The number of terms of the 2nd A.P if its common difference is given as 4 is 76.
What is common difference?
The difference between consecutive integers in an arithematic sequence is a frequent distinction. Simply subtract the first word from the second term, or the second from the third, or anything similar, to find it. See how we have to add 8 each time to reach the following term? Thus, our common difference is eight.
1st A.P
Let 1st term be a d = 6
Therefore T51 = a + ( 51 - 1 )6
= a + 300
Now 2nd A.P
let the 1st term be a
Therefore for n no. of terms,
lats term, a + ( n - 1 )4
But according to the question:
a + ( n - 1 )4 = a + 300
n - 1 = 300/4
n = 75 + 1
n = 76
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Which of the contexts below represents exponential growth?
The amount of a certain medication in a person's bloodstream decreases by
every hour.
Snow was falling at a rate of 1.75 inches per hour.
A population of 200 bacteria quintuples every week.
A car depreciates at a rate of 5.3% per year.
Answer:
I believe it would be "A population of 200 bacteria quintuples every week"
Step-by-step explanation:
If it is quintupling each week then the number is getting larger and larger exponentially.
The height of square room is Sm and volume is 180m³. Find the length.
Answer:
length = 6m
Step-by-step explanation:
H=5m
V=180m^3
Here
V=l^2 ×H ( being a square)
180=a^2×5
a^2=36
a=6m
What is the percentage of 150 out of 329.5 million?
The number 150 is 0.0000455 % out of 329.5 million
How to determine the percentage?The statement is given as
the percentage of 150 out of 329.5 million
The percentage can be calculated as
Percentage = 150 out of 329.5 million *100%
Express as fraction
So, we have
Percentage = 150/329.5 million *100%
Rewrite as
Percentage = 150 *100/329.5 million %
Evaluate the product
Percentage = 15000/329.5 million %
Evaluate the quotient
Percentage = 0.0000455 %
Hence, the percentage of 150 out of 329.5 million is 0.0000455 %
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evaluate log49 base 1/7
Answer:
Step-by-step explanation:
Exact Form:
1/2
Decimal Form:
-0.5
Answer:
- 2
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{\frac{1}{7} }[/tex] 49 = n , then
49 = [tex](\frac{1}{7}) ^{n}[/tex]
49 = [tex](7^-1)^{n}[/tex] , that is
7² = [tex]7^{-n}[/tex]
since bases on both sides are equal then equate exponents
- n = 2 ( multiply both sides by - 1 )
n = - 2
Sum of 8 consecutive numbers is 124. Find the numbers
i will mark you as brainliest for giving breif explanation step by step
Answer:
x = 12
Step-by-step explanation:
Be the 8 consecutive numbers like this:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) = 124
8x + 28 = 124
8x = 124 - 28
8x = 96
x = 12
help me i need help.
Answer:108 inches
Step-by-step explanation:
to find the area of one of the right triangles you do.
base = 6/2 =3
3x6=18
18/2=9
there are 8 right triangles so you would do
9x8 = 72.
then you would add 72 and the area of the square in the middle
6x6=36
36+72= 108
so Area of SA = 108 inches ^2
Find the absolute value of x
4-|x|=1
Answer:
3
Step-by-step explanation:
Absolute value is how far away the value is from 0. The only value of x that would make this equation true is 3.
Create an Equivalent expression for 18^-7*18^5
4(-8x + 5) - (-33x - 26)
Answer:
x+46
Step-by-step explanation:
Distribute
Combine like terms
twice the diffrence of a number and 2 equals 8
Answer:
2(x - 2) = 8
x = 6
Step-by-step explanation:
2(x - 2) = 8
2(x - 2) = 8
2x - 4 = 8
+4 +4
-----------------
2x = 12
÷2 ÷2
----------
x = 6
I hope this helps!
On a plane, 2 men had 135 kilograms of luggage added together. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage. The charge was at a flat rate. If all of the luggage belonged to one person, the ecess luggage charge would have been $8.10. At most, how many kilograms of luggag is each person permitted to bring onto the plane free of an additional charge?A. 55 kilogramsB. 50 kilogramsC. 45 kilogramsD. 40 kilograms
Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.
Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as
[tex]\begin{gathered} x=a+z \\ y=a+w \end{gathered}[/tex]Since their total amount of luggage added together was 135 kg, this gives to us the following equation
[tex]x+y=135[/tex]The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore
[tex]\begin{gathered} zr=1.35 \\ wr=2.70 \end{gathered}[/tex]If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.
[tex]\begin{gathered} \frac{zr}{wr}=\frac{1.35}{2.70} \\ \frac{z}{w}=\frac{1}{2} \\ w=2z \end{gathered}[/tex]If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be
[tex]a+p=135[/tex]Using the "rate formula" we created before, we can also write p as a function of z.
[tex]pr=8.10\Rightarrow\frac{pr}{zr}=\frac{8.10}{1.35}\Rightarrow p=6z[/tex]Rewritting all the total amounts, we have
[tex]\begin{gathered} a+6z=135 \\ a+2z=y \\ a+z=x \end{gathered}[/tex]If we add the equations for x and y together, we have
[tex]\begin{gathered} (a+z)+(a+2z)=(x)+(y) \\ a+z+a+2z=x+y \\ 2a+3z=x+y \end{gathered}[/tex]From the first equation, we know that the sum between both total amounts of luggage is equal to 135.
[tex]\begin{cases}x+y=135 \\ 2a+3z=x+y\end{cases}\Rightarrow2a+3z=135[/tex]Now, we have two equations for our two variables.
[tex]\begin{cases}2a+3z=135 \\ a+6z=135\end{cases}[/tex]If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).
[tex]\begin{gathered} 2\cdot(2a+3z)-(a+6z)=2\cdot(135)-135 \\ 4a+6z-a-6z=270-135 \\ 3a=135 \\ a=45 \end{gathered}[/tex]The amount of luggage permitted to bring onto the plane for free is 45 kilograms.
Elyse uses 42 gallons of water for a 10-minute
shower. Write and solve a prediction problem that uses this information.
Water used in three minutes in the shower is 12.6 gallons.
What is unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given Data
Elyse uses 42 gallons of water for a 10-minute shower,
Let
the time in minutes at position x
y=the quantity of water in gallons
The fact that
[tex]\frac{y}{x}[/tex] = [tex]\frac{42}{10}[/tex] = 4.2x
The unit price equals
The slope of the linear equation is equal to the unit rate.
then
y=4.2x
Problem
How much water will Elyse use in her shower for three minutes?
x = 3 minutes
substituting in the previous equation
y = 4.2x
y = 4.2(3)
y = 12.6
Water used in three minutes in the shower is 12.6 gallons.
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Mia is factoring the polynomial
x^2+4x−12. She uses the steps shown.
x^2+4x−12
Step 1
x^2+6x−2x−12
Step 2
(x^2+6x)−(2x+12)
Step 3
x(x+6)−2(x+6)
Step 4
(x+6)(x+2)
In which step did Mia make an error?
Answer:
Step 4
Step-by-step explanation:
Mia made a mistake in step 4.
Step3: x(x + 6) -2(x + 6)
In both terms, (x + 6) is common.
Step 4: When we take (x + 6) out, it will be (x + 6 ) (x - 2)
The assets and liabilities of a credit union banker are listed below.
What is the total net worth is the banker pays off the student loans?
A. $219,869
B. $247,517
C. $233,693
D. $252,304
Given the credit union banker's assets and liabilities, their total net worth is C. $233,693.
What is the net worth?The net worth of an individual is the difference between their assets (long-term and short-term) and their liabilities (long-term and short-term).
The net worth is equivalent to the equity of a business, which refers to the net assets owned by the stockholders after paying off all debts.
Assets:Car Value = $29,850
Savings Accounts = $12,409
Treasury Bonds = $10,000
Checking Account Balance = $19,419
Home Value = $194,450
Total assets = $266,128
Liabilities:Car loan = $10,560
Student Loans = $13,824
Credit Card Balance = $8,051
Total liabilities = $32,435
Net worth = $233,693 ($266,128 - $32,435)
Thus, the banker's net worth is not $219,869, $247,517, or $252,304 but Option C.
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Answer:
$247,517
Step-by-step explanation:
ITS RIGHT ON THE TEST GUYS ! :)
-(8-²)=
Evaluate the expressions
After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which means 2 times x plus 3.So, -(8⁻²):
Now, evaluate -(8⁻²) as follows:
-(8⁻²)-(1/64)- 1/64Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.
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Find the area of square plot of land whose each side measures 17/2
The area of the land is 289/4 square units
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the shape?The given parameters are
Shape = Square
Side length = 17/2
The area of a square shape is
Area = Side length^2
So, we have
Area = (17/2)^2
Evaluate the exponent
Area = 289/4
Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units
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he function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval −1≤x≤0?
The estimate of the average rate of change f is -2
How to estimate the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-1 ≤ x ≤ 0
This can be rewritten as
x = -1 to x = 0
This can also be represented as
(a, b) = (-1, 0)
From the attached graph, we have
f(-1) = 7
f(0) = 5
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(-1) - f(0)]/[-1 - 0]
So, we have
Rate = [7 - 5]/[-1 - 0]
Evaluate
Rate = -2
Hence, the average rate of change f is -22
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Question 1 (10 points)
[tex] = 2^{3} \\ = 2 \times 2 \times 2 \\ = (2 \times 2) \times 2 \\ = 4 \times 2 \\ = 8[/tex]
ATTACHED IS THE SOLUTION
LAST OPTION IS THE ANSWER.
By what number should you multiply $3\frac{1}{3}$ to get a product of $4$? Express your answer as a mixed number.
The number you should multiply 3 1/3 to get a product of 4 is 1 1/5
How to determine the number?From the question, the statement is given as
What number should you multiply 3 1/3 to get a product of 4
Let the number be x
So, we have the following representation
3 1/3 * x = 4
Express 3 1/3 as an improper fraction
So, we have the following representation
10/3 * x = 4
Multply both sides by 3
So, we have
10 * x = 12
Divide both sides by 10
This gives
x = 12/10
Express as mixed numbers
x = 1 1/5
Hence, the number is 1 1/5
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Hello, please I need the right answer for this:
Answer: (4) [tex]y=2x[/tex]
When you look at the table, you can see that the y values are double the x values they are associated with. Therefore, to get to the y value, the x values must be multiplied by 2, which would be the equation [tex]y=2x[/tex]
Please help!!!
Have school tomorrow
This is due tomorrow!
I have no clue how to do this
Yes , ∠WGR is congruent ∠GHR because both angles are on one line.
What does the word "congruent" mean in math?
If it is possible to impose one geometric figure on the other such that their surface area coincides, that geometric figure is seen to be congruent, or to be in the connection of congruence.Congruent Figures Examples Two butterflies that are the same size and form. Two candy ice creams of equal size and shape. Two equal Lego bricks in respect of size and shape.a) No, ∠PHG is not congruent ∠MGH because both angles are not equal.
b) No, ∠RHG and ∠MGH are not supplementary angle because in supplementary angle is equal to 180° .
c) No, ∠SGW is not congruent ∠PHV.
d) Yes , ∠WGR is congruent ∠GHR because both angles are on one line.
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A line has a slope of 1/4 and includes the points (-6, -7) and (z, -5) what is the value of z
Fill in the blank to make a perfect square trigeminal x^+18x+
The number that fills in the blank to make a perfect square trigeminal of the given expression is 81.
Given expression:
[tex]x^2+18x +[/tex] _
We have to find the number that will fill the blank.
A perfect square trigeminal is an algebraic expression that is of the form ax 2 + bx + c, which has three terms. It is obtained by the multiplication of a binomial with itself.
Let the number that fills the blank be a.
Hence, the expression becomes:-
[tex]x^2+18x +a[/tex]
To make it a perfect square geminal, the expression must be a perfect square of a binomial.
We know that,
[tex](x+y)^2=x^2+2xy+y^2[/tex]
Comparing it with given expression, we get
2xy = 18x and,
[tex]y^2=a[/tex]
Hence,
y = 9
a = [tex]9^2[/tex] = 81
Hence, the number that fills the blank is 81.
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Julie is flying to New York. She has budgeted $200 to
rent a car for 3 days while she is there. If the car rental
is $44 per day plus $0.25 per mile, what is the
maximum number of miles Julie can drive the car?
The maximum number of miles Julie can drive the car is 272 miles.
Let's check how:
Julie's budget for renting a car is $200.
number of days she'll rent a car is 3.
car rental per day is $44 + $0.25 per mile.
so to know maximum no. of miles she can drive
we'll first subtract the 3 days rent from Julie's budget = $200 - ( 3 x $44 )
= $200 - $132
= $132
Now, the left money is $68.
so, we will divide $68 by $0.25 to know how much miles she can drive.
= $68 ÷ $0.25
= 272 miles
Hence, the maximum number of miles Julie can drive the car for 3 days is 272 miles.
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Answer:
Step-by-step explanation:
6b³ +16b² -15b-40
Factor
Answer:
(2[tex]b^{2}[/tex] - 5) (3b + 8)
Step-by-step explanation:
First factor out 2[tex]b^{2}[/tex] from the first set of parentheses and -5 from the second
2[tex]b^{2}[/tex] ( 3b + 8) - 5 (3b + 8)
Next factor out (3b + 8)
(2[tex]b^{2}[/tex] - 5) (3b + 8)
(9) 0.5= A. 3 B. 4.5 C. 1/81
The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]. The evaluated expression is 3a+4.5b+c=40.5
Given that,
The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]
We have to evaluate the expression
Evaluating an algebraic expression involves determining its value when a particular integer is substituted for a variable. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
Take,
0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]
0.5×81=a×3+b×4.5+c
40.5=3a+4.5b+c
The expression can be written in 4 ways
1st- 3a+4.5b+c=40.5
2nd- a=[tex]\frac{40.4-4.5b-c}{3}[/tex]=13.4-1.5b-c (this is the expression with subject a)
3rd- b= [tex]\frac{40.5-3a-c}{4.5}[/tex]=9-1.6a-c (this is the expression with subject b)
4th- c= 40.5-3a-4.5b (this is the expression with subject c)
Therefore, The evaluated expression is 3a+4.5b+c=40.5
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Mr. Mole left his burrow and started digging his way down. A represents Mr. Mole's altitude relative to the ground (in meters) after t minutes.
Based on the model that shows the altitude of Mr. Mole relative to the ground, the rate at which Mr. Mole was digging was 2.3 meters down per minute.
How to find the rate?When given a linear function, the rate that the model progresses is given by the slope. The slope in a linear function can be found as:
y = mx + b
m = slope
b = y-intercept
In the model given for Mr. Mole's digging, which is -2.3t - 7, the slope is -2.3.
This means that Mr. Mole is digging downwards at 2.3 meters per minute.
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Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.
The value obtained for z-score for the given sample mean is 0.5.
What is described as the z-score?A Z-score is a numerical quantification that describes the relationship of a value to the mean of a set of values. The Z-score is expressed in standard deviations of the mean. A Z-score of 0 signifies that the data point's points tally is the same as the mean score.For the given question;
The formula for finding the z-score is;
z = (x - μ)/σ
x = sample size
μ = population mean
σ = standard deviation population.
The given values are-
μ = 25σ = 20x = 35Put the value in the z-score.
z = (35 - 25)/20
z = 10/20
z = 0.5
Therefore, the value obtained for z-score for the given sample mean is 0.5.
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The correct question is-
Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.
the ratio as a fraction in simplest form, 26.1 miles : 3.6 hours ?
Answer:8.7:1.2
Step-by-step explanation: divide both by 3
The table shows information about the
masses of some dogs.
a) Work out the minimum number of
dogs that could have a mass of more than 27 kg.
b) Work out the maximum number of
dogs that could have a mass of more than 27 kg.
a) The minimum number of dogs that could have a mass of more than 27 kg is 4.
b) The maximum number of dogs that could have a mass of more than 27 kg is 17.
The given table shows information about the masses of some dogs.
a) Because we need the minimum number of dogs,
Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.
b) Because we need the maximum number of dogs,
Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17
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Answer:
Step3
-by-step explanation: