=7 Eqn 1
5x+6y=40 Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=7)\\5x+5y=35\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+6y)-(5x+5y)=40-35\\5x+6y-5x-5y=5\\y=5[/tex]
Putting y=5 in Eqn 1
[tex]x+5=7\\x=7-5\\x=2[/tex]
Daniel bought 2 spoons and 5 forks.
Keywords: linear equation, elimination method
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Daniel bought 2 spoons and 5 forks by using a system of equations and solving for the number of each utensil.
Explanation:The question involves determining how many spoons and forks Daniel bought given that spoons cost $5, forks cost $6, he bought a total of 7 utensils, and spent $40. To solve this, we can use a system of equations where s represents the number of spoons and f represents the number of forks.
The first equation represents the total number of utensils bought:
s + f = 7
The second equation represents the total amount spent:
5s + 6f = 40
To find the values of s and f, we can solve the system of equations. Subtracting the first equation from the second equation (multiplied by 5) gives:
5s + 6f = 40
-(5s + 5f = 35)
------------------
f = 5
Substituting f = 5 into s + f = 7, we get s = 2. Hence, Daniel bought 2 spoons and 5 forks.
During a phone call, Beyunka was told of the most recent transactions in her company's business account. There were deposits of $1, 250 and $3,040.57, three withdrawals of $400 each, and the bank removed two separate $35 penalties to the account that resulted from the bank's errors. Based on the information, how much did the balance of the account change?
Answer:
The amount of change in the balance of the account is an increase of $3160.57.
Step-by-step explanation:
i) first deposit is given as $1250
ii) second deposit is given as $3040.57
iii) first withdrawal is given as $400
iv) second withdrawal is given as $400
v) third withdrawal is given as $400
vi) first penalty removed is $35
vii) second penalty removed is $35
viii) therefore the change to the balance is given by
$1250 + $3040.57 - $400 - $400 - $400 + $35 + $35 = $3160.57
viii) Therefore the amount of change in the balance of the account is an increase of $3160.57.
For what value of x do expressions 2x+3 and 3x-6 have the same value?
Answer:
x = 9
Step-by-step explanation:
To find the value of x to make the 2 expressions equal, then equate them, that is
3x - 6 = 2x + 3 ( subtract 2x from both sides )
x - 6 = 3 ( add 6 to both sides )
x = 9
Then
3x - 6 = 3(9) - 6 = 27 - 6 = 21 and 2x + 3 = 2(9) + 3 = 18 + 3 = 21
A vehicle is moving at a constant speed travels 45 miles in 3/4 hour. The driver thinks he will be late to a meeting that is still 65 miles away and that starts in 1.25 hours. Assume he maintains a constant speed. Find the drivers unit rate of speed and explain whether he was late or not
The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed
Step-by-step explanation:
Given
Distance = d = 45 miles
Time = t = 3/4 hour
The unit rate is defined as the distance per unit time. In this case, the unit rate can also be called speed.
So,
[tex]s = \frac{d}{t}\\s = \frac{45}{\frac{3}{4}}\\s = 45 * \frac{4}{3}\\s = 60\ miles\ per\ hour[/tex]
Using this unit rate we can see if the car can travel 65 miles in 1.25 hours or not
Given
Distance = d1 = 65 miles
Speed = s = 60 miles per hour
Putting the values in the formula for speed
[tex]s = \frac{d_1}{t_1}\\60 = \frac{65}{t_1}\\t_1 = \frac{65}{60}\\t_1 = 1.08\ hours[/tex]
As we can see that 1.08 is less than 1.25 so the driver will reach the meeting before time if he drives on a constant speed of 60 miles per hour
Hence,
The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed
Keywords: Speed, unit rate
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Jada swan 200 meters more than Molly. Jada swam a total of 800 meters. How many meters did Molly swim?
Answer:
600
Step-by-step explanation:
To make the chocolate shake, Dona added 40 mL of chocolate syrup,
200 mL of milk, and 400 mL of water. How much milk, in liters, would be
required if she uses 450 mL of water?
Answer:
0.225 L of milk, would be required if she uses 450 m L of water.
Step-by-step explanation:
Here, to make the shake, ingredients used by Dina are:
40 m L of chocolate syrup,
200 m L of milk, and 400 m L of water.
So, here Amount of water used = 2 x ( Amount of Milk used) ....... (1)
Now,again the amount of water used by Dona = 450 m L
Let us assume the milk used by her = k m L
⇒ 450 m L = 2 x ( k m L) ( from (1))
or, 450 = 2 k
⇒ k = 450/2 = 225
⇒ k = 225 m L
Also, 1 m L = 0.001 L
So, 225 m L = 225 x 0.001 = 0.225 L
⇒ k = 0.225 L
Hence, 0.225 L of milk, would be required if she uses 450 m L of water.
Dona would need 0.225 liters of milk when using 450 mL of water for her chocolate shake.
To find out how much milk would be required if 450 mL of water is used, we should first look at the ratio of water to milk in the original recipe. Dona used 400 mL of water for 200 mL of milk, which is a 2:1 ratio of water to milk. If she uses 450 mL of water, maintaining the same ratio, we would calculate the amount of milk required as follows:
Determine the proportion of milk to water used originally: 200 mL milk / 400 mL water = 1/2.
Using the proportion, calculate the new amount of milk for 450 mL water: (1/2) * 450 mL = 225 mL.
Convert the milk from milliliters to liters: To do this, we know that 1 liter is equivalent to 1,000 milliliters. Therefore, we divide 225 mL by 1,000 to convert to liters.
225 mL / 1,000 = 0.225 liters of milk is needed.
Let f(x)=8x+8 find and simply f(x+1)
Answer:
Step-by-step explanation:
f(x) = 8x + 8
f(x+1) = 8(x+1) + 8
= 8x + 8 + 8
= 8x + 16
Answer:
f(x+1) = 8x + 16
Step-by-step explanation:
f(x+1) = 8(x + 1) + 8 = 8x + 8 + 8 = 8x + 16
the temperature rises 15 degrees Fahrenheit (°F) and then drops by 8°F. If the
temperature started at -11°F, what temperature change would be required to bring
the temperature to 0°F?
Answer:
=4
Step-by-step explanation:
-11+15=4
4-8=-4
-4+4=0
Answer:
decrease of 4F since it started at 8 <3
Step-by-step explanation:
please say thanks !
What does (4x-y) + (-10 + y) equal if x=3 and y=4
Answer:
2
Step-by-step explanation:
plug it in
(4*3-4)+(-10+4)
8+(-6) = 2
Answer: (4x-y) + (-10 + y) = 2 , if x=3 and y=4
Step-by-step explanation:
We can substitute the known values for x and y
(4(3) - 4) + (-10 + 4) = 12 - 4 -10 +4 = 2
Spymore
if x^2=40 what is the value of x?
Answer: +-6.32
Step-by-step explanation:
x = +- √40
x = +-6.324
Note that +- means plus or minus.
Summarize the different ways someone could earn money by owning a share of Exxon.
There are different ways through which you can earn money through a share, either from Exxon or from any other company. These are:
-Through obtaining profits by collecting dividends, which are sums of money that each company pays to shareholders as a way to distribute profits.
-Through the maintenance of the share in the investment portfolio, when it rises in value, it will also cause the shareholder's wealth to rise.
-Through the short investment, seeking to earn money through the "bet" for the fall in the value of the share.
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Which two operations are needed to write the expression that represents “five less than the quotient of a number and three”?
Answer:
'<' (lessthan symbol) and '/' (division symbol) are the two operations needed here to represent the given expression
In the expression [tex]5<(\frac{x}{3})[/tex] we are using the '<' (lessthan symbol) and '/' (division symbol)
The expression that represents “five less than the quotient of a number and three” is [tex]5<(\frac{x}{3})[/tex]
Step-by-step explanation:
Given that “five less than the quotient of a number and three”
To find the two operations that are needed to write the given expression :
Let x be the number
“five less than the quotient of a number and three”
can be written as below
[tex]5<(\frac{x}{3})[/tex]
Therefore “five less than the quotient of a number and three”=[tex]5<(\frac{x}{3})[/tex]
The expression that represents “five less than the quotient of a number and three” is [tex]5<(\frac{x}{3})[/tex]
In the expression [tex]5<(\frac{x}{3})[/tex] we are using the '<' (lessthan symbol) and '/' (division symbol)
'<' (lessthan symbol) and '/' (division symbol) are the two operations needed here to represent the given expression
Answer:
Step-by-step explanation:
division and subtraction
What is 27 divided by 1,581
Answer:
0.01707779886
Step-by-step explanation:
Just do 27/1581
Using the graph, determine the value of the slope.
What is the slope?
Based on the calculations below, the slope of this graph is equal to 2/3.
In Mathematics and Euclidean Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the given data points (0, -2), and (3, 0) into the formula for the slope of a line, we have the following;
Slope of graph = (0 - (-2))/(3 - 0)
Slope of graph = (0 + 2)/(3 - 0)
Slope of graph = 2/3
Based on the graph, the slope is the change in y-axis with respect to the x-axis, and it is equal to 2/3.
Complete Question;
Using the graph, determine the value of the slope.
What is the slope?
solution to the inequality 16x−33x<37x+27.
The solution to the inequality is:
[tex]x>\frac{-1}{2}[/tex]
Solution:
Given inequality is:
[tex]16x-33x<37x+27[/tex]
We have to find the solution to given inequality
[tex]\mathrm{Add\:similar\:elements:}\:16x-33x=-17x[/tex]
[tex]-17x<37x+27[/tex]
[tex]\mathrm{Subtract\:}37x\mathrm{\:from\:both\:sides}[/tex]
[tex]-17x-37x<37x+27-37x[/tex]
Simplify the above inequality
[tex]-54x<27[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
Remember that, change the inequality sign if you divide or multiply both sides by a negative number
If you divide or multiply both sides by a positive number,the inequality sign will not change
[tex]\left(-54x\right)\left(-1\right)>27\left(-1\right)\\\\54x>-27[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}54[/tex]
[tex]\frac{54x}{54}>\frac{-27}{54}\\\\x>-\frac{1}{2}[/tex]
Thus the solution to inequality is found
Jason signed up to receive Internet service for $13 per month, plus a $30 start-up
fee. If
he has $134, how many months of internet can he receive?
Answer:
With $134 he can receive 8 moths of internet. Hope this helps
What is 4.5 divided by .25
Good morning,
Answer:
4.5/25 = 0.18
Step-by-step explanation:
4.5/25 = (4.5×4)/(25×4) = 18/100 = 0.18.
:)
The answer to the division question 'What is 4.5 divided by 0.25' is 18, because a whole (1) can be expressed as 4 parts in 0.25 decimal representation, and when multiplied by 4.5 it gives 18 parts.
Explanation:The student has asked: 'What is 4.5 divided by .25'. This is a division question within the subject of Mathematics.
To solve this, you will need to divide 4.5 by 0.25. If we perform this division, we get 18. Therefore, 4.5 divided by 0.25 equals 18.
This is because if take a whole (which is 1 in decimal and represents 4 parts in 0.25 decimal representation), and we multiply it by 4.5, we get 18 parts of 0.25.
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In Aaron's class 4/5 of the students brought a pencil to class . If 6 people did not have pencils how many students are in Aaron's class
24 students in arons class