Answer:
The recycle percent as a rate per 100 is 0.03 per hour.
And 12 dolls are recycled each hour during production.
Step-by-step explanation:
The question is incomplete so below is the complete question:
A factory produces toy dolls at a rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100. How many dolls are recycled each hour during production?
Now, to express the recycle percent as a rate per 100, And to find the number of dolls are recycled each hour during production.
Number of dolls factory produces at rate per hour = 400.
Percent of recycle = 3%.
So, to express the recycle percent as a rate per 100:
[tex]3\%\ per\ 100[/tex]
[tex]=\frac{3}{100} \ per\ hour[/tex]
[tex]=0.03\ per\ hour.[/tex]
So, to get the number of dolls are recycled each hour during production:
3% of number of dolls factory produces at rate per hour.
[tex]=\frac{3}{100} \times 400[/tex]
[tex]=0.03\times 400[/tex]
[tex]=12.[/tex]
The dolls are recycled each hour = 12.
Therefore, the recycle percent as a rate per 100 is 0.03 per hour.
And 12 dolls are recycled each hour during production.
Johns bank account increased in value from last year to this year by 8% to $250 if the the account increases by the same percentage over the next year what will be the value next year
A.$258
B.$260
C.$264
D.$268
E.$270
Answer:
$ 270
Step-by-step explanation:
Do 250 X 1.08 to get the answer
Using the percentage increase formula, John's bank account value of $250 will increase by 8% to $270 after one year.
To find the future value of John's bank account, we will use the percentage increase formula. If his account increased by 8% this year to $250, we can calculate next year's balance by multiplying $250 by 1.08 (which represents a 100% principal plus an 8% increase).
Step-by-step calculation:
Convert the percentage increase to a decimal: 8% becomes 0.08.Add 1 to the decimal equivalent of the percentage increase to find the growth factor: 1 + 0.08 = 1.08.Multiply the current year's value by the growth factor: $250 times 1.08.Calculate the result: $250 times 1.08 = $270.Therefore, the value of John's bank account if it increases by the same percentage over the next year will be $270.
Maria went to the restaurant and waited 90 seconds to place her order. Use the trend line equation to predict how many employees were working. Round to the nearest whole number if necessary.
Answer:
3 employees
Step-by-step explanation:
The complete question is
The manager of a fast food restaurant collected data to study the relationship between the number of employees working registers and the amount of time customers waited in line to order. He made a scatter plot of the data and created a trend line with the equation y = -70x + 300, where y is the total amount of time waited in seconds and x is the number of employees working registers. Maria went to the restaurant and waited 90 seconds to place her order. Use the trendline equation to predict how many employees were working. Round to the nearest whole number if necessary.
Let
x ---> is the number of employees working registers
y ---> is the total amount of time waited in seconds
we have
[tex]y=-70x+300[/tex]
This is the equation of a line in slope intercept form
where
The slope is equal to
[tex]m=-70\ \frac{seconds}{employee}[/tex] ---> is negative because is a decreasing function
The y-intercept is equal to
[tex]b=300\ sec[/tex]
For y=90 seconds
substitute in the linear equation and solve for x
[tex]90=-70x+300[/tex]
[tex]70x=300-90\\70x=210\\x=3\ employees[/tex]
To predict the number of employees based on a 90-second wait time, substitute 90 into the given trend line equation and solve for y. For example, using y = -0.1x + 10, we get approximately 1 employee. Ensure you use the specific trend line equation provided for accurate results.
To predict how many employees were working based on Maria's wait time of 90 seconds, we need the trend line equation that describes the relationship between waiting time and the number of employees.
Assuming we have a trend line equation of the form y = mx + b,
where y represents the number of employees, x the waiting time in seconds, and m and b are constants,you can substitute 90 for x and solve for y.
For example, if the trend line equation is y = -0.1x + 10, substituting 90 for x:
y = -0.1(90) + 10
y = -9 + 10
y = 1
Therefore, according to this trend line, approximately 1 employee would be working. Always remember to check your specific trend line equation and solve accordingly.
25.) If y varies directly as x, and y = -18 as x = -2, find y for the x-value of 20.
Answer: the value of y is 180
Step-by-step explanation:
If y varies directly as x, then as y increases,x increases and as y decreases, x decreases.
We would introduce a constant of proportionality, k. Therefore,
y = kx
When y = - 18, x = - 2
Therefore,
- 18 = - 2 × k
Dividing the left hand side and the right hand side of the equation by
- 2, it becomes
- 2k/ -2 = - 18/-2
k = 9
The expression becomes
y = 9x
Therefore, when x = 20,
y = 9 × 20 = 180
Yo sup??
since y varies directly with x we can say
y=kx
at y=-18, x=-2 then
-18=k*(-2)
k=9
therefore
y=9x
at x=20
y=9*20
=180
Hope this helps.
if you in invested $500 at 5% simple interest for 2 years, how much interest do you earn? show work and answer in complete sentances to earn full credit. if you invest $500 at 3% compound monthly for 2 years, how much interest do you earn? show work and answer in complete sentances to earn full credit which would you rather do?
Answer:
Step-by-step explanation:
1) The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 2 years
P = $500
R = 5%
Therefore
I = (500 × 5 × 2)/100
I = $50
2) Principal, P = $500
It was compounded monthly. This means that it was compounded 12 times in a year. So
n = 12
The rate at which the principal was compounded is 3%. So
r = 3/100 = 0.03
It was compounded for just 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.03/12)^12 × 2
A = 500 (1.0025)^24
A = $530.88
The interest is
530.88 - 500 = $30.88
Aidan is running for student body president. In today's election, he received 462 votes out of a total of 825 votes cast. What percent of votes did Aidan get? %
Answer:
Aidan got 56% of votes.
Step-by-step explanation:
Given:
Aidan is running for student body president. In today's election, he received 462 votes out of a total of 825 votes cast.
Now, to find the percent of votes did Aidan get.
Total votes cast = 825 votes.
Votes he received = 462 votes.
Now, to get the percent of votes Aidan get:
[tex]\frac{Votes\ he\ received}{Total\ votes\ cast} \times 100[/tex]
[tex]=\frac{462}{825} \times 100[/tex]
[tex]=0.56\times 100[/tex]
[tex]=56\%.[/tex]
Therefore, Aidan got 56% of votes.
Answer:
56%
Step-by-step explanation:
Aidan got fifty-six percent of the votes.
To solve this problem, start by letting p represent the unknown percent and write the percent as the fraction p over one hundred.
Write a second ratio that expresses the part-whole relationship between the numbers four hundred sixty-two over eight hundred twenty-five.
Set up a proportion between the two ratios.
Write the cross product equation. Eight hundred twenty-five p equals one hundred times four hundred sixty-two, or eight hundred twenty-five p equals forty-six thousand two hundred.
Divide each side of the equation by eight hundred twenty-five to solve for p.
p equals fifty-six.
Aidan received fifty-six percent of the votes cast.
Please look at the questions again! Some of the answers are incorrect. Here is a hint: For question 1, you should not spend more than one-third of $2,000? Calculate: $2,000 / 3. For question 2, how much is the rent and housing expenses? Calculate: $650 + $60 + $10 + $20 + $20. How much can you afford? You should not spend more than one-third of $2,100. Looks like the rent and expenses are too high for your budget, right?
Answer:question 1)$6.66.67
Question2) Rent and expenses =$760
Rent and expenses are too high for the budget
Step-by-step explanation:
1)$2000×(1/3)= $666.67
2)Rent and expenses =$(650+60+10+20+20)= $760
$2100×(1/3)= $700
Rent and expenses should not exceed one third of $2100, which is $700 but it exceeded by$60. Therefore budget is too high.
Final answer:
These Mathematics questions involve calculating budgets to manage income and expenses. For budgeting housing costs, the recommendation is not to exceed one-third of income. A budget table is used to track all monthly expenses against income to determine savings potential and necessary adjustments.
Explanation:
The subject of these questions is Mathematics, specifically focusing on budgeting and personal finance. In these scenarios, students are learning to apply mathematical operations to real-life situations involving income, expenses, and budget planning.
For question 1, you would calculate the maximum amount you should spend on housing from a $2,000 monthly budget by dividing $2,000 by 3, which gives you $666.67. This is because it's recommended to spend no more than one-third of your income on housing.
For question 2, adding together the rent and housing expenses ($650 + $60 + $10 + $20 + $20), you get a total of $760. If you have an income of $2,100, you should not spend more than $700 on housing (which is one-third of your income), so $760 is indeed too high for the budget.
Creating a budget table is an essential skill for financial literacy. When constructing one, you list your monthly income and subtract all your expenses, including housing, utilities, groceries, and any other costs, to see what is left for savings and discretionary spending. For example, with an after-tax monthly income of $2,589.10, if you spend $790 on rent, $75 on a cell phone, and have other listed expenses, you'd subtract all these from your income to see if you can save the desired 10%.
Parker was able to pay 44% of his college tuition with his scholarship.The remaining $10,054.52 he paid for with a student loan.What was the cost of Parker's tuition?
Answer: the cost of Parker's tuition is $17955
Step-by-step explanation:
Let x represent the cost of Parker's tuition.
Parker was able to pay 44% of his college tuition with his scholarship. This means that the amount that he was able to pay with his scholarship would be
44/100 × x = 0.44 × x = 0.44x
The amount that is remaining for him to pay would be
x - 0.44x = 0.56x
If he paid the remaining $10,054.52 with a student loan, it means that
0.56x = 10054.52
x = 10054.52/0.56
x = 17954.5
Rounding up to the nearest whole number, it becomes
x = $17955
A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a . 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x) = {((6)/(x)+(-5 x+18)/(x(x-3)), "if", x doesnt = 0 "and" x doesnt =3),( 3, "if", x=0) :} Show that f(x) has a removable discontinuity at x=0 and determine what value for f(0) would make f(x) continuous at x=0 . Must redefine f(0)= ?
The function f(x) has a removable discontinuity at x=0. To make f(x) continuous at x=0, we must redefine f(0) as -1/3.
To determine if f(x) has a removable discontinuity at x=0, we need to check if f(x) is either not defined or not continuous at x=0.
Looking at the definition of f(x), we see that f(0) is defined as 3. Therefore, f(x) is defined at x=0.
Next, let's examine the continuity of f(x) at x=0. We need to evaluate the limit of f(x) as x approaches 0.
Using the given definition of f(x), we have:
lim(x->0) (6/x) + (-5x + 18)/(x(x-3))
To evaluate this limit, we can simplify the expression by finding a common denominator. The common denominator is x(x-3):
lim(x->0) [6(x-3) + (-5x + 18)] / [x(x-3)]
Simplifying the numerator:
lim(x->0) (6x - 18 - 5x + 18) / [x(x-3)]
= lim(x->0) (x) / [x(x-3)]
Now, we can cancel out the x term:
lim(x->0) 1 / (x-3)
As x approaches 0, the denominator (x-3) approaches -3. Therefore, the limit is:
lim(x->0) 1 / (x-3) = 1 / (-3) = -1/3
Since the limit of f(x) as x approaches 0 exists and is equal to -1/3, we can redefine f(0) to be -1/3 to make f(x) continuous at x=0.
Thus, f(x) has a removable discontinuity at x=0, and we must redefine f(0)=-1/3 to make f(x) continuous at x=0.
Ben's car gets between 18 and 21 miles per gallon of gas. If his car's tank holds 15 gallons, what is the range of distance that Ben can drive on one tank of gas?
Answer:
Step-by-step explanation:
Ben's car gets between 18 and 21 miles per gallon of gas. If his car's tank holds 15 gallons, it means that the least distance that Ben can drive on one tank of gas would be
18 × 15 = 270 miles.
Also, the most distance that Ben can drive on one tank of gas would be
21 × 15 = 315 miles.
Therefore the the range of distance that Ben can drive on one tank of gas is between 270 miles and 315 miles. If d represents the distance, then the range is
270 ≤ d ≤ 315)
An escalator at a shopping center is 200ft and 9in long, and rises at an angle of 15 degrees. What is the vertical rise of the escalator. Round to the nearest inch
Answer: 623 inches
Step-by-step explanation:
We can model this escalator as a right triangle, in which its length is the hypotenuse and its vertical rise ([tex]x[/tex]) is on of the sides of the triangle (as shown in the figure).
So, if we want to find [tex]x[/tex] we have to use the trigonometric function sine:
[tex]sin(15\°)=\frac{opposite-side}{hypotenuse}[/tex] (1)
Here, the opposite side is [tex]x[/tex] and the hypotenuse is [tex]200 ft 9 in[/tex].
Now we have to transform [tex]200 ft 9 in[/tex] to inches, in this case we only have to convert [tex]200 ft[/tex] to inches, knowing that [tex]1 ft=12 in[/tex]:
[tex]200 ft \frac{12 in}{1 ft}=2400 in[/tex]
[tex]200 ft + 9 in=2400 in+ 9 in=2409 in[/tex]
Substituting this value in (1):
[tex]sin(15\°)=\frac{x}{2409 in}[/tex] (2)
Isolating [tex]x[/tex]:
[tex]x=frac{sin(15\°)}{2409 in}[/tex]
Finally:
[tex]x=623.49 in \approx 623 in[/tex]
An array with m rows and n columns is not: A: An m-by-n array. B: An n-by-m array. C: A two-dimensional array. D: An n times m dimensional array.
Answer:
B, An n-by-m array.
Step-by-step explanation:
when working with 2D arrays, rows come first and then columns. so all options here are correct except option B
Find the area of the shape (1,3) (5,3) (7,-1) (1,-1)
Step-by-step explanation:
The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)
To find, the area of the shape (quadrilateral) = ?
We know that,
The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]
= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]
= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]
= [tex]\dfrac{1}{2} [4+0-28+0][/tex]
= [tex]\dfrac{1}{2} [32][/tex]
= 16 square units.
Thus, the area of the shape (quadrilateral) is 16 square units.
Bill buys a stock that decreases by 20% on the first day, and then on the second day the stock increases by 30% of its value at the end of the first day. What was the overall percent increase in Bill's stock over the two days?
Answer:
4%
Step-by-step explanation:
Let the stock be $10
A 20% decline = 80/100 * 10
= 8
A 30% increase = 30/100 * 8
= 2.4 + 8 = 10.4.
Overall increase = 10.4 - 10 = 0.4
Percentage overall increase = 0.4/10 * 100
= 4%
Write a formula that describes the value of an initial investment of $300 growing at an interest rate of 6% compounded continuously.
The correct answer would be B.
The lower e is used for continuous compounding and it is raised by the interest rate times the amount of time
Formula that describes the value of an initial investment of [tex]\$300[/tex] growing at an interest rate of [tex]6\%[/tex] compounded continuously is equals to [tex]A(t) = 300e^{.06t}[/tex].
What is compounded continuously?" Compounded continuously is defined as the interest calculation and reinvestment of the amount over infinite period."
Formula used
[tex]A(t) = P e^{rt}[/tex]
[tex]A(t) =[/tex] Final amount
[tex]P =[/tex] Principal amount
[tex]t =[/tex] time period interest is applied
[tex]r=[/tex] rate of interest
According to the question,
Given,
Principal amount [tex]= \$300[/tex]
Rate of interest [tex]= 6\%[/tex]
As per the given condition interest compounded continuously,
Substitute the value in the formula of interest compounded continuously we get,
[tex]A(t) = 300 e^{\frac{6}{100} t}\\\\\implies A(t) = 300 e^{.06 t}[/tex]
Hence, Option (B) is the correct answer.
Learn more about compounded continuously here
https://brainly.com/question/8438875
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When large bags of candies are packaged, the number of candies in each bag must be within 4 of 120 pieces. Write an absolute value equation to represent p
Answer:
Step-by-step explanation:
p = 120 ± 4
Anything will help! Thank you.
Step-by-step explanation:
(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:
g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)
g = 8 − 2.5t
(b) If d is the distance traveled:
d = 60 mi/hr × t hr
d = 60t
(c) When George runs out of gas, g = 0.
0 = 8 − 2.5t
t = 3.2
The distance he travels is:
d = 60(3.2)
d = 192
George travels 192 miles.
3.2 hours after 8AM, the time is 11:12AM.
PLEASSEEEEEEEE HELP!!!
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle
DF represents the hypotenuse of the right angle triangle.
With m∠D as the reference angle,
DE represents the adjacent side of the right angle triangle.
EF represents the opposite side of the right angle triangle.
To determine EF, we would apply the Sine trigonometric ratio
Sin θ = opposite side/hypotenuse. Therefore,
Sin 26 = EF/4.5
0.44 = EF/4.5
EF = 4.5 × 0.44 = 1.98 yo 2 decimal places
suppose sin(a)=3/4
use the trig identity sin^2(a)+cos^2(a)=1
and the trig identity tan(a)=sin(a)/cos(a)
to find tan (a) in quad II.
Round to the nearest hundredth.
well, we know the sine, and we also know that we're on the II Quadrant, let's recall that on the II Quadrant sine is positive whilst cosine is negative.
[tex]\bf sin^2(\theta)+cos^2(\theta)=1~\hspace{10em} tan(\theta )=\cfrac{sin(\theta )}{cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ sin^2(a)+cos^2(a)=1\implies cos^2(a) = 1-sin^2(a) \\\\\\ cos^2(a) = 1-[sin(a)]^2\implies cos^2(a) = 1-\left( \cfrac{3}{4} \right)^2\implies cos^2(a) = 1-\cfrac{3^2}{4^2} \\\\\\ cos^2(a) = 1-\cfrac{9}{16}\implies cos^2(a) = \cfrac{7}{16}\implies cos(a)=\pm\sqrt{\cfrac{7}{16}}[/tex]
[tex]\bf cos(a)=\pm\cfrac{\sqrt{7}}{\sqrt{16}}\implies cos(a)=\pm\cfrac{\sqrt{7}}{4}\implies \stackrel{\textit{on the II Quadrant}}{cos(a)=-\cfrac{\sqrt{7}}{4}}\\\\[-0.35em]~\dotfill\\\\tan(a)=\cfrac{sin(a)}{cos(a)}\implies tan(a)=\cfrac{~~\frac{3}{4}~~}{-\frac{\sqrt{7}}{4}}\implies tan(a)=\cfrac{3}{4}\cdot \cfrac{4}{-\sqrt{7}}\\\\\\tan(a)=-\cfrac{3}{\sqrt{7}}\implies \stackrel{\textit{rounded up}}{tan(a) = -1.13}[/tex]
The person is a member for super for a female boss over in the and loss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss.
Answer:
1998
y=6x+1944
Step-by-step explanation:
The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss
it is explicit from the question that 9% of male workers prefer female boss in 1998. but we can predict a model for this by getting the slope of the graph
y=the year
x=the percentage of men who prefer a female boss
s=y2-y1/(x2-x1)
s=1998-1974/(9-5)
s=24/4
s=6
therefore we have
y=mx+c
y=6x+c........1
when y=1998,x=9
1998=6(9)+c
c=1944
from equation 1
y=6x+1944
A consumer survey indicates that the average household spends μ =$155 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation σ =$25. Based on this distribution,
What proportion of the population spends more than $175 per week on groceries?
How much money do you need to spend on groceries each week to be in the top 20% of the distribution?
How much does your family spend per week on groceries, what is your family�s percentile?
Answer:
a) 21.2%
b) $176.05 or more
c) 15.87%
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $155
Standard Deviation, σ = $25
We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(spends more than $175 per week on groceries)
P(x > 175)
[tex]P( x > 175) = P( z > \displaystyle\frac{175 - 155}{25}) = P(z > 0.8)[/tex]
[tex]= 1 - P(z \leq 0.8)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%[/tex]
b) P(X > x) = 0.2
We have to find the value of x such that the probability is 0.2
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 155}{25})=0.2[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 155}{25})=0.2 [/tex]
[tex]=P( z \leq \displaystyle\frac{x - 155}{25})=0.8 [/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < 0.842) = 0.8[/tex]
[tex]\displaystyle\frac{x - 155}{25} = 0.842\\\\x = 176.05[/tex]
A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.
c) My family spends on average $130 dollars on groceries.
P(less than $130)
[tex]P( x < 130) = P( z < \displaystyle\frac{130 - 155}{25}) = P(z < -1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]
Thus, my family percentile is 15.87%
a) 21.2%
b) $176.05 or more
c) 15.87%
We are given the following information in the question:
Mean, μ = $155
Standard Deviation, σ = $25
We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_(score) = \displaystyle(x-\mu)/(\sigma)[/tex]
a) P(spends more than $175 per week on groceries)
[tex]P(x > 175)P( x > 175) = P( z > \displaystyle(175 - 155)/(25)) = P(z > 0.8)= 1 - P(z \leq 0.8)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 175) = 1 - 0.788 = 0.212 = 21.2\%\\[/tex]
b) [tex]P(X > x) = 0.2[/tex]
We have to find the value of x such that the probability is 0.2
[tex]P(X > x) \\P( X > x) = P( z > \displaystyle(x - 155)/(25))=0.2 \\= 1 -P( z \leq \displaystyle(x - 155)/(25))=0.2 \\=P( z \leq \displaystyle(x - 155)/(25))=0.8[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < 0.842) = 0.8\\\displaystyle(x - 155)/(25) = 0.842\n\nx = 176.05[/tex]
A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.
c) My family spends on average $130 dollars on groceries.
P(less than $130)
[tex]P( x < 130) = P( z < \displaystyle(130 - 155)/(25)) = P(z < -1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 130) = 0.1587 = 15.87\%[/tex]
Thus, my family percentile is 15.87%
A golden rectangle has side lengths in the ratio of about 1 to 1.62. To the nearest tenth, what is length of the shorter side of a golden rectangle with a longer side length of 40 inches?
Answer: The length of the shorter side of a golden rectangle is about 24.7 inches.
Step-by-step explanation:
Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.
Since 1.62 > 1 , so
[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]
If the length of the longer side is 40 inches , then we have
[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]
Hence, the length of the shorter side of a golden rectangle is about 24.7 inches.
To find the length of the shorter side of a golden rectangle with a longer side of 40 inches, divide 40 by the golden ratio (1.62), yielding approximately 24.7 inches as the length of the shorter side, rounded to the nearest tenth.
Explanation:To calculate the length of the shorter side of a golden rectangle with a longer side length of 40 inches, we use the ratio of the sides of a golden rectangle. Given that this ratio is about 1 to 1.62, we divide the length of the longer side by the golden ratio (approximately 1.62) to find the length of the shorter side.
Using this method:
Length of longer side = 40 inchesLength of shorter side = 40 inches / 1.62Let's do the calculation:
Length of shorter side ≈ 24.7 inches (rounded to the nearest tenth)
A mathematically proficient students would approach a challenging problem solving task with a certain disposition. Describe at least two examples of what that disposition would look and sound like in a classroom.
Answer:
g6h12
Step-by-step explanation:
Answer: mmmmm.
Step-by-step explanation:
How do you do this problem?
Answer:
C) ¼ ∫ u⁵ du, where u = sin(4x)
Step-by-step explanation:
∫ cos(4x) sin⁵(4x) dx
Using u substitution:
u = sin(4x)
du = 4 cos(4x) dx
¼ du = cos(4x) dx
¼ ∫ u⁵ du
Can someone please help me?!?
Write an equation for the sine wave. What is the amplitude and period?
Now, you are going to determine the frequency of the tone you created.
Frequency=1/period
Part2
Finally, do some research on different frequencies. Pick 3 different sounds and determine their frequency. Compare and contrast those sounds to the frequency of your tone. What conclusions can you make about frequency?
Answer:
See the explanation.Step-by-step explanation:
Part 1:
An equation of sine wave can be written as y = 5 Sin(2x + 3).
The amplitude of the above equation is 5.
The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].
The frequency of the function is [tex]\frac{1}{\pi }[/tex].
Part 2:
[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]
The above given equations numbered 1, 2 and 3 represents three different sound waves.
For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].
For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].
For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].
Frequency of sounds refers the speed of vibration.
The taken three siounds has different frequencies.
Rebeca spent $32.55 for a photo album and three identical candles. The photo album cost $17.50 and the sales tax was $1.55. How much did each candle cost
Answer: $4.50 per candle
Step-by-step explanation:
$32.55 - $17.50 - $1.55 = $13.50 for all the candles
To find the price of a single candle we divide our answer by 3
13.50/3 = $4.50
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles. a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has. b.Write an algebraic expression to represent the number of large marbles she has. c.If Amy has a total of 560 marbles, how many of each size does she have? Show your work. (please i need help im really stuck)
Answer: she has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
Let w represent the number of small marbles Amy has.
Let x represent the number of medium marbles Amy has.
Let y represent the number of large marbles Amy has.
a) She has five times as many small marbles as medium marbles. This means that
w = 5x
b) The number of large marbles is two more than three times the number of medium marbles. This means that
y = 3x + 2
c) If Amy has a total of 560 marbles, it means that
5x + x + 3x + 2 = 560
9x = 560 - 2
9x = 558
x = 558/9 = 62
w = 5x = 62 × 5
w = 310
y = 3x + 2 = 3 × 62 + 2
y = 188
Answer:
A. s = 5x
B. y = 3x + 2
C y=166
Step-by-step explanation:
Geoff wants to purchase a circular area rug for his room, but he can't decide between the small size and the large size. A small rug covers an area of approximately 67 square feet. If a large size rug has twice the dimensions of a small rug, how many times larger is the large rug?
Answer: The larger rug is 4 times larger
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
The small circular rug covers an area of approximately 67 square feet. This means that
67 = πr²
r² = 67/π = 67/3.14 = 21.34
r = √21.34 = 4.62
If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be
2 × 4.62 = 9.24
The area of the larger rug would be
3.14 × 9.24² = 268.06ft²
Therefore
268.06/67 = 4
The larger rug is 4 times larger
Multiples of 3 and 5 Problem 1 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.
Answer: 233,168
Step-by-step explanation:
Formula: 1 + 2 + 3 + ... + n = n(n+1)/2
Sum of all the numbers below 1000 that is divisible by 3:
3 + 6 + 9 + ... + 999 = 3 (1 + 2 + 3 + ... + 333) = 3 x 333 x 334 / 2 = 166,833
Sum of all the numbers below 1000 that is divisible by 5:
5 + 10 + 15 + ... + 995 = 5 (1 + 2 + 3 + ... + 199) = 5 x 199 x 200 / 2 = 99,500
As we add up 166,833 and 99,500, the numbers that are divisible by 3*5 = 15 would be counted double. Therefore, subtract the result for numbers divisible by 15 just once:
Sum of all numbers below 1000 that is divisible by 15:
15 + 30 + 45 + ... + 990 = 15 (1 + 2 + 3 + ... + 66) = 15 x 66 x 67 / 2 = 33165
Therefore, [ 166,833 + 99,500 ] - 33,165 = 233,168
To find the sum of all the multiples of 3 or 5 below 1000, you need to find the sum of the multiples of 3 and 5 separately and then subtract the sum of the multiples of 15. The sum is 233,003.
Explanation:To find the sum of all the multiples of 3 or 5 below 1000, we can use the concept of arithmetic series. First, we need to find the sum of the multiples of 3 and the sum of the multiples of 5 below 1000. Then, we need to subtract the sum of the multiples of 15 (since numbers that are multiples of both 3 and 5 have been counted twice).
Using the formula for the sum of an arithmetic series, the sum of the multiples of 3 below 1000 is given by:
3 + 6 + 9 + ... + 999 = (1/2)(3 + 999)(333) = 166,833
Similarly, the sum of the multiples of 5 below 1000 is:
5 + 10 + 15 + ... + 995 = (1/2)(5 +995)(199) = 99,500
Finally, the sum of the multiples of 15 below 1000 is:
15 + 30 + 45 + ... + 990 = (1/2)(15 + 990)(66) = 33,330
Now, we can calculate the sum of all the multiples of 3 or 5 by adding the sum of the multiples of 3 to the sum of the multiples of 5 and then subtracting the sum of the multiples of 15:
166,833 + 99,500 - 33,330 = 233,003
Learn more about Sum of multiples here:https://brainly.com/question/16629105
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Given triangle ABC with altitude labeled x. Angles ADB and CDB are right angles by _____1._____, making triangle ABD and triangle BCD right triangles. Using the trigonometric ratios and . Multiplying to isolate x in both equations gives x = _____2._____ and x = a ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by ac gives: .
Answer:
(1) ADB = CDB = 90°
(2) c sinA
(3) (sinA)/a = (sinB)/b
Step-by-step explanation:
1. ADB = CDB = 90°
2. c sinA
since,
sin A = x/c , sin C = x/a
so x = c sinA and a sinC
3. from reflective property of x,
since x = c sinA
and x = a sinC
we substitute each equivalently
that is,
c sinA = a sinC
dividing each sides of the equation by ac we have ,
(c sinA)/ac = ( a sinC)/ac
simplifying we have,
(sinA)/a = (sinB)/b
Therefore the above equation is referred to as the SINE RULE.
I needz duh help pwease and tank chu?
Answer:
Step-by-step explanation:
Let h represent the number of hours that Jamarcus can rent the truck.
To rent a truck, the charge is $16 per hour and also a fueling fee of $25
The total cost of renting the truck for x hours would be
16h + 25
Since Jamarcus wants to rent the truck and can spend no more than $125, the inequality representing the situation would be
16h + 25 ≤ 125
16h ≤ 125 - 25
16h ≤ 100
h ≤ 6.25
2) 3x - 5 ≥ - 11
3x ≥ - 11 + 5
3x ≥ - 6
x ≥ - 6/3
x ≥ - 2
The correct graph is option A
Answer:
a
Step-by-step explanation: