Answer:
Step-by-step explanation:
First add what you have.
Sum = 5 + 7 +7+8 + x + 5 + 4 +3 + 1 +2
Sum = x + 42
Now when you divide this by the number of terms, you get
(x + 42) / 10
The answer is 4.5
(x + 42) / 10 = 4.5 Multiply by 10
x + 42 = 4.5 * 10
x + 42 = 45 Subtract 42
x = 45 - 42
x = 3
Write the recursive rule for the given sequence: 58, 65, 72, 79, 86
Hello!
58, 65, 72, 79, 86
86+7 = 93
93+7 =100
100+7 =107
Simplify: 1/2(8 - 6y) + 1/5(10y - 25)
Hey there!
1/2(8 - 6y) + 1/5(10y - 25)
DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES
= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)
= 4 - 3y + 2y - 5
COMBINE the LIKE TERMS
= (-3y + 2y) + (4 - 5)
= -3y + 2y + 4 - 5
= -1y - 1
≈ -y - 1
Therefore, your answer is: -y - 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
1/2(x+2y)+5/3(3x-2y)=-3/2; 5/4(x+2y)-3/5(3x-2y)=61/60. Find x and y?
Answer:
(x, y) = (-1/6, 1/4)
Step-by-step explanation:
This is a system of equations in expressions of two variables. You could solve it by expanding the expressions to the base variables, or you could solve it by first finding the values of the expressions.
Let's see what happens when we expand the equations all the way.
First equation:
[tex]\dfrac{1}{2}(x +2y)+\dfrac{5}{3}(3x-2y)=-\dfrac{3}{2}\\\\3(x+2y)+10(3x-2y)=-9\qquad\text{multiply by 6}\\\\3x+6y+30x-20y=-9\qquad\text{eliminate parentheses}\\\\\boxed{33x-14y+9=0}\qquad\text{collect terms, add $9$ to get general form}[/tex]
__
Second equation:
[tex]\dfrac{5}{4}(x+2y)-\dfrac{3}{5}(3x-2y)=\dfrac{61}{60}\\\\75(x+2y)-36(3x-2y)=61\qquad\text{multiply by 60}\\\\75x+150y-108x+72y=61\qquad\text{eliminate parentheses}\\\\-33x +222y = 61\qquad\text{collect terms}\\\\\boxed{33x-222y+61=0}\qquad\text{write in general form}[/tex]
__
The solution process looks like it might be messy for either substitution or elimination, so we choose to solve these equations using the cross-multiplication method.
Δ1 = (33)(-222) -(33)(-14) = -6864
Δ2 = (-14)(61) -(-222)(9) = 1144
Δ3 = (9)(33) -(61)(33) = -1716
x = Δ2/Δ1 = 1144/-6864 = -1/6
y = Δ3/Δ1 = -1716/-6864 = 1/4
The solution is (x, y) = (-1/6, 1/4).
_____
Additional comment
The weird numbers notwithstanding, the solution by elimination might be easily achieved by subtracting the second equation from the first. This would give ...
208y -52 = 0 ⇒ y = 52/208 = 1/4
Direct substitution of this into either equation will require arithmetic with fractions to obtain the solution for x.
This system can be directly solved by a graphing calculator using the equations as given.
__
You can read more about the cross multiplication method of solving a system of linear equations here:
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Step-by-step explanation:
Given equation are: [1/{2(x+2y)}] + [5/{3(3x-2y)}] = -3/2 →Eqn(1)
[5/{4(x+2y)}] - [3/{5(3x-2y)}] = 61/60 →Eqn(2)
Let {1/(x+2y)} = a ; {1/(3x-2y)} = b then
{1/(2a)} + {5/(3b)} = -3/2 →Eqn(3) * 5/2
{5/(4a)} - {3/(5b)} = 61/60 →Eqn(4) * 1
__________________________________
{5/(4a)} + {25/(6b)} = -15/4
{5/(4a)} - {3/(5b)} = 61/60
(-) (+) (-)
______________________
{23/(6b)} + {3/(5b)} = -(15/4) - (61/60)
⇛{(125b + 18b)/(30b²)} = {(-225 - 61)/60}
⇛{(143b)/(30b²)} = -286/60
⇛{143/(30b)} = -286/60
⇛1/b = -1
Therefore, b = -1
Substitute the value of b in equation (3) then we have
{1/(2a)} + (5/3) = -3/2
⇛{1/(2a)} = -(3/2) - (5/3)
= (-9-10)/6
⇛{1/(2a)} = -19/6
⇛1/a = -19/3
a = -3/19
Now, {1/(x+2y)} = a ⇛-3/19
⇛x+2y = -19/3. ⇛3x + 6y = -19 →Eqn(5)
{1/(3x-2y)} = 1⇛ 3x - 2y = 1 →Eqn(6)
(-) (+) (-)
______________
8y = -20
y = -20/8
Therefore, y = -5/2From equation (6)
3x - 2 * (-5/2) = 1
⇛3x - 5 = 1
⇛3x = 1+5
⇛3x = 6
⇛x = 6/3
Therefore, x = 2/1 = 2Answer: Hence, the required value of x and y with be -5/2 and 2 respectively.
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Triangle OPQ is similar to triangle RST. Find the measure of side ST. Round your answer to the nearest tenth if necessary
Given that triangles OPQ and RST are similar triangles, the measure of side ST is: 75.3.
What are Similar Triangles?The ratio of the corresponding sides of two similar triangles are always equal, meaning the sides are proportional to each other.
Given:
OP = 17ST = 31PQ = 7Since Triangle OPQ is similar to triangle RST, therefore:
RS/OP = ST/PQ
Substitute
RS/17 = 31/7
Cross multiply
RS = (31 × 17)/7
RS = 75.3
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In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.
Let the total number of apples in the basket be m
12% of the apples are rotten, and apples in good condition are 66
Therefore, according to the question,
[tex]88\% \: of \: m= 66[/tex]
[tex]→ \frac{88}{100}× m = 66[/tex]
[tex]→ m = \frac{(66 \times 100)}{88} [/tex]
[tex]→ m = 3 \times 25[/tex]
[tex]→ m = 75[/tex]
Therefore, total number of apples in the basket is 75.
[tex]\red\bigstar \huge \color{blue}{ \tt{answer}}[/tex]
Let the total number of apples in the basket be x
• The apples are rotten = 12%
• The apples in good condition = 66
So ,
[tex]\bold{88\% \: of \: x = 66 }[/tex]
[tex] \bold{↪\frac{88}{100} × x = 66 }[/tex]
[tex]\bold{↪x = \frac{(66×100)}{88} }[/tex]
[tex]\bold{↪x = 3 × 25}[/tex]
[tex] \bold{↪x = 75}[/tex]
[tex]\bold{∴}[/tex]Total number of apples in the basket is 75
What is the area of a regular triangle with perimeter = 36 in??
Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
Equilateral triangle
Solve for area
A≈62.35in²
P Perimeter
36
in
a
a
a
a
a
a
a
P
A
Using the formulas
A=3
4a2
P=3a
Solving forA
A=3P2
36=3·362
36≈62.35383in²
If <2 and <3 are supplementary angles, and measure of <3 = 170°; find the measure of <2.
Answer:
<2=10
Step-by-step explanation:
because if they are supplementary, they are on the same line, and a line is 180-degrees so 180-170=10-degrees which is angle 2.
Suppose you buy a 6 percent corporate bond. The face value of the bond is $5,000, but you buy the bond at 92. What is the yield on this bond? (Calculate to one decimal place.)
Based on the coupon rate on this corporate bond and the face value, the yield on the bond is 15.2%.
What is the yield on this bond?The number of periods is missing so we shall assume a maturity period of one year.
The rate can be found using an Excel worksheet or a financial calculator.
Using an Excel worksheet, the relevant function is the RATE function and the following details will be needed:
Nper = 1 year
Pmt = 6% x 5,000
= $300
Pv = (5,000 * 0.92)
= $4,600
Pv = -4600 because it should be negative.
Fv = $5,000
The yield you will get is 15.2% as shown in the attached image.
Find out more on bond yields at https://brainly.com/question/7967102.
2(r+7)
———— < r+3
-6
Answer:
3 +7> 9-^2 = 47
Step-by-step explanation: i did this
Barbara used the distributive property to write an expression that is equivalent to 7 d 63. Her work is shown below. The greatest common factor is 7 so 7 d 63 = 7 (d 63) What was Barbara’s error? Barbara wrote (d 63) instead of 63 d). Barbara wrote (d 63) instead of (d 9). Barbara wrote (d 63) instead of (d 56). Barbara wrote (d 63) instead of (10 d).
The error that Barbara's made is that Barbara wrote (d+63) instead of (d+9).
What is Distributive property?The distributive property of multiplication is that when two numbers are added such as (a+b) and multiplied by a third number such as x, then the result will be the sum of multiplication of the third number with the first number (xa) and the third number with the second number (xb).
x(a+b) = xa + xb,
The expression which is equal to the expression 7d+63 can be written as,
[tex]7d+63\\\\=7(d+9)[/tex]
Hence, the error that Barbara's made is that Barbara wrote (d+63) instead of (d+9).
Learn more about Distributive property:
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Answer:
Step-by-step explanation:
wrote (d 63) instead of (d 9). Barbara
The measure of an angle is 11.3°. What is the measure of its supplementary angle?
Answer: 168.7 degrees
Step-by-step explanation:
Supplementary angles have measures that add to 180 deg, so 180-11.3=168.7
Evaluate a + (-b) where a = 4 and b = 2
Ivy invested $150 000 in a savings account that offers to pay simple interest of 0.2% per year. How much interest will she receive at the end of one year?
Answer:
The answer is the CD was for 3 years.
Step-by-step explanation:
First, write the equation.
I=Prt
Next, substitute the given values.
$198=$1,200×5.5%×t
Next, write the percent as a decimal.
$198=$1,200×0.055×t
Next, simplify.
$198=$66×t
Then, solve for t.
3=t
Ivy will receive $300 in interest at the end of one year.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the interest Ivy will receive at the end of one year, we need to multiply the amount she invested by the interest rate:
Interest = Principal x Rate
Here, the principal is $150,000 and the rate is 0.2% or 0.002 (as a decimal):
Interest = $150,000 x 0.002
Interest = $300
Thus,
Ivy will receive $300 in interest at the end of one year.
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HELP, URGENT!!!!!!!!!!!
Question: Quadrilateral GABE is a square. Assume that point A is the centre of the circle. If the circumference (perimeter of a circle) is 201 ft., find AE.
Solution:
πd = C
πd = 201
3.14(d) = 201
diameter = 64.01
radius is half of the diameter.
radius = 64.01/2
radius = 32
GA = 32
As its sqaure, all sides are equal
GA = AB = GE = EB = 32
using Pythagoras theorem:
32² + 32² = AE²
AE = √2048.8
AE = 45.3 ft
Answer:
Step-by-step explanation:
C = πd = 2πr
201 = 2*3.14*AB
AB = 201 / (2*3.14) = 32
AE is the diagonal of square ABEG
Using Pythagoras theorem,
AE^2 = AB^2 + BE^2 = 2*AB^2
AE^2 = 2*32^2
AE = sqrt(2*32^2)
= 45.255
= 45.3 ft
27.)A candy bar sale totals to $5.50. What is the total cost with tax?
28.) Your Uncle Joe purchased three candy bars at $1.50 a piece. What is the total with
tax?
Answer:
27.) the candy bar sells for $5.90 with tax
28.) the candy bars sell for $4.80 with tax
Step-by-step explanation:
For amounts between $1.00 and $2.00, the tax is $0.10
For amounts greater than $2.00 and less than or equal to $4.00, the tax is $0.20.
For amounts greater than $4.00 and less than or equal to $6.00, the tax is $0.30.
For amounts greater than $6.00 and less than or equal to $8.00, the tax is $0.40.
For amounts greater than $8.00 and less than or equal to $10.00, the tax is $0.50
2) Find the maturity value of a loan of $2500 at simple interest that is to be repaid in 8 months. The interest rate is 4. 3%
Answer:
The answer is 71.67
Step-by-step explanation:
I=PRT
P=2500
r=4.3%
t=8months which is two thirds of a year
2500×4.3%×2/3
I=71.67
John is only allowed to work after school for 3 hours Monday to Friday and can work 7 hours on Saturday. He is not working on Sunday. How many school days and saturdays does he need to work to reach the needed amount ?
Answer:
the needed amount of what? community service?If so about 6 days of work on saturday and 3 school days. :)
solve for p:
p/-2 + -27 = 3
Answer:
p=-60
Step-by-step explanation:
When you add a negative, you are just subtracting.
p/-2-27=3
p/-2-27+27=3+27
2(-p/2)=2(30)
-p=60
-p/-1=60/-1
p=-60
Hope this helps! Pls give brainliest!
Please answer fast! (100 points)
Answer:
x = 2.25
Step-by-step explanation:
X equals to 2.25. This is because the scale factor between 8 and 6 is 1 1/3.
Next, we take 3 and divide it with 1 1/3, ending up with 2.25.
To the nearest foot, what amount of fencing is needed to surround the perimeter of the flower bed? 17 feet 33 feet 40 feet 50 feet.
We have two flower beds in this example, the first has a perimeter of 100 feet, and the second has a perimeter of 180 feet
The total is 280 feet
Perimeter of RectangleGiven Data
Dimension of the first flower bed
Length = 17 feet
Width = 33 feet
Perimeter = 2L + 2W
Perimeter = 2*17 + 2*33
Perimeter = 34 + 66
Perimeter = 100 feet
Dimension of the second flower bed
Length = 40 feet
Width = 50 feet
Perimeter = 2L + 2W
Perimeter = 2*40 + 2*50
Perimeter = 80 + 100
Perimeter = 180 feet
The total length will be 100+180 = 280 feet
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Answer:
It's 50
Step-by-step explanation:
D on edge
Distance 32 km; Time 20 minutes; Speed ? ___ kpm *
Answer:
56kmp
Step-by-step explanation:
That is all I know.
Answer:
1.6 kpm
Step-by-step explanation:
(32km)/(20min) = 1.6 km/min or kpm
The graph of an exponential model in the form y = a ⋅ bx passes through the points (3, 5) and (4, 10). Which point is also on the graph?
Answer:
The answer is D
Step-by-step explanation:
First, find a and b from the given points.
y = abx
5 = ab3
10 = ab4
b = 10/5 = 2
5 = a(23)
a = 5/8
y = (5/8) 2x
Test the choices:
x = 2 ⇒ y = 5/2
This rules out (a) and (b).
x = 5 ⇒ y = 20
In a group of 31 students, 7 study both Art and Biology.
14 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answer:
7/10 or 0.7 or 70%
Step-by-step explanation:
I would use a venn diagram, and fill it in! Then there are 7 do A &B and 3 who just do A. That as a probaility, your answer!
What is the minimum value for the function shown in the graph?
Enter your answer in the box
Answer:
The minimum value is -7 because of the negative sign on the number
Answer: Its -6
Step-by-step explanation:
its -6 because the functions lowest points are -6
70 Points+Brainliest for a good answer! Need help to finish homework for 7th-grade math! Only helpful answers or I will delete and report! Thanks <3
Answer:
L = 2.25 feet.
Step-by-step explanation:
My work is shown in the attached image! Let me know if there are any errors or if you have any questions. Best wishes.
I need help on this ASAP
Answer:
B and D
Step-by-step explanation:
Distributive property on 3(c-3) is 3c-12=20. D is the same. Divide instead.
Answer:
the 2nd and 4th one
Step-by-step explanation:
4( c - 3 ) = 8
you can either distribute the 4 which means multiply whats inside of the parenthesis by 4 , 4 * c = 4c and 4 * -3 = -12 to get 4c - 12 = 8
or you can divide both sides by 4 which will get you c - 3 = 2
4(c-3)/4 = c - 3
8/4 = 2
c - 3 = 2
The posted speed limit along Elm Street is 25 mph. Homeowners living on Elm Street claim that the
average speed of automobiles traveling on Elm Street is greater than the posted limit of 25 mph and plan to
investigate their claim by measuring the speed of 20 randomly selected cars. If the data support the claim,
the residents plan to ask the city council for more police patrol along Elm Street. Here are the speeds (in
mph) of the 20 cars:
26. 2 22. 9 28. 8 29. 0 24. 8
24. 7 24. 0 24. 4 25. 2 31. 1
25. 6 21. 6 27. 4 25. 6 26. 4
23. 7 28. 2 24. 1 26. 7 26. 8
(a) Is there convincing evidence at the a = 0. 05 significance level that the true mean speed of all cars
traveling on Elm Street is more than 25 mph?
(b) Referring to your conclusion, what type of error may have been made? Describe the error in the
context of this study
The sample of the speeds of 20 cars and at a 0.05 confidence level, we
have;
(a) There is not enough convincing evidence to suggest that the true mean speed of all cars travelling on Elm Street is more than 25 mph
(b) Type II error
What are the process to test the hypothesis?(a) Based on the given data, using MS Excel, we have;
The sample size, n = 20
The mean, [tex]\overline x[/tex] = 25.86
The standard deviation of the sample, s = 2.284
The null hypothesis, H₀; [tex]\overline x[/tex] = 25 mph
Alternative hypothesis, Hₐ; [tex]\overline x[/tex] > 25 mph
Given that the sample size is less than 30, the t-test is used, and the t-score is found as follows;
[tex]t= \mathbf{\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}}[/tex]
Which gives;
[tex]t=\dfrac{25.86-25 }{\dfrac{2.284}{\sqrt{20}}} \approx \mathbf{1.684}[/tex]
Using a graphing calculator, we have;
The probability ≈ 0.054
The critical-t ≈ 1.729
Given that the probability is larger than the significance level, we fail to
reject the null hypothesis.
There is not enough convincing statistical evidence to conclude that the
true mean of all cars travelling on Elm Street is more than 25 mph.
(b) The type of error is Type II error, given that there is a possibility that
the null hypothesis is failed to be rejected when it is actually false.
Given that the sample size is less than 30, it may be insufficient for the
Central Limit Theorem to be in effect.
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Which expression correctly shows the difference between the product of 2 and 10 and the sum of 7 and 3?
Answer:
(2*10)-(7+3)
Parentheses are used to avoid unwanted results.
BA=5 AC=3 What is the length of side BD? If needed, write your answer as a simplified fraction using the form a/b. units
Answer:
4
Step-by-step explanation:
a²+b²=c²
|BD|²+|AC|²=|AB|²
|BD|²+3²=5²
|BD|²+9=25
|BD|²=25-9
|BD|²=16
then you root both sides
therefore |BD|=4
A money jar contains only quarters and dimes. The ratio of quarters to dimes in a money jar is 2:7. How many dimes are in the money jar if there are 63 total coins?
A 14
B 18
C 49
D 54