Answer:
Jane's share of the cost is £156
Step-by-step explanation:
Since the cost is to be shared equally amongst the 6 friends, to get the amount to be paid by Jane, we must work out the total cost to be incurred first.
Total cost = £216 + £404 + £316
= £936
Since there are 6 friends willing to bear this cost equally, the amount to be paid by Jane
= £936/6
= £156
How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze
Answer:
67 gallons.
Step-by-step explanation:
To determine how many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze, the following calculation must be performed:
0.15 x 90 + 0.70 x 10 = 20.5 / 100 = 0.20
0.15 x 90 + 0.70 x 30 = 34.5 / 100 = 0.34
0.15 x 90 + 0.70 x 60 = 55.5 / 100 = 0.55
0.15 x 90 + 0.70 x 67 = 60.4 / 100 = 0.60
Thus, 67 gallons of 70% antifreeze solution will be needed to achieve a 60% mix of that solution.
Help plz:)))I’ll mark u Brainliest
Answer:
x = 12
Step-by-step explanation:
Consider this solution to a problem.
Problem: -4(6-y)+4=-4
Step 1: -24-4y+4=-4
Step 2: -20-4y=-4
Step 3: -4y = 16
Step 4: y=-4
In the first response box, enter the number of the step where the mistake is made.
Step:
In the second response box, enter the correct solution to the problem.
Answer:
1. The mistake was the sign that was put negative instead of positive.
2. y = 4
Step-by-step explanation:
In the first response box, enter the number of the step where the mistake is made.
Step:
The mistake is on step 1: This is the distributive property, however it was distrubuted wrong since the signs were used wrong.
-4(6-y)+4=-4 does not equal -24-4y+4=-4
The reason is because -4 x -y is not equal to -4y because negative x negative = positive. So, it's equal to +4y.
In the second response box, enter the correct solution to the problem.
Problem: -4(6-y)+4=-4
Step 1: -24 + 4y + 4 = -4 (Distributive Property Of Equality)
Step 2: -20 + 4y = -4 (Combine Like Terms)
Step 3: 4y = 16 (Addition Property Of Equality)
Step 4: y = 4 (Division Property Of Equality)
The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.
Given:
The sum of two terms of GP is 6 and that of first four terms is [tex]\dfrac{15}{2}.[/tex]
To find:
The sum of first six terms.
Solution:
We have,
[tex]S_2=6[/tex]
[tex]S_4=\dfrac{15}{2}[/tex]
Sum of first n terms of a GP is
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex] ...(i)
Putting n=2, we get
[tex]S_2=\dfrac{a(1-r^2)}{1-r}[/tex]
[tex]6=\dfrac{a(1-r)(1+r)}{1-r}[/tex]
[tex]6=a(1+r)[/tex] ...(ii)
Putting n=4, we get
[tex]S_4=\dfrac{a(1-r^4)}{1-r}[/tex]
[tex]\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}[/tex]
[tex]\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}[/tex]
[tex]\dfrac{15}{2}=6(1+r^2)[/tex] (Using (ii))
Divide both sides by 6.
[tex]\dfrac{15}{12}=(1+r^2)[/tex]
[tex]\dfrac{5}{4}-1=r^2[/tex]
[tex]\dfrac{5-4}{4}=r^2[/tex]
[tex]\dfrac{1}{4}=r^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{\dfrac{1}{4}}=r[/tex]
[tex]\pm \dfrac{1}{2}=r[/tex]
[tex]\pm 0.5=r[/tex]
Case 1: If r is positive, then using (ii) we get
[tex]6=a(1+0.5)[/tex]
[tex]6=a(1.5)[/tex]
[tex]\dfrac{6}{1.5}=a[/tex]
[tex]4=a[/tex]
The sum of first 6 terms is
[tex]S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}[/tex]
[tex]S_6=\dfrac{4(1-0.015625)}{0.5}[/tex]
[tex]S_6=8(0.984375)[/tex]
[tex]S_6=7.875[/tex]
Case 2: If r is negative, then using (ii) we get
[tex]6=a(1-0.5)[/tex]
[tex]6=a(0.5)[/tex]
[tex]\dfrac{6}{0.5}=a[/tex]
[tex]12=a[/tex]
The sum of first 6 terms is
[tex]S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}[/tex]
[tex]S_6=\dfrac{12(1-0.015625)}{1.5}[/tex]
[tex]S_6=8(0.984375)[/tex]
[tex]S_6=7.875[/tex]
Therefore, the sum of the first six terms is 7.875.
The equation of a circle is x2 +y2 =81 what is the diameter of the circle
Answer:
pretty sure it's 9.
Step-by-step explanation:
square root of 81 is 9. 3 is its radius.
Help plz I’m stuck on this
Can you find the mass of the angles?
b=48
c=137
enjoy :) ....
Here is a rectangle with some right triangles inside it. Which triangles are similar to triangle AED?
The triangle that is similar to this triangle from the given rectangle is triangle FED
Similar shapesSimilar shapes are shaped with similar sides and angles. From the given diagram, we are to determine with the triangle is similar to the triangle AED.
This means we need to determine which of the triangles has similar sides as triangle AEDThe triangle that is similar to this triangle from the given rectangle is triangle FEDLearn more on similar shapes here; https://brainly.com/question/2644832
The two figures are similar. Identify the similar sides, and then write the similarity statement. Fill in each blank, then complete the sentence by explaining your reasoning.
• AB is similar to ____ because:
• AC is similar to ____ because:
• CB is similar to ____ because:
Step 2: Write the similarity statement.
Answer:
- AB is similar to YZ because all the sides from triangle ABC got multiplied by 3/4, and 40 times 3/4 = 30.
- AC is similar to YX because 50 times 3/4 = 37.5.
- CB is similar to XZ because 60 times 3/4 = 45.
hope this helps!
identify the independent variable for this function
Explanation:
Time progresses without any control over it, so it's something that does not depend on any other factor such as distance. On the other hand, as the time value changes, the distance changes. So the distance is dependent on the time.
The horizontal axis is the x axis, and the x value is always the independent variable. The vertical y axis is the distance. The y value is always the dependent variable.
Factor completely 2x3 + 6x2 + 2x + 6
Answer:
2(x+3)(x2+1)
Step-by-step explanation:
help pls? If mF= 109*, mQ=122*, mR=44, find mJ
Answer:
∠J=85°
Step-by-step explanation:
Theory to know when answering this question:
1. The sum of the angles in a quadrilateral (shape with four sides) is 360°
2. Similar shapes have the same angles
Point 1 tells us that ∠P+∠Q+∠S+∠R=360
Point 2 tells us that ∠F=∠P, ∠G=∠Q, ∠J=∠S, and ∠H=∠R.
∴∠F+∠Q+∠J+∠R=360
109+122+∠J+44=360
∠J=360-275=85°
Solve the inequality for the missing variable
24 -1t
1/5
Answer:
−t+24
Step-by-step explanation:
what is the square root of 9? thank you hoomans in advance :P
Answer:
it's 3 =^_^=
Step-by-step explanation:
Answer:
3 I think :)
Step-by-step explanation:
square root of 9 is 3
HELP HELP HELP HELP IM BEGGING YOU PLEASE PLEASE!!!
Answer:
2n + 18.....
Step-by-step explanation:
yea
there was 5/8 of a pie left on the fridge Daniel ate 1/4 of the leftover .how much of a pie did he have?
Answer:
3/8
Step-by-step explanation:
Your need to change the 1/4 to eighths
so multiply it by 2
1/4 x 2/2
which equals 2/8
then you need to subtract it from the 5/8
5/8 - 2/8 = 3/8
Iman’s favorite colors are \blue{\text{blue}}bluestart color #6495ed, start text, b, l, u, e, end text, end color #6495ed and \pink{\text{pink}}pinkstart color #ff00af, start text, p, i, n, k, end text, end color #ff00af.
She has \blue{\text{1 blue shirt}}1 blue shirtstart color #6495ed, start text, 1, space, b, l, u, e, space, s, h, i, r, t, end text, end color #6495ed, \pink{\text{1 pink shirt}}1 pink shirtstart color #ff00af, start text, 1, space, p, i, n, k, space, s, h, i, r, t, end text, end color #ff00af, \blue{\text{1 blue hat}}1 blue hatstart color #6495ed, start text, 1, space, b, l, u, e, space, h, a, t, end text, end color #6495ed, \blue{\text{1 blue belt}}1 blue beltstart color #6495ed, start text, 1, space, b, l, u, e, space, b, e, l, t, end text, end color #6495ed, \blue{\text{1 blue pair of pants}}1 blue pair of pantsstart color #6495ed, start text, 1, space, b, l, u, e, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #6495ed, and \pink{\text{1 pink pair of pants}}1 pink pair of pantsstart color #ff00af, start text, 1, space, p, i, n, k, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #ff00af.
Iman selects one of these garments at random. Let AAA be the event that she selects a pink garment and BBB be the event that she chooses a shirt.
What is P(A\text{ or }B)P(A or B)P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that the garment Iman chooses is pink or a shirt?
Answer:
1/2
Step-by-step explanation:
i got this from camellarosegarcia. thank you camellarosegarcia!!!
also got it right on Khan :)
The answer of probability that the garment Iman chooses is pink or a blue shirt is 1/2
What is Probability ?Probability means possibility.
It is a branch of mathematics that deals with the occurrence of a random event.
The value is expressed from zero to one.
The meaning of probability is basically the extent to which something is likely to happen.
Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring.
In this case Iman has 2 choices pink or blue
So the probability that the garment Iman chooses is pink or a blue shirt
is 1/2 .
To know more about Probability
https://brainly.com/question/23298290
#SPJ2
Marcus rolled a number cube and recorded his results in the table. What is the experimental probability that the next roll is a five? Round your answer to the nearest whole percent.
Answer:
The probability is 13.33%
Step-by-step explanation:
Probability
The probability of an outcome is defined as the frequency of the number of times the outcome occurs (f) relative to the number of times that it could have occurred (n).
The formula to calculate the probability is:
[tex]\displaystyle P=\frac{f}{n}[/tex]
Marcus rolled a number cube and the results are recorded in a table where it can be noted that the number five rolled f=24 times. The total number of trials is n=30+45+30+28+24+23=180.
The probability that the next roll is a five is:
[tex]\displaystyle P=\frac{24}{180}[/tex]
Simplifying:
[tex]\displaystyle P=\frac{24}{180}[/tex]
[tex]\displaystyle P=\frac{2}{15}[/tex]
Dividing:
[tex]\displaystyle P=0.1333 = 13.33\%[/tex]
The probability is 13.33%
- في الشكل المجاور برهن أن
m<E <m<CAD
B
D A
E
-
Answer:
B
Step-by-step explanation:
PLEASE HELP!!! ASAP
determine the number and type of solutions to the equation: x^2+7x=-11
a.) two real solutions
b.) one real solution
c.) two imaginary solutions
d.) one imaginary solution
Answer:
b i think because for it to be imaginary, im sure there has to be an i in the equation
Answer:
A) Two Real Solutions
Step-by-step explanation:
Correct on Big Ideas Math :)
The two triangles above are similar. What is the value of x ?
A) 5
B) 7.5
C) 8
D) 13 1/5
Answer:
7.5
Step-by-step explanation:
[tex]\frac{6}{8} =\frac{x}{10}\\crossmultiply\\60=8x\\solvefor x\\ x=7.5[/tex]
Similar triangles are those triangles whose corresponding sides are in the same ratio. In the two similar triangles, the value of x is 7.5 units.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by the ‘~’ symbol.
Given that the two of the given triangles are similar triangles. Therefore, the ratio of the sides of the triangle can be written as,
6/x = 8/10
Solving the ratio for x,
x = (6×10)/8
x = 60/8
x = 7.5 units
Hence, in the two similar triangles, the value of x is 7.5 units.
Learn more about Similar Triangles here:
https://brainly.com/question/25882965
#SPJ2
What is the slope of the line?
Answer:
the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.
Step-by-step explanation:
You didn't put a picture, so I didn't know if you meant what it means, or from a line?
If you invested $250 at 16% interest, how much would you have after 18 years?
Answer:
4,000
Step-by-step explanation:
I’ll give
Brainly What is the surface area of the figure below?
Answer:
36
Step-by-step explanation:
You do 6+6+12+12
*3 times 4= the two twelves
Write an algebraic expression for the phrase. 12 minus m
A. m/12 B. 12-m C. 12m D. m-12
Answer:
it's b
Step-by-step explanation:
literally twelve minus m
Answer:
B
Step-by-step explanation:
12 minus m is, 12 - m
ava pours 3 gallons of paint equally into 5 cans. how many gallon of paint will there be in each can?
Answer:
15 gallons of paint
Step-by-step explanation:
5 x 3 = 15
equal groups !
Solve the Equation.
y = 5 = 125
If Y = 5 and the X is = 1 then Y = 125 is X = 25
For each of the situations described below,give an example(if it’s possible) or explain why it’s not possible.
a. A set of vectors that does not span R^3. After adding one more vector, the setdoes spanR3.
b. A set of vectors that are linearly dependent. After adding one more vector, theset becomes linearly independent.
Step-by-step explanation:
a) If the given set of vectors does not span [tex]\mathbb{R}^{3}[/tex] , it means the number of linearly independent vectors are less than 3. So by adding one or more linearly independent vectors with respect to existing vectors, we can convert the set to basis and basis always spans vector space.
eg. [tex]S= \left \{ (1,0,0)^{T},(1,2,0)^{T} \right \}[/tex] this set does not span [tex]\mathbb{R}^{3}[/tex] . Since it has only two vectors and both vectors are linearly independent, so adding one linearly independent vector with respect to the vectors of S viz. (0,0,1)^{T} can span whole [tex]\mathbb{R}^{3} [/tex].
b) It is not possible. Since if a set of vectors is linearly dependent then after adding linearly independent vectors it will also linearly dependent i.e. addition of a linearly independent vector does not effect on the set.
Please answer this correctly without making mistakes
Answer:
0 tablespoons and 2 teaspoons
Step-by-step explanation:
method 1:
Do the calculation in teaspoons for accuracy:
1173 tablespoons and 1 teaspoons = 1173*3 + 1 = 3520 teaspoons
Now 3520 / 1760 = 2 teaspoons exactly.
Hence the answer is 2 teaspoons.
method 2:
1173 / 1760 ≈ 0.666 tablespoons ≈ 1.998 teaspoons
1 / 1760 ≈ 0.00057 teaspoons
1.998 + 0.00057 ≈ 2 teaspoons
Method 1 is clearly more accurate
Sydney invested $440 in an account paying an interest rate of 5.6% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $640?
Answer:
The time required to get a total amount of $ 640.00 from compound interest on a principal of $ 440.00 at an interest rate of 5.6% per year and compounded 365 times per year is approximately 7 years.
Step-by-step explanation:
Given
Principle Amount P = $440 Accrued Amount A = $640Interest rate r = 5.6% = 0.056Compounded daily n = 365To determine:
Time period t = ?
Using the formula
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
solving for t
t = ln(A/P) / n[ln(1 + r/n)]
substituting the values A = 640, P = 440, n = 365 and r = 0.056
t = ln(640/440) / ( 365 × [ln(1 + 0.00015342465753425/365)] )
t = 6.691
t ≈ 7 (nearest year)
Therefore, the time required to get a total amount of $ 640.00 from compound interest on a principal of $ 440.00 at an interest rate of 5.6% per year and compounded 365 times per year is approximately 7 years.