Answer:$ 2.25 per km
Ste) = p-by-step explanation:
32 / (14 2/9
32 / (128/9) =
32 * 9 / 128 =
288 / 128 =
$ 2.25 per km
4. A horse is tethered to one corner of a square plot of side 42 m, by a rope 35 m long. Find i) what area it can graze ii) what area will be left ungrazed.
Answers:
i) It can graze an area of approximately 961.625 square meters
ii) The ungrazed area is roughly 802.375 square meters
note: I used pi = 3.14 which is approximate; if you want more accuracy, use more decimal digits in pi
===============================================
Explanation:
Check out the attached image below for a visual diagram.
The area of a circle is the formula
A = pi*r^2
Use r = 35 as the radius and pi = 3.14 as the approximation for pi, to get,
A = pi*r^2
A = 3.14*35^2
A = 3846.5
Then divide this by 4 to get the area of a quarter circle
A/4 = 3846.5/4 = 961.625
This is the approximate area the horse can graze
------------
Subtract this from 42^2 = 42*42 = 1764 because this is the area of the entire square. Doing this will get you the ungrazed area
Ungrazed area = (entire plot) - (grazed area)
Ungrazed area = (entire area of square) - (area of quarter circle)
Ungrazed area = 1764 - 961.625
Ungrazed area = 802.375
The ratio of boys to girls in Anaya’s class is 10 to 15. There are 20 boys how many girls are there
Answer:
30 girls
Step-by-step explanation:
10 x 2= 20
15x2=30
For every 10 boys there are 15 girls. since 20 is just 10 multiplied by 2 you can multiply 15 by 2
Pizza is cut into six equal pieces each slice is then cut in half to create two smaller equal pieces. what fraction of the total pizza does one of the small pieces represent??
Answer:
1/12
Step-by-step explanation:
6 x 2 = 12
6 = the original amount of slices
2 = it was cut in half so multiply by 2
each slice now represents 1/12
Answer:
Each slice represents 1/12th of the total pizza.
Step-by-step explanation:
1 = 1/6 = 1/12
Naomi and Sofia go to the movie theater and purchase refreshments for their friends. Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn. Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer: popcorn = $5.75 per bag
Step-by-step explanation:
Set up the equation for each person.
Let x represent the cost of one drink and y represent the cost of one bag of popcorn.
drinks popcorn Cost EQUATION
Naomi: 9 8 $111.25 9x + 8y = 111.25
Sofia: 3 2 $33.25 3x + 2y = 33.25
Next, solve the system:
9x + 8y = 111.25 → 1(9x + 8y = 111.25) → 9x + 8y = 111.25
3x + 2y = 33.25 → -3(3x + 2y = 33.25) → -9x - 6y = -99.75
2y = 11.50
y = 5.75
Answer:
System of equations :
$111.25=$9x+$8y
$33.25=$3x+$2y
The cost of 1 drink = $x = $7.25
The cost of 1 popcorn bag = $y = $5.75
Step-by-step explanation:
Given :
Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.
Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.
To Find : A system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Solution :
Let cost of 1 drink = $x
⇒ cost of 9 drinks = $9x
⇒ cost of 3 drinks = $3x
Let cost of 1 popcorn bag = $y
⇒Cost of 8 popcorn bags = $8y
⇒Cost of 2 popcorn bags = $2y
Since Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.
So, equation will be : $111.25=$9x+$8y --(A)
Since, Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.
So, equation will be : $33.25=$3x+$2y--(B)
SOLVING A and B by using substitution method
finding value of x from equation B :
[tex]x=\frac{33.25-2y}{3}[/tex]
Putting this value in Equation (A)
⇒[tex]111.25=9(\frac{33.25-2y}{3})+8y[/tex]
⇒[tex]111.25=99.75-6y+8y[/tex]
⇒[tex]111.25=99.75+2y[/tex]
⇒[tex]y = 5.75[/tex]
Thus, cost of 1 popcorn bag =y = $5.75
Now put this value of y in equation A to get value of x
⇒$111.25=$9x+$8(5.75)
⇒$111.25-$46 = 9x
⇒$65.25 = 9x
⇒65.25/9 = x
⇒$7.25 = x
Thus, The cost of 1 drink = $x = $7.25
Ally brought 1/2 pound of cashews 5/6 pound of granola.plot the fractions on the number line.which quantity is greater?explain.
Sue has 7/8 of her book left to read. If she reads another 2/7 of the book how much of the book will she have left?
A 33/56
B 1/5
C 5/8
D 23/40
Answer:
A. 33/56
Step-by-step explanation:
Make them have the same denominator of 56
so you get for the first one 49/56
the second one will be 16/56
subtract both and you get your answer of 33/56
Answer: A. 33/56
Step-by-step explanation:
To get the number of pages left, all we need to do is to subtract 2/7 from 7/8
number of pages left = 7/8 - 2/7
=49 - 16 / 56
= 33/56
Karin wants to use the distributive property to mentally find the value of 19 x 42+ 19x 58. Which expression can she use?
Answer:
19(42 + 58)
Step-by-step explanation:
Assuming x = multiply, you are trying to solve the distributive property. Divide common factors from both terms (in this case 19).
~
Answer:
19(42 + 58)
Step-by-step explanation:
19 * 42 + 19 * 58 =
= 19 * (42 + 58) <------- this is the expression
= 19 * 100
= 1900
I need help with numbers 7-9 please
Answer:
C
5(10)+10=60
-2(-5)+7=17
Step-by-step explanation:
Write an explicit formula fo the sequence 7,2,-3,-8,-13.... Then find the 14th term
(please explain)
Answer:
The 14th term is -58
Step-by-step explanation:
The formula for an arithmetic sequence is
an = a1+d(n-1)
where a1 is the first term
d is the common difference and
n is the term number
a1 = 7
d = 2-7 = -5
Check -3-2 = -5 so d = -5
an = 7 -5(n-1)
We want the 14th term
a14 = 7 -5(14-1)
a14 = 7 -5(13)
a14 = 7 -65
a14 = -58
PLLLZ HELP I'LL GIVE BRAINLISET
Answer:
Step-by-step explanation:
Sandy only because the 2 prisms overlap
if two angles of a triangle each measure 45 degrees what is the third angle
Since we know that there are exactly 180 degrees in any triangle, and if each angle is equal to 45 degrees, we must add 45 to 45 and then subtract the result from 180 to find the 3rd angle. Since 45+45=90,we subtract 180-90 and get 90 degrees or a right angle.
The measure of the third angle is 90° a right angle isosceles triangle.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is 180°.'
Given, a triangle with a measure of its two angles is 45° and 45°.
∴ The measure of the third angle is 180° - (45 + 45)°.
= 180° - 90°.
= 90°.
It is an isosceles right-angle triangle.
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please answer this, Thnks, also, whoever does, is amazing and i love you for it. LOL IM CrAzY
Answer:
35[tex]\pi[/tex]
Answer:
C = 35 * pi
Step-by-step explanation:
The circumference is pi * d
The new diameter is 5 cm longer than the given one.
d = 30 + 5
d = 35
C = 35 * pi
Use a graphing calculator or online application to find the solution to 3 -x = x 3 + x to the nearest tenth.
The solution is approximately x = a0.
Answer:
x=1
Step-by-step explanation:
Question says to use a graphing calculator or online application to find the solution to [tex]3-x = x^3 + x[/tex] to the nearest tenth.
So we will create two equations y = 3-x and [tex]y = x^3 + x[/tex] using each sides of the given equation.
Now we graph both equation using some online calculator or graphing calculator. I'm going to use Desmos calculator.
Intersection point of both graphs will give the solution.
From graph we see that intersection point is at (1,2).
We are looking for value of x only.
Hence final answer is x=1
Answer:5
Step-by-step explanation:
Find the distance between the two points shown in the coordinate plane below to the nearest hundredth.
(-2, -2)
(3, 4)
Answer:
7.81
Step-by-step explanation:
Given points (-2,-2) and (3, 4)
To find distance between points we apply distance formula
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
(x1,y1) is (-2,-2) and (x2,y2) is (3,4)
Plug in the values in the formula
[tex]D = \sqrt{(3-(-2))^2+(4-(-2))^2}[/tex]
[tex]D = \sqrt{(5)^2+(6)^2}[/tex]
[tex]D = \sqrt{25+36}[/tex]
[tex]D = \sqrt{61}[/tex]
D= 7.810249676
Round to nearest hundredth
So distance = 7.81
Roger is having a picnic for 72 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality gives the minimum number of packages he will need to buy? A) p ≥ 9 B) p ≥ 6
C) p ≤ 6 D) p ≤ 9
Answer:
The answer is A.
Step-by-step explanation:
To solve this problem, use the inverse operation of multiplication, which is division. 72 ÷ 8 = 9. Since the problem stated "which inequality gives the minimum number of packages he will need to buy?" 9 is the minimum number. Therefore, A is the answer.
Show Work:
8p ≥ 72
÷8 ÷8
p ≥ 9
Answer:
A p≥9
Step-by-step explanation:
The cost of an online movie rental service is $89.94 for 6 month. What is the cost per month? Please show work
Evaluation the expression when x=-1 and y=3.
5x^-6y^-2
—————
Y
Put the vales of x and y to the expression:
[tex]x=-1;\ y=3\\\\\dfrac{5x^{-6}y^{-2}}{y}=\dfrac{5(-1)^{-6}(3)^{-2}}{3}=\dfrac{5(-1)^6\left(\dfrac{1}{3}\right)^2}{3}=\dfrac{5(1)\left(\dfrac{1}{9}\right)}{3}=\dfrac{\dfrac{5}{9}}{3}\\\\=\dfrac{5}{9}\cdot\dfrac{1}{3}=\boxed{\dfrac{5}{27}}[/tex]
the length of a rectangle is 2 cm more than the width. if the area of the rectangle is 24 cm2 what is the length of the rectangle?
The question is about finding the length of a rectangle. By creating and solving a quadratic equation with provided information, the width and length of the rectangle are 4 cm and 6 cm respectively.
Explanation:The problem involves finding the length of a rectangle. To solve this, we need to consider the fact that we know information about the dimensions and area of the rectangle. The area of a rectangle is obtained by performing the multiplication of the length and the width. In this specific problem, it's stated that the length is 2 cm more than the width, and we also know that the area of the rectangle is 24 cm2.
Let's represent the width by x. Therefore, the length would be x+2. Since the area is the length multiplied by the width, we create the equation x*(x+2) = 24, which simplifies to x2+2x=24. Subtracting 24 from both sides, we get x2+2x-24 = 0.
This a quadratic equation and we'll solve for x using the quadratic formula, which results in x = 4 or x = -6. Since the width cannot be negative, x = 4 cm. After this, substitute the width (x) into the length equation. The length (x + 2) is 4 cm + 2 cm = 6 cm.
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The length of the rectangle is [tex]\( 2\sqrt{7} \)[/tex]cm.
To solve this problem, let's denote the width of the rectangle as [tex]\( w \)[/tex] cm. According to the information given, the length of the rectangle is then [tex]\( w + 2 \)[/tex] cm. The area of a rectangle is given by the product of its length and width, so we can set up the following equation:
[tex]\[ w \times (w + 2) = 24 \][/tex]
Expanding the equation, we get:
[tex]\[ w^2 + 2w = 24 \][/tex]
To solve for [tex]\( w \)[/tex], we need to rearrange the equation into standard quadratic form:
[tex]\[ w^2 + 2w - 24 = 0 \][/tex]
Now, we can factor this quadratic equation:
[tex]\[ (w + 6)(w - 4) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:
[tex]\[ w + 6 = 0 \quad \text{or} \quad w - 4 = 0 \] \[ w = -6 \quad \text{or} \quad w = 4 \][/tex]
Since the width of a rectangle cannot be negative, we discard[tex]\( w = -6 \)[/tex] and accept [tex]\( w = 4 \)[/tex] cm as the width of the rectangle.
Now that we have the width, we can find the length by adding 2 cm to the width:
[tex]\[ \text{Length} = w + 2 = 4 + 2 = 6 \text{ cm} \][/tex]
However, we need to check if this length satisfies the area condition:
[tex]\[ \text{Area} = w \times \text{Length} = 4 \text{ cm} \times 6 \text{ cm} = 24 \text{ cm}^2 \][/tex]
This confirms that the length is indeed 6 cm when the width is 4 cm. Therefore, the length of the rectangle is [tex]\( 2\sqrt{7} \)[/tex] cm, since [tex]\( 6 = 2\sqrt{7} \)[/tex] when rounded to the nearest whole number.
Determine whether the lines are parallel. Use slope to explain your answer. Use the graph shown below.
The slope is of the red line is ___
The slope is of the blue line is ___
The lines do/do not have the same slope so they are/are not parallel.
Answer:
red 2/3
blue 1/2
The lines do not have the same slope so they are not parallel
Step-by-step explanation:
We can find the slope of the red line by using the formula
m = (y2-y1)/(x2-x1)
We have the points (0,2) and (3,4)
m= (4-2)/ (3-0)
= 2/3
We can find the slope of the blue line by using the formula
m = (y2-y1)/(x2-x1)
We have the points (0,-2) and (4,0)
m= (0--2)/ (4-0)
= (0+2)/(4-0)
= 2/4
=1/2
The lines do not have the same slope so they are not parallel
Population density is the number of people per unit of area. What is the population density of a state that has 1,627,260 people in 1,490 square miles? Round to the nearest whole number
Answer:
= 1092 people/ sq mile
Step-by-step explanation:
Population density is the number of people per unit of area.
We know the population is 1627260
The are is 1490 mi ^2
Population density = 1627260/1490
=1092.120805 people / sq mile
Round to the nearest whole number
= 1092 people/ sq mile
i'm not really sure whats the answer is
work out the value of (10^4)^2
plsssssss this is urgentttttt
[tex](10^4)^2[/tex]
When you multiply an exponent directly into another exponent, you multiply the exponents.
For example:
[tex](x^{2})^3=x^{2(3)}=x^6[/tex]
[tex](x^5)^3=x^{5(3)}=x^{15}[/tex]
So:
[tex](10^4)^2=10^{4(2)}=10^8=100,000,000[/tex]
Answer:
it is 200000
Step-by-step explanation: ok you want me to show you! huh! :)
so you do 10 times the 4 which is 100000
next you times it by 2 which is equal to 200000
so your answer is 200000
Create an expression without parentheses that is equivalent to 4(6x + x).
what is the 52nd term for the following sequence ? 14,6,-2,-10,-18
Answer:
[tex]a_{52}[/tex] = - 394
Step-by-step explanation:
these are the terms of an arithmetic sequence with nth term
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
where d is the common difference and [tex]a_{1}[/tex] the first term
d = - 18 - (- 10) = - 10 - (- 2) = - 2 - 6 = - 8 and [tex]a_{1}[/tex] = 14, hence
[tex]a_{52}[/tex] = 14 + (51 × - 8) = 14 - 408 = - 394
Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020. Create the inequality that represents this situation and plot the solution set to the inequality on the number line.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&7020\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill \end{cases}[/tex]
[tex]\bf 7020\geqslant 4500(1+0.03t)\implies \cfrac{7020}{4500}\geqslant 1+0.03t\implies \cfrac{39}{25}\geqslant 1+0.03t \\\\\\ \cfrac{39}{25}-1\geqslant 0.03t\implies \cfrac{14}{25}\geqslant 0.03t\implies \cfrac{~~\frac{14}{25}~~}{0.03}\geqslant t\implies \cfrac{56}{3}\geqslant t \\\\\\ 18\frac{2}{3}\geqslant t\impliedby \textit{18 years and 8 months}~\hfill \boxed{0 \leqslant t \leqslant 18\frac{2}{3}} \\\\\\ ~\hspace{34em}[/tex]
check the picture below.
bearing in mind that "t" cannot be less than 0.
What is the better buy? 1.50 for 5 oz 1.20 for 3 oz
To find the better buy, calculate the unit price of each item by dividing the cost by the weight, and compare them. The first item at $1.50 for 5 oz has a lower unit price ($0.30 per oz) than the second item at $1.20 for 3 oz ($0.40 per oz), so it is the better buy.
Explanation:To determine which is the better buy between two products, you need to calculate the unit price for each and then compare them.
The unit price is the cost per unit of weight or volume.
Calculate the unit price of the second item: $1.20 for 3 oz means the cost per ounce is $1.20 ÷ 3 oz = $0.40 per oz.Compare the unit prices: The first item has a lower unit price ($0.30 per oz) compared to the second item ($0.40 per oz), making it the better buy.Final answer:
To find the better buy between $1.50 for 5 oz and $1.20 for 3 oz, calculate the cost per ounce for each and compare. The first option is cheaper at $0.30 per ounce compared to the second option at $0.40 per ounce.
Explanation:
To determine which is the better buy between $1.50 for 5 oz and $1.20 for 3 oz, we need to calculate the cost per ounce for each option.
Step-by-step Comparison
Calculate the cost per ounce for the first option: Divide $1.50 by 5 oz to get $0.30 per ounce. Calculate the cost per ounce for the second option: Divide $1.20 by 3 oz to get $0.40 per ounce. Compare the two cost per ounce figures: The first option at $0.30 per ounce is cheaper than the second option at $0.40 per ounce.
Therefore, the better buy is the first option, $1.50 for 5 oz, since it has a lower cost per ounce.
*20 points*
Four times a number is
six less than twice the number what is the number?
Answer:
your number is n= -3
Step-by-step explanation:
Answer:
n=-3
Step-by-step explanation:
4n-2n=-6
2n=-6
2 x n / 2 = 6 / 2 then simplify to get the answer! Hope this is Helpful! ;3
NEED HELPPPP ASAP PLEASEEEE
Answer: 35.6 (choice A)
To get this answer, add up the values: 39+42+27+45+25 = 178
Next, divide that result by 5 because there are 5 scores added up in the previous step. Doing this division gets us to: 178/5 = 35.6
Jamal is shopping with a gift card he received for his birthday. After he purchases two T- shirts the gift card balance has dropped from $50 top $20.02. What is the unit rate of the cost per T- shirt?
Answer:
14.99
Step-by-step explanation:
20.02=50-2t
20.02-50= -2t
-29.98= -2t
draw a bar model that shows how the number of hours in March compared with the number of hours in February of this year
Answer: Your answer will be 1,416
Step-by-step explanation: First you see how many day March and February had March had 31 days and 31 days= 744 hours and February has 28 days and 28 days= 672 hours so know I add the two numbers 744 + 672 = 1,416.
Answer:
You should multiply with the days in March which is 744 hours. And then you have to multiply with the days in February witch is 696 and then you have to subtract them.
Step-by-step explanation:
have a nice day.