Answer:
£850
Step-by-step explanation:
We can compute the left-over amount by comparing that to the amount spent.
__
setupWritten as ratios, we have ...
spent : left-over = 3/8 : 1 -3/8 = 3/8 : 5/8 = 3 : 5
Writing this using fractions, we have ...
left-over / spent = 5 / 3
solutionSolving for left-over gives ...
left-over = spent × (5/3) = £510×5/3 = £850
Nate had £850 left over.
_____
Additional comment
Nate's money totaled £510 +850 = £1360.
The fraction spent is £510/£1360 = 3/8, as required.
Find the amount of money
accumulated after investing a
principle P for years t at interest
rate r, compounded continuously.
t = 6
P = $1,500 r = 7%
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500e^{0.07\cdot 6}\implies A=1500e^{0.42}\implies A\approx 2282.94[/tex]
interest rate of 2.99% compounded monthly for a 4 year loan, find the regular monthly payments required to repay the loan.
Using it's formula, considering a loan of $10,000, the regular monthly payments required to pay off the loan will be of $221.3.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, we have that the parameters are given as follows:
P = 10,000, r = 0.0299, n = 4 x 12 = 48.
Then:
r/12 = 0.0299/12 = 0.00249167.
Hence, the monthly payment will be given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 10000\frac{0.00249167(1+0.00249167)^{48}}{(1+0.00249167)^{48} - 1}[/tex]
A = 221.3.
More can be learned about the monthly payment formula at https://brainly.com/question/22846480
#SPJ1
A line is parallel to y=-2x-5 and intersects the point (-1,3) input the correct values into the point slope formula y-[?] = [__}(x- [__])
The equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
A line is parallel to y=-2x-5 and intersects the point (-1,3)The equation of the new line will be:-
y - y₁ = m ( x - x₁ )
Since the line is parallel to the line y = -2x - 5 so slope will be same m = -2 now the coordinates are ( -1, 3).
y - ( 3) = -2 [( x - (-1) ]
y - 3 = -2x - 2
y = -2x + 3 -2
Y = -2x + 1
Therefore the equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ1
please explain
Convert the angle θ= 9/14pi radians to degrees.
Answer:
280°
Step-by-step explanation:
using the relationship
π radians = 180° , then substituting gives
[tex]\frac{14\pi }{9}[/tex] = [tex]\frac{14(180)}{9}[/tex] = 14 × 20 = 280°
The watermelon bought by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya?
Answer:
12.6
Step-by-step explanation:
4.2×3=12.6
I hope this answer can help you
Answer:
1.4 kg
Step-by-step explanation:
Given :
⇒ Watermelon (Peter) = 3 × Papaya (Paul)
⇒ Watermelon (Peter) = 4.2 kg
=============================================================
Solving :
⇒ 4.2 = 3 × Papaya (Paul)
⇒ Papaya (Paul) = 1.4 kg
Therefore the mass of the papaya is 1.4 kg.
Which expression is a perfect cube
Answer: some perfect cubes are
8 (2^3)
27 (3^3)
64 (4^3)
there are many perfect cubes
maybe there is more to this question?
Step-by-step explanation:
A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.
Pls help me with no26
Answer:
a) 8
Step-by-step explanation:
The prime factors for 24 are 2, 2, 2, 3 -> The greatest is 3
The prime factors for 35 are 5, 7 -> The smallest is 5
So the sum is 3+5=8
write a rule for the nth term of the arithmetic sequence
-11, -4, 3, 10...
Answer: aₙ = -11 + 7(n - 1)
Step-by-step explanation: The equation of an arithmetic sequence is
aₙ = a₁ + d(n - 1).
a₁ is the first term.
d is the common difference.
What is the solution for x in the equation?
9-10x=2x + 1 - 8x
x = -2
x=1/2
x=2
x=-1/2
Solve for X.
6
X = [?]
Enter the number, in decimal form,
that belongs in the green box.
Answer:
By proportional method
[tex] \frac{4}{6} = \frac{5}{x} [/tex]
4x= 30
x= 7.5
b solve each problem . use ñ= 3.14 1. what is the volume of a regular cylinder whose base has radius of 5 cm and has height of 4 cm? 2. the diameter of sphere is 10 cm. find the volume. 3. juice is sold in aluminum cans that measure 7 inches in height and 4 inches in diameter. how many cubic inches of juice are contained in a full can? 4. the square pyramid has a volume of 297 cm³. the area of the base is 81 cm². What is the height.? 5. A glass is 10 cm deep and 8 cm wide . How much liquid the glass hold?
#1
Volume
πr²hπ(5)²(4)100π3.14(100)314cm³#2
Radius=10/2=5cm
Volume
4/3πr³4/3π(5)³125(4/3π)500π/3523.3cm³#3
Volume
π(4/2)²(7)2²(7π)28π87.92in³#4
V=1/3a²hV=1/3(81)h27h=297h=11cm#5
radius=8/2=4
Volume
π(4)²(10)160π502.4cm³502.4mLAnswer:
1) 314 cm³
2) 523.33 cm³
3) 87.92 in³
4) 11 cm
5) 502.4 cm³
Step-by-step explanation:
Part 1[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 5 cmh = 4 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]
Part 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]
Given:
d = 10 cm ⇒ r = 5 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]
Part 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 4 in ⇒ r = 2 inh = 7 inπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]
Part 4[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]
Given:
Volume = 297 cm³Area of base = 81 cm²[tex]\implies 81=a^2[/tex]
[tex]\implies a=\sqrt{81}[/tex]
[tex]\implies a=9\: \sf cm[/tex]
Substitute the given values into the formula and solve for h:
[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]
Part 5[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 8 cm ⇒ r = 4 cmh = 10 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]
Select the best definition of repeating decimal.
A. any number that does not repeat, or terminate, that can not be written as a fraction.
B. a decimal that has a recurring sequence of numbers that follow a pattern
C. any number that can be written as a fraction, repeating or terminating decimal
D. a decimal which has digits that do not go on forever.
The correct option that defines repeating decimals correctly is Option B;
a decimal that has a recurring sequence of numbers that follow a pattern.
What is a Repeating Decimal?A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.
From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.
Read more about repeating decimal at; https://brainly.com/question/22063097
#SPJ1
50 points Find the lateral surface area of the prism.
Answer:
Lateral surface area = 36 ft²Step-by-step explanation:
Formula:
Lateral surface area = perimeter of the base × height
………………………………………………………………
perimeter of the base = 2×(1.5+3) = 9
height = 4.
then
Lateral surface area = 9 × 4 = 36
Area of two bigger rectangles
2LB24(3)2(12)ft²24ft²Area of two smaller rectangles
2×1.5(4)2×612ft²LSA
12+2436ft²When 2(3/5 x + 2 3/4 y - 1/4 x - 1 1/2 y + 3) is simplified, what is the resulting expression?
Answer:
6 + 7/10x + 2/y
Step-by-step explanation:
Hope this helps :)
Write the point-slope form of the equation for a line that passes through (−1, 4) with a slope of 2.
The value of x₁ is
The value of y₁ is
The point-slope form of the equation is
Can you please factorize 2x²+6x
To factorize something:
⇒ need to simplify the equation to its most basic form
Let's solve:
[tex]2x^2+6x=2(x^2+3x)=2x(x+3)[/tex]
Thus the factorized form is ⇒ [tex]2x(x+3)[/tex]
Answer: 2x(x+3)
Hope that helps!
Answer:
Solution:
→ 2x(x + 3)
Step-by-step explanation:
Method:
Grouping→ Common factor
2x² + 6x2(x² + 3x)→ Rewrite in factored form
2(x² + 3x)2x(x + 3)Can someone tell me what is 9x46288
Find the value of x.
6
14
8
0
21
x = [ ? ]
3x-12
Answer: 7
Step-by-step explanation:
By the angle bisector theorem,
[tex]\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}[/tex]
A survey asked people how many siblings they have, and the results were recorded in this line plot.
How many people surveyed have 4 or more siblings?
dot plot
Answer:
we need a pic of the graph to be able. to work this out.
THANK YOU
Answer:
It's 5.
Step-by-step explanation:
8-3= 5
Which of the following is the graph of the inverse of F(x) = 2x - 3?
I need help asap!!! I will without hesitation give brainliest to whomever gets this
Answer:
A. [tex]y\leq \frac{1}{2}x+2[/tex]
Step-by-step explanation:
First, let's find the slope of the line, so we can eliminate some answers.
From point (0,2) we can go up 1 and over to the right 2 to the point of (2,3). Slope is rise over run so 1 over 2.
This eliminates C and D.
The last part is to recognize that y being less than the equation will result in the shaded region being below the line. If y was greater than the equation then the shaded region would be above the line.
Therefore, the correct answer would be A. [tex]y\leq \frac{1}{2}x+2[/tex].
Hope this helps! If you have questions about my work please let me know down in the comments!
Answer:
[tex]y\leq \frac{1}{2}x+2[/tex]
Step-by-step explanation:
The first part of finding our answer is finding the slope of the line. The image attached shows this.
[tex]\frac{rise}{run} = \boxed{\frac{1}{2}}[/tex]
This means the slope is [tex]\frac{1}{2}[/tex], removing the bottom 2 answer choices.
Now we have to choose between the [tex]\leq[/tex] and [tex]\geq[/tex] sign. Since the shaded area is below the line, it will be the [tex]\leq[/tex]. (If it was the [tex]\geq[/tex] sign, the shaded area would be above the line.) This marks the first answer as the correct answer.
ہے
Solve for k.
4k - 10
k
k=
-
= 8
Answer:
The formation of the equation is odd, but I assume it's supposed to be:
4k - 10k = -8k
-6k = -8k
-6k + 8k = -8k + 8k
2k = 0
[tex]\frac{2k}{2}[/tex] = [tex]\frac{0}{2}[/tex]
k = 0
Arun took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4 plus $4.25 per mile. The total fare was $110.25, not including the tip. How many miles was the taxi ride?
Answer:
Answer = 25 miles
Step-by-step explanation:
We can make an equation based off of this information in the form of 4.25x+4=110.25. When we solve for x we find that it equals 25.
Hope that helps! :)
The ________________ measures the spread of the middle 50% of the data set.
A. median
B. range
C. interquartile range
D. mode
Answer:
C. interquartile range
Step-by-step explanation:
using this to show im right
"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."
Hope This Helped
A cone has a height of 8 yards and a radius of 3 yards. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
cubic yards
Submit
Yea
The volume of the given cone.
Solution:[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]
[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]
Let's solve!
Substitute the values according to the formula.
[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]
[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]
Therefore, the volume of the given cone is 75.36 cubic yards.
Aaron solved an inequality and then graphed the solution as shown below.
-8-7
1 0 1 2 3 4 5
Which inequality did Aaron solve?
|x+2| <3
Ox+2| >3
|x+3| <2
|x+31 > 2
Based on the graph that Aaron made, we can infer that the inequality he solved is | x + 2 | < 3.
What inequality was solved by Aaron?
The value of x in the graphed inequality is:
-5 < x < 1
If 2 was added to both sides, the least value would be - 3 and the highest value would be 3.
The inequality then becomes:
-3 < x < 3
This in line with the first option which is that when 2 is added to any value of x, it will be less than 3.
Find out more on graphing inequalities at https://brainly.com/question/24372553.
#SPJ1
PLEASE HELP ME I WILL GIVE BRAINLYEST
Answer:
your answer will be 85 1/3ins
Step-by-step explanation:
16x 5 1/3 = 85.3333333333
then I took the 85 and the 1/3
and just put em together
Which of the following points is not coplanar with points C, D and E?
The point R is the point which is not coplanar with points C, D and E.
We need to find the point which is not coplanar with points C, D and E.
What are coplanar points?The points that lie on the same plane are called coplanar points.
In the given figure there are five planes which are as follows:
BCUD, BRAE, BRAC, BTDE, ACUDE
Now, points C,D and E lie in plane ACUDE.
In the plane ACUDE points A, C, U, D, E and S lies.
From the options point, R is not lining in the same plane as C, D and E lies.
Therefore, the point R is the point which is not coplanar with points C, D and E.
To learn more about coplanar points visit:
https://brainly.com/question/1593959
#SPJ1
I'd appreciate the help!!
Answer:
B
Step-by-step explanation:
look at the graph. y is negative from x>2, so interval is 2<x<infinity.
in other case y=0 for x=2, y<0 for infinity<x<2
Answer:
The intervel that describes where the graph is negative is C :)
I hope this helps you!
Step-by-step explanation:
A square has a triangular hole in it. What is the area of the figure?
9 in. 3 in.
76.5 in 2
89 in 2
72 in 2
3 in.
9 in.
Answer:
76.5in²
Step-by-step explanation:
First we will find the area of the square. This is done by multiplying the side length (9in) by itself.
[tex]9 * 9 = \boxed{81}[/tex]
The area of the square is 81in².
Next we will find the area of the triangular hole. We can use the formula [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle (3) and h is the height of the triangle (3).
[tex]\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}[/tex]
The area of the triangle is 4.5in².
Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.
[tex]81 - 4.5 = \boxed{76.5}[/tex]
The area of the figure is 76.5in².
That is the answer
- Kan Academy Advance