The total weight of the bag that the salesman is carrying for selling a machine including some personal stuff is 13.9 Kg.
What is a fraction?A fraction is a rational number that consists of a numerator and a denominator, used to represent a part of the whole thing.
Calculation:It is given that,
A salesman is carrying a big bag for selling a machine.
Consider the weight of the machine = w
So,
The weight of his machine is three kilograms and half a machine. I.e.,
w = 3kg +w/2
⇒ w/2 = 3kg
∴ w = 6kg
Thus, the weight of the machine is 6 Kg.
So, the weight of the repair tool for the machine = a half kilogram and one-fourth of the machine
⇒ 1/2Kg + 1/4w
⇒ 1/2 + 6/4
⇒ 2 Kg
The personal stuff weighs - four kilograms minus a fourth of the weight of the machine.
⇒ 4Kg - w/4
⇒ 4 - 6/4
⇒ 2.5 Kg
He has some supplies that weigh two-fifth of the machine and personal stuff combined.
⇒ 2/5(w + 2.5)
⇒ 2/5 × 8.5
⇒ 3.4 Kg
Thus, the total weight of the bag = 6 Kg + 2 Kg + 2.5 Kg + 3.4Kg = 13.9Kg.
Therefore, the total weight of the salesman's bag is 13.9 Kg.
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Complete the following conversions. i) 1 m2 = a cm2 ii) 1 cm2 = b mm2 iii) 1 km2 = c m2
The values that complete the conversions are
a = 10000
b = 100
c = 1000000
Conversion of unitsFrom the question, we are to complete the given conversions
i)
1 m² = a cm²
NOTE: 1 m² = 10000 cm²
∴ a = 10000
ii)
1 cm² = b mm²
NOTE: 1 cm² = 100 mm²
∴ b = 100
iii)
1 km² = c m²
NOTE: 1 km² = 1000000 m²
∴ c = 1000000
Hence, the values that complete the conversions are
a = 10000
b = 100
c = 1000000
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If Triangle DEF is congruent to Triangle ABC and AB=4.4 units, what is the length of DE?
2.2 units
6.6 units
8.8 units
4.4 units
Answer:
8.8
Step-by-step explanation:
If DEF///ABC
AB=4.4
Lizette wanted to see if it would be possible to use a little less materials in a tea infuser but still not be required to be at full capacity. Her rectangular pyramidal tea infuser would be 7 cm high, 3 cm long and 1.5 cm wide. The tea infuser from the example, was the same except 7.9 cm high and was filled to 80% capacity.
Would these dimensions work, if so to what percent would Lizette's infusers have to be filled to use the same amount of tea?
Considering the volume of a rectangular prism, since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.
What is the volume of a rectangular prism?
The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
The original dimensions are:
h = 7.9 cm, l = 3 cm, w = 1.5.
Hence the volume in cm³ was:
V = 7.9 x 3 x 1.5 = 35.55 cm³.
The infuser was filled to 80% capacity, hence:
Vf = 0.8 x 35.55 = 28.44 cm³.
For the new dimensions, we have that h = 7 cm, hence the volume is:
Vn = 7 x 3 x 1.5 = 31.5 cm³.
28.44/31.5 x 100% = 90.29%.
Since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.
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x is directly proportional to w²
When w = 4, x = 48
y is inversely proportional to x³
When x = 2, y = 14
Find a formula for y in terms of w.
Give your answer in its simplest form.
The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³
Variationx = k × w²
w = 4, x = 48
48 = k × 4²
48 = k × 16
48 = 16k
k = 48/16
k = 3
So,
x = k × w²
x = 3 × w²
x = 3w²
y = k/x³
x = 2, y = 14
14 = k / 2³
14 × 2³ = k
14 × 8 = k
112 = k
So,
y = k/x³
y = 112/x³
y = (1/112)x³
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Anya was rowing up the river and noticed it takes longer to row upstream than downstream. She knows that in still water she can row 9 mph. She timed herself rowing approximately 4 miles upstream and then back in 1.5 hours. She then calculated the current of the river.
If the speed of boat in still water iss 9 mph and takes 1.5 miles to go and come 4 miles uptream and downward then the current of the river is 9.24 mph.
Given that the speed in still water be 9 mph, time to travel 4 miles upstream and downward is 1.5 hours.
We are required to find the speed of current of the river.
let the speed of current be c mph.
Effective speed in downstream=9+c
Effective speed in upstream=9-c
Total time=1.5 hours.
Total distance=4 miles.
Time for upstream stream+ time for downward stream=1.5 hours
2/(9+c)+2/(9-c)=1.5
18-2c+18+2c=1.5(9+c)(9-c)
36=1.5(81-[tex]c^{2}[/tex])
36=121.5-1.5[tex]c^{2}[/tex]
1.5[tex]c^{2}[/tex]=121.5-36
[tex]c^{2}[/tex]=85.5
c=9.24 mph.
Hence the speed of the current of the river is 9.24 mph.
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In an algebra class, there are 10 less than twice as many boys as girls. If the total number of students is 38, how many boys and girls are there in class?
Answer: 16 girls and 22 boys
Step-by-step explanation:
This can be solved with simple algebra.
Let's say that the number of girls is x.
Since there are 10 less than twice as many boys as girls, the number of boys would be 2x-10. (2x for twice as many, and -10 for ten less.)
The total number of students is 38. Adding the girls, the equation is now 3x-10=38.
3x=48
x=16.
2x-10=the number of boys, as said earlier. SO, 32-10=22=the number of boys.
To check our work, add 16+22. This equals 38.
Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?
The amount invested in the account that has a rate of 14% is $1767
The amount invested in the account that has a rate of 6% is $1425.
What are the linear equations that represent the question0.06a + 0.14b = 342 equation 1
b - a = $950 equation 2
Where:
a = amount invested in the account that has a rate of 6%
b = = amount invested in the account that has a rate of 14%
How much was invested in each account?Multiply equation 2 by 0.06
0.06b - 0.06a = 57 equation 3
Subtract equation 3 from equation 2
285 = 0.2a
a = 285 / 0.2
a = 1425
Substitute for a in equation 2
b - 1425 = 342
b = 1425 + 342
b = $1767
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Gloria says the two expressions 1/4 (12x + 24) -9x and -6(x + 1) are equivalent. is she correct? Explain how you know
Answer:
No
Step-by-step explanation:
Lets simplify both expressions:
We will start with Gloria's first expression:
[tex]1/4 (12x + 24) -9x[/tex]
Apply distributive property:
[tex](3x + 6) -9x[/tex]
Combine like terms, we are then left with:
[tex]6-6x[/tex]
Now lets simplify the second expression
[tex]-6(x+1)[/tex]
Apply distributive property
[tex]-6x-6[/tex]
Rearrange:
[tex]-6-6x[/tex]
Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.
the half life of an element in the periodic table measured over a period of time, t, is modeled by the function f(t)=16(1/2)^t. what is the initial amount of the element
The initial amount of the element is 16
How to determine the initial amount?The function is given as:
f(t) = 16(1/2)^t
Set t = 0, to determine the initial amount
f(0) = 16(1/2)^0
This gives
f(0) = 16 * 1
Evaluate
f(0) = 16
Hence, the initial amount of the element is 16
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Type the correct answer in the box. Use numerals instead of words.
What is the length of the diagonal shown in the rectangular prism? Round your answer to the nearest tenth.
7 ft
ft
4 ft
5 ft
The length of diagonal is 9.5 ft
What is Pythagoras theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
We will find the length of diagonal as shown below:
l= 7 ft
h= 5 ft
w= 4 ft
Let diagonal be d.
Let v be the diagonal of the base.
Using Pythagoras theorem
[tex]v=\sqrt{7^2+4^2}[/tex]
[tex]=\sqrt{49+16}[/tex]
[tex]v=\sqrt{65}[/tex]
For finding the value of d again using Pythagoras theorem
[tex]d=\sqrt{v^2+h^2}[/tex]
[tex]=\sqrt{(\sqrt{65})^2+5^2 }[/tex]
[tex]=\sqrt{65+25}[/tex]
[tex]=\sqrt{90}[/tex]
=9.4868
Rounding to nearest tenth
=9.5
Hence, the length of diagonal is 9.5 ft
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1. when y=7 , what is the value of x?
2. what is the y-intercept of the graph?
1) Correct.
2) The y-intercept is when x=0, so it is (0,5).
Which of the following is equal to the fraction below?
(5/9)^8
A. 8(5/9)
B. 5^8/9
C. 5/9^8
D. 5^8/9^8
Answer:
D. [tex]\displaystyle{\dfrac{5^8}{9^8}}[/tex]
Step-by-step explanation:
The law of exponent defines that:
[tex]\displaystyle{\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}}[/tex]
In word, you simplify the expression by expanding an exponent to both numerator and denominator.
So from the expression [tex]\displaystyle{\left(\dfrac{5}{9}\right)^8}[/tex], you expand the exponent 8 in both numerator and denominator then you'll end up with D choice!
If you have any questions then please let me know in comment!
What is the volume of this rectangular prism?
3/2cm
1/2
4 cm
Answer:
7.62
Step-by-step explanation:
length* width* height = 3/2*1/2*4=7.62 cm
After working 80 hours at his job, Tyshawn earned a total of $1080. How much does Tyshawn earn
per hour?
The amount Tyshawn earn per hour is $13.5
Ratio and proportionFractions are written as a ratio of two integers
If after working 80 hours at his job, Tyshawn earned a total of $1080, then;
80 hrs = $1080
In order to calculate the amount earned per hour
Amount per hour = 1080/80
Amount per hour = $13.5
Hence the amount Tyshawn earn per hour is $13.5
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Freddie has 2 times as many comic books as David. The ratio of the number of comic books David has to the number of comic books Gary has is 5 : 3. Freddie has 110 comic books. How many comic books do David and Gary have in total?
Answer:
88
Step-by-step explanation: make me brainliest if it is correct
Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
Solving an inequality, we will see that there is less than $280 in the pile of money.
How much money is originally in the pile?Let's say that the amount of money is defined by the variable.
First, we know that Jeri keeps $80, so now in the pile we have:
M - $80.
Now she gives one third of that, then the leftover is:
(2/3)*(M - $80) + $80
We know that this is more than:
M - $200
Then we have the inequality:
(2/3)*(M - $80) + $80 > M - $200
And we can solve this for M.
(2/3)*M - (2/3)*$80 + $80 > M - $200
(1/3)*$80 + $200 > M - (2/3)*M
(1/3)*$80 + (1/3)*$200 > (1/3)*M
$280 > M
Then we conclude that there is less than $280 in the pile of money.
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Select the correct answer.
Which expression and quotient does the diagram model?
The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.
Which expression and quotient is depicted by the diagram model as in the task content?It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).
Additionally, the dividend in the quotient by observation is the sum of terms as follows;
x² + x +x -x -1 -1 = x²+x -2.
Ultimately, the result of the division according to the model is; (x +2).
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i need help!!!!!!!!!!!!!! how many pound are in 40 ounces. this is off or i ready. please help me!!!
Answer:
2.5 pounds
Step-by-step explanation:
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
Answer:
C. Best models this relationship
Step-by-step explanation:
Answer:
C: y=1/3x
Step-by-step explanation:
I'll set up an equation for this.
When x = 6, y needs to be 2.
--> 2 = 6 times ___
since 6 times 1/3 is 2, ___ is 1/3.
Now we know that 1/3 is the slope. In a complete equation, this will be shown as y = 1/3 x.
This can be proven by reinserting the value of x and y.
2 = 1/3 (6)
Since this equation works, we can be sure that C: y=1/3 x is correct.
Find the term that must be added to the equation x2−6x=7 to make it into a perfect square.
answer:
+16
steps:
number without the x should be 9
number without the x should be 9c to be 9 needs +16
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divide the number next to the x by 2
-6 divided by 2 is -3
find the square
-3 squared is 9
number without the x should be 9
x²-6x=7
make the equation = 0
x²-6x-7=0
a is the number next x²
b is the number next to x
c is the number without the x
c has to be 9
c is -7
c to be 9 needs +16
x²-6x+9 =0
x²-6x+(-3)² =0
(x-3)²
Answer:
9
Step-by-step explanation:
Completing the square is a method used to solve the quadratic equation.
Divide the co efficient of 'x' by 2.Coefficient of x is '6'. 6 ÷ 2 = 3
Square the quotient of (x ÷ 2) and add to the both side of the equation.3² = 9
x² - 6x + 9 = 7 + 9
Answer: To make into a perfect square, 9 must be added.
A right cylinder and an oblique cylinder have the same radius and the same height. How do the volumes of the two
cylinders compare?
A. The volumes are the same, based on Cavalieri's principle.
B. The volumes are not the same, because Cavalieri's principle does not apply to oblique solids.
C. The volumes are not the same, because the two solids do not have the same cross-sectional
area at every level parallel to the bases.
D. The volumes are not the same, because an oblique solid has less volume thanits corresponding
right solid with the same height.
Answer:
A. The volumes are the same, based on Cavalieri's principle.
Step-by-step explanation:
Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.
ApplicationA right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.
Find the area of the figure
Answer:
100
Step-by-step explanation:
Lets first find the area of the greater square:
[tex]8*14=112[/tex]
And now the area of the cut inside of the square:
[tex]3*4=12[/tex]
Now subtract the area cut from the area of the greater square:
[tex]112-12=100[/tex]
The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.
The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.
Definition for Period of a Trigonometric Function :
The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.
If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.
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Select the correct answer. Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -62 -30 -14 -6 -2 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-2, 1]? A. Only function f is increasing, and only function f is negative. B. Only function f is increasing, and both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Both functions are increasing, but function f increases at a faster average rate.
based on the given exponential functions, we can tell that C. Both functions are increasing, but function g increases at a faster average rate.
what function is increasing faster?function g is represented by the model:
g(x) = -18 x (1/3)^x + 2
g(x)=-18(1/3)^x In(1/3)
In1/3 < 0
this means that:
g (x) > 0
for any interval, g(x) > f(x)
this means that g is increasing at a faster rate than f which is increasing as shown by the table given in the question.
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The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
Given the graph of w(x), w(2) = ?
(the graph is below)
Based on the graph of the cupcakes done, we find that w(2) = 5.
How many cupcakes are made by the cooker?
Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.
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Next, you will make a scatterplot. Name a point that will be on your scatterplot and describe what it represents.
The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius
How to make a scatter plot?To do this, we make use of the following points
(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)
Where x represents the number of hours and y represents temperature
See attachment for the scatter plot.
The description of a pointTo do this, we make use of the point (12, 190)
This means that the temperature after 12 hours is 190 degrees Celsius
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Zoe keeps track of the miles per gallon her car gets per week. she has accumulated the following data: (1,24), (2,24,38), (3,24,76) (4,25,14) what is the common difference or ratio?
The common difference is (1,0.38).
An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In this type of progression, there is a possibility to derive a formula for the nth term of the AP. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term.
x1 = 1 , y1 = 24
x2 = 2, y2 = 24.38
x3 = 3 , y3 = 24.76
x4 = 4 , y4 = 25.14
Thus the common difference equals :-
x2 - x1 = x3 - x2 = x4 - x3 = 1
y2 - y1 = y3 - y2 = y4 - y3 = 0.38.
Thus the common difference is (1,0.38).
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Jack's cow is tied to a
beanstalk with a piece
of rope that is 15 ft long.
What is the area of the
circle in which the cow can graze
Answer:
706.86ft² or 225π ft²
Step-by-Step Explanation:
r = 15ft
Now solve the area of the circle! :)
A=πr²
A=π15²
A=225π ft²
or to simplify further!
A=706.86ft²
You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area
The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.
Dimensions to Minimize the Surface Area of the Box
It is given that the box is square based with an open top.
⇒ The box has one square and 4 rectangles
Thus, the total surface area of the box is given as,
S= a²+ab+ab+ab+ab
S= a²+4ab ______________ (1)
Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.
This equation is later used for minimization of the surface area.
Also, the volume, V = a²b
It is also given that volume of the box is 184 in³.
⇒ 184 = a²b _____________ (2)
Forming a One-Variable Equation
From equation (2), b=184/a²
Now, substitute this value of b in equation (1) to get,
S = a² + 4a(184/a²)
S = a² + 4(184/a)
S = a² + 736/a
Minimization of Surface Area to find the Dimension
We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0
dS/da = 2a -736/a²
0 = 2a -736/a²
⇒ 0 = 2a³- 736
2a³ = 736
a³ = 736/2
a³ = 368
a = ∛368
a= 7.17 in
∵V = a²b
184 = (7.17)²b
b = 184/7.17²
b = 184/51.4089
b = 3.58 in
Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..
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A spiral tile has a width of 1/4 foot how many tiles will fit end to end on a 4 foot wall
16 tiles will fit end to end on a 4 foot wall.
In unitary method we will learn how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
When we go to the market to buy any article, we ask the shopkeeper to tell the price of the article. This is called unit price. We calculate the price of number of articles, we want to buy, with the help of this unit price. Sometimes, we calculate unit price when the price of a multiple is given.
1 tile in 1/4 foot
So in 4 foot wall the number of tiles = 4/(1/4) = 16 tiles.
Thus 16 tiles will fit end to end on a 4 foot wall.
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