Answer:
The increase is $18.
(In case you are asked about the percent increase,
percent increase = 20%)
Step-by-step explanation:
To find an increase, subtract.
$108 - $90 = $18
The increase is $18.
Answer: The increase is $18.
If you are asked about the percent increase, then use this formula:
percent change = (new number - old number)/(old number) × 100%
Here, the new number is $108. The old number is $90.
percent change = ($108 - $90)/($90) × 100%
percent change = $18/$90 × 100%
percent change = 0.2 × 100%
percent change = 20%
Since the percent change is a positive number, it is a percent increase.
Answer: percent increase = 20%
Find the area between the following curves.
y=x^3-x^2+x+8 ; y=5x^2-7x+8
Find where the two curves meet.
[tex]x^3 - x^2 + x + 8 = 5x^2 - 7x + 8 \\\\ \implies x^3 - 6x^2 + 8x = 0 \\\\ \implies x (x-2) (x - 4)= 0 \implies x=0, x=2, x=4[/tex]
The area between the curves is
[tex]\displaystyle \int_0^4 \left|\left(x^3-x^2+x+8\right) - \left(5x^2 - 7x + 8\right)\right| \, dx = \int_0^4 \left|x(x-2)(x-4)\right| \, dx[/tex]
When [tex]x[/tex] is between 0 and 2, [tex]x(x-2)(x-4)[/tex] is positive; when [tex]x[/tex] is between 2 and 4, [tex]x(x-2)(x-4)[/tex] is negative. So we split the integral at [tex]x=2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_2^4 x(x-2)(x-4)\,dx[/tex]
In the second integral, substitute [tex]y=x-2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_0^2 (y+2)y(y-2)\,dy[/tex]
[tex]\displaystyle \int_0^2 x(x-2) \bigg((x-4) - (x+2)\bigg) \, dx[/tex]
[tex]\displaystyle -6 \int_0^2 x(x-2) \, dx[/tex]
[tex]\displaystyle 6 \int_0^2 \left(2x - x^2\right) \, dx[/tex]
[tex]\displaystyle 6 \left(x^2 - \frac13x^3\right)\bigg|_0^2 = \boxed{8}[/tex]
Triangular prism advertising boards are being placed along the edge of the arena’s stage with the following dimensions: Select which of the nets below are labelled with the correct dimensions. What should the dimensions be of any advertisement that wants to fill the longest side of the shape?
The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m
According to the statement
we have given that the Triangular prism of size 0.75 m, 1m and length of 2m.
And we have to find the by which size of advertisement board need to fill the longest side of the shape.
A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
So, for this purpose,
we know that the longest side of triangular prism is 2m and we have to cover it with the advertising board.
Obviously the length of the advertising board is of 2m to cover the longest side of the shape.
So, The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m
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Write the expression. Then, check all that apply. twice the difference of a number and six A 2-column table with 4 rows. Column 1 is labeled Key Words with entries twice, the difference of, a number, six. Column 2 is labeled Replace with entries 2 times, (minus), n, 6. Replace “a number” with the variable, n. The two operations are multiplication and addition. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6). The expression is written as 2 × 6 – n.
The statements that apply to the algebraic expression are
Replace “a number” with the variable, n. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6)How to determine the algebraic expression?The complete question is added as an attachment
The statement is given as:
Twice the difference of a number and six
Represent the number with n.
So, the statement becomes
Twice the difference of a n and six
Twice means 2 *
So, we have
2 * difference of a n and six
Express difference as minus i.e. -
So, we have
2 * (n - 6)
Hence, the expression is written as 2(n - 6)
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How many 4-digit numbers can be created using
the digits 1, 3, 5, 7, and 9 without repeating any
digits within that 4-digit number?
Answer:
120 four digit numbers can be created from the gives.
Step-by-step explanation:
Solution
You are given 5 digits in the givens.
1 3 5 7 9
Therefore
5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.
Wich solutions are correct
Answer:
Rhoda and Ming are both correct, but Ming's prediction is closer because the result is accurate to two decimal places.
Step-by-step explanation:
A photograph is 3 in. longer than it is wide. When a 2-in. border is placed around the photograph, the total area of the photograph and the border is 108 in^2. Find the dimensions of the photograph.
width = 7
length = 10
Step-by-step explanation:
solve for the one letter that gets talked about the most
which is w or width
width = w
length = 3 + w
2 inch border means
width = w + 2
length = 3 + w + 2
area = length times width
area = ( 3 + w + 2 ) times (w + 2 )
108 = ( 3 + w + 2 ) times (w + 2 )
108 = ( w + 5 ) times (w + 2 )
( w + 5 ) times (w + 2 ) = 108
w^2 + 7w +10 = 108
w^2 + 7w - 98 = 0
going to make w = x
x^2+7x-98=0
(x-7)(x+14)
x = 7
x = -14
w=7
w= -14
cant have a negative measurement so w=7 is used
width = w
length = 3 + w
width = 7
length = 3 + 7 = 10
Please help me I’m stuck
Answer:
-1/3
5
Step-by-step explanation:
We need to complete
y = mx + b
with a slope, m, and with the y-intercept, b.
From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.
We now have y = mx + 5.
Now we need the slope.
We pick two points that are easy to read, (0, 5) and (3, 4).
m = slope = rise/run
To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.
Then we go left horizontally 3 units. The run is -3.
m = slope = rise/run = 1/(-3) = -1/3
Now we have the slope, so we can finish.
y = -1/3 x + 5
Answer:
-1/3
5
PLEASE I NEED THIS FAST a three dight number has one more ten than it has hundreds, and it also has one more than twice as many units as tens the sum of the number and that number reversed is 31 less than 10 cubed find the reverse number
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
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Determine the fifth term of the binomial expansion (x+y)^4
The expression, the fifth term of the binomial expansion is y^4
Binomial expansionBinomial expansion is a means of expanding expressions into terms
Given the expression (x+y)^4, according to the theorem, as the power of x is decreasing, the power of y will be increasing up till the power of the expression.
Expand (x+y)^4
(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + xy^3 + x^0y^4
Include the coefficients according to the Pascal triangle to have:
(x+y)^4 = x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4xy^3 + x^0y^4
(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4
From the expression, the fifth term of the binomial expansion is y^4
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Research suggests that students could benefit from later school starting times. A school administrative team is considering a proposal to move the starting time of the local schools one hour later than the current start time. To measure interest in the proposal, members of the team randomly select subjects attending a large high school soccer tournament played on the high school grounds on a Saturday morning. The team finds that 58% of those surveyed support a later high school start time. Which type of bias is most likely to be present in the survey results?
This is undercoverage bias because adults with older children are more likely to be included in the sample.
This is question wording bias because the phrasing of the later start times question may be confusing to some subjects.
This is nonresponse bias because some of those selected may choose to not provide their opinion on later start times.
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
The type of bias which is most likely to be present in the survey results is undercoverage bias because adults with older children are more likely to be included in the sample.
ResearchThis is a diligent inquiry or examination to seek or revise facts, principles, theories,or applications. It is used to make an extensive investigation or search for truth in an experiment.
Bias
In statistics, bias is the difference between the expectation of the sample estimator and the true population value, which reduces the representativeness of the estimator by systematically distorting it
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From the sample space S={1,2,3,4,...,15} a single number is to be selected at random. Given the following events, find the indicated probability.
A. the selected number is even
B. the selected number is a multiple of 4.
C. the selected number is a prime number.
P(BIA)
The probabilities of the given events are:
A. P(even) = P(A) = 7/15
B. P(multiple) = P(B) = 3/15
C. P(prime) = 6/15
D. P(B|A) = 3/7
What is probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.
P(E) = n(E)/n(S)
Calculation:The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
So, n(S) = 15
A. The selected number is even:
Consider the event as A.
The set of even numbers in the given sample is {2,4,6,8,10,12,14}
So, n(A) = 7
Then, the required probability is
P(A) = n(A)/n(S)
= 7/15
B. The selected number is a multiple of 4:
Consider the event as B.
The set of multiples of 4 in the given sample is {4,8,12}
So, n(B) = 3
Then, the required probability is
P(B) = n(B)/n(S)
= 3/15
C. The selected number is prime:
Consider the event as C.
The set of prime numbers in the given sample is {2,3,5,7,11,13}
So, n(C) = 6
Then, the required probability is
P(C) = n(C)/n(S)
= 6/15
D. calculate P(B|A):
Since events B and A are dependent events of the same sample,
n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is
P(B|A) = n(A∩B)/n(A)
⇒ P(B|A) = 3/7
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A rectangular tank 60cm long, 50cm wide and 24cm height was 1/3 filled with water at first. A tap was turned on to completely fill the tank. The rate of water flowing from the tap into the tank was 3 litre per minute. How long did it take to fill the tank completely? Give your answers in minutes.
What is the slope of the graph shown below?
Answer:
Option 3: -2
Step-by-step explanation:
The slope of the graph is negative, and the only option with a negative term for the slope is -2.
So the slope of the graph is -2.
if (a+10) and a are in straight line find the value of a
Answer:
a=170
Step-by-step explanation:
(a+10)=180[because being a straight line]
or, a+10=180
or,a=180-10
a=170
Therefore,a=170
-y(-6y-3) I need to combine like terms and simplify. I got 6y^2 + 3y by distributing. It's wrong and in the explanation it says use the distributive property to remove the parentheses and it gave -6y -3 -y as the first step answer. How the heck did they remove the parentheses or use the distributive property correctly?
if any number or variable is outside a parenthesis it will go to all the number rin the parenthesis.
in this case -y is outside the parenthesis so it will got to both the sides :
-y(-6y-3) = -6y x y - 3 x y
= -6y² -3y//
Enter the correct answer in the box.
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 1/3 What is the equation of function g?
Substitute a numerical value for k into the function equation.
Using translation concepts, the equation for function g is given by:
g(x) = 7x/3 + 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Supposing that we have a function f(x), a horizontal compression by a factor of a is equivalent to finding f(ax).
In this problem, the function is:
f(x) = 7x + 1.
For the horizontal compression by a factor of 1/3, we have that:
g(x) = f(1/3x) = 7x/3 + 1.
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jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
The required answers are calculated by using the simple interest formula:
a. She needs to deposit $793.65 in the account each month
b. The total money she put into an account for a year is $285,714.29
c. The total interest she earns is $514,285.71
What is the formula for simple interest?The formula for the simple interest is
A = P(1 + RT)
Where,
A - amount after T years
P - principal amount
R - the rate of interest
T - time (years)
Calculation:It is given that,
A = 8,00,000
T = 30 years
R = 6% = 0.06
So,
a. Finding the amount needs to deposit in the account each month:
We have A = P(1 + RT)
⇒ P = A/(1 + RT)
On substituting,
P = 8,00,000/(1 + 0.06×30)
= 8,00,000/2.8
= $285,714.29(per year)
Thus, the amount needs to deposit in the account for each month
= P/T×12
= 285,714.29/30×12
= $793.65
b. Finding the total money that she put into account:
That is nothing but,
P = A/(1 + RT)
On substituting,
P = 8,00,000/(1 + 0.06×30)
= 8,00,000/2.8
= $285,714.29(per year)
c. FInding the total interest:
We have I = A - P
⇒ I = 8,00,000 - 285,714.29
∴ I = $514,285.71
Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71
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How much is a one time investment of 250 be when invested at 6% for 40 years in compound annually
Answer:
600
Step-by-step explanation:
250/1 times 6/ 100 times 40/1
Please help me with this geometry question
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
HJ = 23.5 in[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = x, GH = y and GJ = z
x = y + 2z = x + y - 17x + y + z = 73put the value of x from equation 1 in equation 2
[tex]{ \qquad❖ \: \sf \:z = (y + 2) + y - 17} [/tex]
[tex]{ \qquad❖ \: \sf \:z = 2y - 15} [/tex]
now, put the value of x and z in equation 3
[tex]{ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73} [/tex]
[tex]{ \qquad❖ \: \sf \:4y - 13 = 73} [/tex]
[tex]{ \qquad❖ \: \sf \:4y = 86} [/tex]
[tex]{ \qquad❖ \: \sf \:y = 21.5 \: \: in} [/tex]
Now, we need to find HJ (x)
[tex]{ \qquad❖ \: \sf \:x = y + 2} [/tex]
[tex]{ \qquad❖ \: \sf \:x = 21.5 + 2} [/tex]
[tex]{ \qquad❖ \: \sf \:x = 23.5 \: \: in} [/tex]
[tex]{ \qquad \large \sf {Conclusion} :} [/tex]
HJ = 23.5 in3y+4z = -37
2x + 4y - 3z= 127
4y = 52
Answer:
x = 9, y = 13 , z = - 19
Step-by-step explanation:
3y + 4z = - 37 → (1)
2x + 4y - 3z = 127 → (2)
4y = 52 → (3)
divide both sides by 4 in (3)
y = 13
substitute y = 13 into (2) and solve for z
3(13) + 4z = - 37
39 + 4z = - 37 ( subtract 39 from both sides )
4z = - - 76 ( divide both sides by 4 )
z = - 19
substitute y = 13 and z = - 19 into (2) and solve for x
2x + 4(13) - 3(- 19) = 127
2x + 52 + 57 = 127
2x + 109 = 127 ( subtract 109 from both sides )
2x = 18 ( divide both sides by 2 )
x = 9
solution is x = 9, y = 13 , z = - 19
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the standard normal table to estimate the proportion.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
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The guy wire is approximately blank feet long
Answer: The guy wire = 393.4 ft
Step-by-step explanation:
Given images:
Refer to the attachment below (I apologize for the bad writing on the computer)
Given information:
Height of the tower = 175 ft
Height of the wire = 15 ft from the top (Opposite)
Angle with the ground = 24°
Length of wire = Unknown (Hypotenuse)
Determine the trigonometric function:
The primary choice will be the Sine function because the angle is opposite to the height and the wire is the hypotenuse of the system.
Determine the equation:
sin θ = (Opposite) / (Hypotenuse)
sin (24°) = (175 - 15) / (Length)
Simplify value in parenthesis
sin (24°) = (160) / (Length)
Multiply the Length of wire on both sides
sin (24°) * (Length) = (160) / (Length) * (Length)
sin (24°) * (Length) = (160)
Divide sin (24°) on both sides
sin (24°) * (Length) / sin (24°) = (160) / sin (24°)
Length = 160 / sin (24°)
[tex]\Large\boxed{Length~=~393.4~ft}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
There are 3 denominations of bills in a wallet: $1, 5$, and $10. There are five fewer $5-bills than $1-bills. There are half as many $10-billsas $5-bills. If there are $115 altogether, find the number of each type of bill in the wallet.
Answer:
15 $1 bills
10 $5 bills
10 $10 bills
Step-by-step explanation:
Let x = number of $1 bills
"There are five fewer $5-bills than $1-bills."
The number of $5 bills is x - 5
"There are half as many $10-bills as $5-bills."
The number of $10 bills is (x - 5)/2.
A $1 bill is worth $1.
x $1 bills are worth x × 1 = x dollars
A $5 bill is worth $5.
x - 5 $5 are worth 5(x - 5) dollars.
A $10 bill is worth $10.
(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.
Now we add the value of each type of bills and set it equal to $115.
x + 5(x - 5) + 5(x - 5) = 115
x + 10(x - 5) = 115
x + 10x - 50 = 115
11x = 165
x = 15
There are 15 $1 bills.
$5 bills: x - 5 = 10 - 5 = 10
There are 10 $5 bills
$10 bills: (x - 5)/2 = (15 - 5)/2 = 5
There are 5 $10 bills
Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills
Check:
First, we check the total value of the bills.
15 $1 bills are worth $15
10 $5 bills are worth $50
10 $10 bills are worth $50
$15 + $50 + $50 = $115
The total does add up to $115.
Now we check the numbers of bills of each denomination.
The number of $1 is 15.
The number of $5 is 5 fewer that 15, so it is 10.
The number of $10 bills is half the number of $5 bills, so it is 5.
All the given information checks out in the answer. The answer is correct.
SAT Math Question
Correct Answer: D
I was confused with A and D while solving this problem.
I get why D is the right answer but why is A wrong?
I'm tentatively changing my answer to say this kind of relies on practical knowledge of how stores tend to operate. If 20 coupons are given out, the store has sold all 500 shirts, arguably at a loss to the retailer. They have to have more shirts in stock to be sold at full price because, well, that's how they make money. It's more likely that such a store would carry more than just 500 shirts at the start of each day, so A is (probably) wrong.
WILL GIVE BRAINLIEST!!!
Warning: If you do not meet the requirements which I have listed below, I will report you.
1. Give the right answer
2. Do not say, "I don't think any of them work"
3. GIve a clear and concise explanation (no skipping steps)
4. Explain what you are doing and why you are doing it.
(Attached below is a photo of the equation)
Without using general formula we will solve it in bit lengthy manner
For first half
Time=Distance/Speed
340/2721.25hFor second half
Time
1000/(228+272)1000/5002hSo
Average speed
Total distance/Total time(1000+340)/(2+1.25)1340/3.25412.3km/hOption C
The answer is 412.3 km/h.
The formula to find average velocity is :
[tex]\boxed {V_{avg} = \frac{d_{1}+d_{2}}{t_{1}+t_{2}}}[/tex]
Let's find t₁ and t₂.
t₁ (from London to Paris) : 340/272 = 85/68 = 5/4 hourst₂ (from Paris to Barcelona) : 1000/500 = 2 hoursNow, let's substitute in the formula to get the answer.
v (avg) = [(1000 + 340) / (5/4 + 2)]v (avg) = 1340/ (13/4)v (avg) = 5360/13v (avg) = 412.3 km/hExplain why [tex]x[/tex] and [tex]3x + 5[/tex] are factors of the expression [tex]x(3x + 5)^{2}[/tex] and not terms of the expression.
[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.
Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.
What are terms and factors in an expression?
Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.
For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.
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f(x)=2x-6 Match each transformation of f(x) with its description
The transformation of the function is illustrated below
How to match the transformation?Parent function is: f(x) = 2x - 6
Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10
stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24
shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14
compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6
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Use a table of values to graph the function ƒ(x) = |x + 2| – 1. Select the correct graph below.
Evaluate each expression given the variable. 3x+7, when x=2
Answer:
13
Step-by-step explanation:
3x + 7
x = 2
3 × 2 + 7 = 6 + 7 = 13
Hi there.
3x+7
x=2 :
3(2)+7
6+7
13
That's it.
A total load of 28,800 watts is distributed equally over 15 circuits. What is the load per circuit in watts? i need help with solving this, need a step by step for later on
Answer:
1,920 watts per circuit
Step-by-step explanation:
To find the load for 1 circuit (per circuit) we can divide 28,800 watts by 15 circuits
28800/15 = 1,920 watts per circuit