Answer:
3.45
Step-by-step explanation:
24.84/7.2 = 3.45
The unit rate is $3.45 per gallon
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Linda pays $24.84 for 7.2 gallons of gas.
Thus unit rate ( dollars per gallon) = $24.84/7.2
=$3.45 per gallon
Hence, The unit rate is $3.45 per gallon
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What if the vertices of the county were (-5,8), (8,8), (8,-6), and (-5,-6)? What would the perimeter of the county be?
Answer:
54 units
Step-by-step explanation:
We can graph the vertices given to make this easier to solve.
-> See attached.
-> This will help us in finding the lengths of the sides.
-> We can also use mathematics.
8 + 5 = 13 and 8 + 6 = 14
Next we will find the perimeter.
-> This can be found with either of these formulas:
[] P = 2L + 2W
[] P = W + W + L + L
P = 2L + 2W
P = 2(14) + 2(13)
P = 54
The perimeter of the county is 54 units
Substitution method
Y = 3x - 2
Y - 3x = 4
Answer:
[tex]\mathrm{No\:Solution}[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}Y=3x-2\\ Y-3x=4\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}Y=3x-2[/tex]
[tex]\begin{bmatrix}3x-2-3x=4\end{bmatrix}[/tex]
[tex]\mathrm\:{Combine\:like\:terms:[/tex]
[tex]\begin{bmatrix}-2=4\end{bmatrix}[/tex]
[tex]-2=4\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}[/tex]
[tex]\mathrm{No\:Solution}[/tex]
Sam has sheets of metal which are 36 cm by 36 cm square. He wants to cut out identical squares which are x cm by I cm from the corners of each sheet. He will then bend the sheets along the dashed lines to form an open container. a Show that the volume of the container is given by V(2) = x(36 – 2x)2 cm? . b What sized squares should be cut out to produce the container of greatest capacity? 36 cm 36 cm
Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity.
How to model and analyse an open boxa) The volume of the box ([tex]V[/tex]), in cubic centimeters, is equal to the area of the base ([tex]A[/tex]), in square centimeters, multiplied by the height of the box ([tex]h[/tex]), in centimeters. The area of the surface is the product of the width ([tex]w[/tex]) and length (l), both in centimeters:
[tex]V = w\cdot l\cdot h[/tex]
[tex]V = (36-2\cdot x)^{2}\cdot x[/tex] (1)
The volume of the container is [tex]V = (36-2\cdot x)\cdot x[/tex] cubic centimeters. [tex]\blacksquare[/tex]
b) We need to apply first derivative analysis and second derivative analysis to determine the dimensions of the maximum squares to be cut:
FDT[tex]-4\cdot (36-2\cdot x)\cdot x+(36-2\cdot x)^{2} = 0[/tex]
[tex]-4\cdot x + 36-2\cdot x = 0[/tex]
[tex]6\cdot x = 36[/tex]
[tex]x = 6[/tex]
SDT[tex]V'' (x) = -4\cdot [(-2)\cdot x+(36-2\cdot x)]-4\cdot (36-2\cdot x)\cdot x + (36-2\cdot x)^{2}[/tex]
[tex]V''(x) = 8\cdot x-4\cdot (36-2\cdot x)-4\cdot (36\cdot x-2\cdot x^{2})+(36-2\cdot x)^{2}[/tex]
[tex]V'' (6) = -48[/tex]
Since [tex]V''(6) < 0[/tex], the critical value of [tex]x[/tex] leads to a maximum.
Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity. [tex]\blacksquare[/tex]
To learn more on optimization, we kindly invite to check this verified question: https://brainly.com/question/5425085
#2 please help me ty if u o
Answer:
the answer is (B) I used an app to solve it
Answer:
The answer would be "B" because you have to cross multiply, which would give you: -3k = 180. Then, you have to divide 180 by -3, which would give you -60.
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
x = 15°
Step-by-step explanation:
Linear pair = 180°
⇒ (6x - 5) + (6x + 5) = 180°
⇒ 12x = 180°
⇒ x = 15°
Since line m is parallel to line n, (6x - 5) and (6x + 5) are a linear pair.
Linear pair means that the sum of two angles equaling 180°.
This means that:[tex](6x - 5) + (6x + 5) = 180[/tex]
Step-by step calculations:
Opening the parenthesis:
[tex](6x - 5) + (6x + 5) = 180 \\\\6x - 5 + 6x + 5 = 180[/tex]
Combining like terms:
[tex]6x - 5 + 6x + 5 = 180 \\\\ (6x + 6x) + (-5 + 5) = 180[/tex]
Simplify the LHS:
[tex](6x + 6x) + (-5 + 5) = 180\\\\(12x) = 180[/tex]
Divide 12 both sides and simplify:
[tex]\frac{12x}{12} = \frac{180}{12} \\\\ x = 15[/tex]
Thus, the value of x is 15.
What property can solve 2x-2+2=12+2
Answer:
7Step-by-step explanation:
2x-2+2=12+2
= 2x+0=14
= 2x=14
= X=14÷2
= X=7
Thank you ☺️☺️☺️☺️
Conner buys 4 balloons. Each balloon costs $2. Conner pays for the balloons with two $5 bills.How much change does Conner get back
Answer:
Conner should get 2 $ back
Step-by-step explanation:
conner should get 2$ back
Pls answer i will mark u brainlist
a) x(x+12) + 27
b) m(2n-3k) - 2p(3k + 2n)
500g to 2kg in fraction
Answer:
1∶ 4
explanation
how do you graph y=-4/3x+1
Answer:
Step-by-step explanation:
Answer:
Hope this helps any!
Step-by-step explanation:
100-475.50<1200 slove
Answer:
-375.5<1200
True
Step-by-step explanation:
100-475.5 = -375.5
Brainliest please!!
9y-2y+8=4y+38 answer
Answer: y = 10
Step-by-step explanation: Hi there!
To get started, first, we have to subtract 2y from 9y on the left side.
7y + 8 = 4y + 38
Then subtract 4y on both sides.
3y + 8 = 38
Then subtract 8 on both sides
3y = 30
Finally divide by 3 on both sides.
y = 10
The answer is y = 10.
Answer: y=10
Step-by-step explanation:
9y-2y+8=4y+38
[tex]\mathrm{Add\:similar\:elements:}\:9y-2y=7y[/tex]
7y+8=4y+38
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
7y+8-8=4y+38-8
[tex]\mathrm{Simplify}[/tex]
7y=4y+30
[tex]\mathrm{Subtract\:}4y\mathrm{\:from\:both\:sides}[/tex]
7y-4y=4y+30-4y
[tex]\mathrm{Simplify}[/tex]
3y=30
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3y}{3}=\frac{30}{3}[/tex]
Simplify
y=10
What is the standard deviation of the data set? 1, 4, 2, 2, 8, 7, 3 Round your answer to the nearest tenth.
Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.
How to calculate the standard deviation of a data set?Step 1: Find the mean
Step 2: Find each score’s deviation from the mean
Step 3: Square each deviation from the mean
Step 4: Find the sum of squares
Step 5: Apply the formula
[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}[/tex]
The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.
Step 1: Find the mean
The mean of the given data set can be written as,
[tex]Mean, \mu=\dfrac{1+4+2+2+8+7+3}{7} = 3.857[/tex]
Step 2: Find each score’s deviation from the mean
1 - 3.857 = -2.857
4 - 3.857 = 0.143
2 - 3.857= -1.857
2 - 3.857= -1.857
8 - 3.857 = 4.143
7 - 3.857 = 3.143
3 - 3.857 = -0.857
Step 3: Square each deviation from the mean
-2.857² = 8.162
0.143² = 0.02
-1.857² = 3.447
-1.857² = 3.447
4.143² = 17.165
3.143² = 9.877
-0.857²= 0.735
Step 4: Find the sum of squares
8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857
Step 5: Apply the formula
[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}\\\\SD = \sqrt{\dfrac{42.857}{7}} \\\\SD= 2.474[/tex]
Hence, the standard deviation of the data set is 2.474.
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HELPPOO PLEASE EASY POINTS !!
A figure is reflected over the y = x line and then rotated 90° clockwise about the origin.
Write the coordinate rule for the transformation.
Under this series of transformations, the point (-4,-1) maps to
Would it make a difference if the order of transformations were reversed?
Justify
not an answer but I’m working on the same worksheet and if u wanna work on it together than u should add my discord: kuispe#1715
What are the FACTORS in this equation:
3 x 4 = 12
Answer:
3 &4
Step-by-step explanation:
Factor is something that is being multiplied together.
Sarah hit the ball 3 times out of the 8 times. What is the experimental probability (as a percent) that she will hit the ball next? A 22.5% B 37.5% 45% 3% asap
Answer:
B
Step-by-step explanation:
3/8 is equal to 0.375, also known as 37.5%.
The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.
What do we mean by the experimental probability of an event?The experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.
How do we solve the given question?In the question, we are given that Sarah hit the ball 3 times out of the 8 times.
We are asked to find the experimental probability (as a percent) that she will hit the ball next.
As we know, the experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.
∴ The experimental probability = The number of times Sarah hit the ball/The number of times she experimented = 3/8
or, The experimental probability = (3/8)*100 % = (3*25)/2 % = 75/2 % = 37.5%.
∴ The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.
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1. A quadratic function fis defined by f(x) = (x - 7)(x + 3).
a. Without graphing, identify the x-intercepts of the graph of f. ( , ) and ( , )
b. If x=___, then (____- 7) = 0. If x = ____, then (____+ 3) = 0
c. Expand (x - 7)(x + 3) and use the expanded form to identify the y-intercept of the graph of f. Show work
Expanded form f (x) =_______
y-intercept ( , )
Answer:
a) (-3, 0) and (7, 0)
b) If x = 7 then (7 - 7) = 0
If x = -3 then (-3 + 3) = 0
c) f(x) = x² - 4x - 21
y-intercept (0, -21)
Step-by-step explanation:
a)
x-intercepts are when f(x) = 0
Therefore, if f(x) = (x - 7)(x + 3) then (x - 7)(x + 3) = 0
⇒ x - 7 = 0
⇒ x = 7
and
⇒ x + 3 = 0
⇒ x = -3
So x-intercepts are (-3, 0) and (7, 0)
b) If x = 7 then (7 - 7) = 0
If x = -3 then (-3 + 3) = 0
c) Expand f(x) = (x - 7)(x + 3)
⇒ f(x) = x² + 3x - 7x - 21
⇒ f(x) = x² - 4x - 21
The y-intercept is when x = 0 ⇒ (0, -21)
The diameter of a cylinder is 3 yd. The height is 8 yd. What is the volume of a cylinder ( put the answer in yd)
Answer:
18[tex]\pi[/tex] yd.³ or 56.54867 yd.³
Step-by-step explanation:
The volume of a cylinder can be written as: height × base, where the base of the cylinder is [tex]\pi[/tex]r².
Since the radius (r) is half the diameter, it should be 1.5 or 3/2 yd.
r = 1.5
So, the area of the base of the cylinder is 1.5²([tex]\pi[/tex]), which is equal to 2.25[tex]\pi[/tex].
Now multiply that by the height, 8 yd.
2.25[tex]\pi[/tex] × 8 = 18[tex]\pi[/tex]
The area of the cylinder is 18[tex]\pi[/tex] or 56.54867
Answer:
56.55 yd.³ OR 56.52 yd.³
Step-by-step explanation:
The formula for the volume of a cylinder is; V=πr^2h
To find the volume let's put in the values they gave us.
Now: V=π times 1.5^2 times 8
(If you don't know what pi or π is its the area of a unit circle. So the area of a circle with diameter 2 or radius 1)
Continuing the volume would be 3.141592.. * 2.25 * 8 ( '*' indicates multiplication) Now the answer after you multiply would be approx. 56.54867 which rounded would be 56.55
NOW if your teacher prefers to use 22/7 or 3.14 as pi then here is your answer:V=πr^2h so 3.14*2.25*8 which would be 56.52 yd.³ (if this is the way you need it ignore ANY other answers)
the first one will get the brianlist please help answer these two
Answer:
Hello bakugo here!
Step-by-step explanation:
I don't see anything, is there supposed to be anything here? if not
Thank you extra for FREE points! :D
Find slope and Y intercept of the line, and write the equation of the line, plzz helppp:(
Answer:
Slope = rise/run
= 1/4
Y-intercept = 0
Equation of the line:
y = 1/4x
What value of x is in the solution set of 2x - 3> 11 - 5x?
A. -3
B. 0
C. 2
D. 4
Answer:
The answer is D : 4.
Step-by-step explanation:
=2x-3>11-5x
=2x-3+5x>11
=7x-3>11
=7x>11+3
=7x>14
=7x/7>14/7
=x>2
By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.
I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.
Someone please help me on this I’m stuck
A store offers a loan for $900 to buy a computer. The terms of the loan
are for 9% simple interest and equal monthly payments for three years.
What is the monthly payment?
O $1143
O $700
o $31.75
o $92.50
Answer:
(c) $31.75
Step-by-step explanation:
First of all, you need to use some number sense to estimate an answer.
If the $900 loan had no interest, 1/3 of it would be paid off in each of the 3 years, or about $300 each year. You will be making 12 monthly payments each year, so the amount of principal being paid with each payment is $300/12 = $25. Any answer much above this amount will not make sense, so you can immediately reject all choices except $31.75.
__
The simple interest on the loan is ...
I = Prt = $900×0.09×3 = $243
That, too, is divided among the 36 payments, so adds ...
$243/36 = $6.75 to each of the $25 payments we calculated above.
The monthly payment is ...
$25 +6.75 = $31.75
What is the value of x?
102°
xº
O 51
O 102
O 12
O 78
Answer:
102(vertically opposite angle)
Point I is on line segment HJ. Given HJ = 15 and IJ
HI.
10, determine the length
Answer:
Point I is on line segment HJ; which means HI and IJ are equal.
HJ = 15
IJ = 10
Finding the length of HI, given the above statements:
Length of HI = 10 (reason: HI and IJ are congruent)
While in transit, the antitoxin had to stay between 36ºF and 46ºF. The dogsled teams stopped along the route often to warm the antitoxin by a fire to prevent it from freezing. A range of how many degrees Fahrenheit was ideal for the antitoxin?
Finding an angle measure given extended triangles
Check the picture below.
1/2 times -1/4 PLEASEEEEEE
Answer:-0.125 or 1/8
Step-by-step explanation: :)
Answer:
-1/8
Step-by-step explanation:
1/2 times -1/4 = -1/8
Please someone help me solve c no.
Answer:
Step-by-step explanation:
Find the value of x. Then , find the measure of each angle.
Answer:
I got you :)
Step-by-step explanation:
All angles of a triangle add up to 180 degrees so you can make the equation
3x-2+4x+9+3x-9=180 this equation will help you find x
I used the equation to find out that x=18.2 (i can explain this part further if you would like)
so now you know x=18.2 and all you have to do is plug in
m<H = 3 x 18.2 - 2 = 52.6
m<I = 4 x 18.2 + 9 = 81.8
M<J = 3 x 18.2 - 9 = 45.6
Hope this helps! :)
Also to check work you can do 52.6+81.8+45.6= 180 :) you know its right because it equals 180 degrees at the end
Alexis is drawing jolly ranchers from two bags the fist bag has 4 red 2 green and one blue the second bag has 4 red and 2 orange what is the probability that he would choose a purple jolly rancher from the first bag and a red jolly rancher from the second
Answer and explanation:
The two events of choosing jolly ranchers from each bag, first and second are independent events so the probability of first event AND second event will be multiplied
First bag has 4 red 2 green and one blue
Second bag has 4 red and 2 orange
what is the probability that he would choose a purple jolly rancher from the first bag and a red jolly rancher from the second
Probability = number of favourable outcomes /total number of favourable outcomes
The first bag does not have a purple jolly rancher and so probability is zero
the second bag's probability of choosing a red jolly rancher =4/6
probability of choosing a purple jolly rancher from first bag and red jolly rancher from second bag
=0*4/6=0
Answer=0