Answer:
The area of the scale drawing is [tex]67.5\ cm^{2}[/tex]
Step-by-step explanation:
The scale drawing is
[tex](1\frac{1}{2})/2\ \frac{cm}{ft}[/tex]
Convert to an improper fraction
[tex](1\frac{1}{2})=3/2[/tex]
substitute
[tex](1\frac{1}{2})/2=(3/4)=0.75\ \frac{cm}{ft}[/tex]
The area is equal to
[tex]120\ ft^{2}[/tex]
substitute
[tex]120*(0.75)^{2}=67.5\ cm^{2}[/tex]
The area of the scale drawing of Charlene's swimming pool is [tex]\( 67.5} \)[/tex] square feet.
To find the area of the scale drawing of Charlene's swimming pool, we need to understand the scale given and how it applies to the dimensions and area.
Given:
Actual area of the swimming pool: [tex]\( 120 \) ft\(^2\)[/tex]
Scale of the drawing: [tex]\( 1 \frac{1}{2} \) centimeters = 2 feet[/tex]
First, convert the scale to centimeters:
[tex]\[ 1 \frac{1}{2} \text{ centimeters} = 1.5 \text{ centimeters} \][/tex]
Now, determine the scale factor for the dimensions:
[tex]\[ \text{Scale factor} = \frac{1.5 \text{ cm}}{2 \text{ ft}} \][/tex]
To find the area of the scale drawing, we need to square the scale factor, because area is two-dimensional:
[tex]\[ \text{Area scale factor} = \left(\frac{1.5}{2}\right)^2 \][/tex]
[tex]\[ \text{Area scale factor} = \left(0.75\right)^2 \][/tex]
[tex]\[ \text{Area scale factor} = 0.5625 \][/tex]
Now, calculate the area of the scale drawing:
[tex]\[ \text{Area of scale drawing} = 0.5625 \times 120 \text{ ft}^2 \][/tex]
[tex]\[ \text{Area of scale drawing} = 67.5 \text{ ft}^2 \][/tex]
What is the phase shift of the function ?
Answer:
The Phase Shift is how far the function is shifted horizontally from the usual position.
Step-by-step explanation:
Your swim team competes in the 200-meter freestyle relay. The individual times for the four team members are 27.81, 26.89, 26.55, and 25.48 seconds. What is the total relay time for the team?
Add all the times together:
27.81 + 26.89 + 26.55 + 25.48 = 106.73 seconds.
1 minute = 60 seconds.
106 - 60 = 46
Total time: 1 minute and 46.73 seconds.
Answer:
106.73
Step-by-step explanation:
27.81 + 26.89 + 26.55 + 25.48 = 106.78
So in conclusion, the answer is 106.78
Which table represents exponential growth?
Answer:
B
Step-by-step explanation:
The exponential function [tex]y=a^x[/tex] shows the exponential growth if [tex]a>1.[/tex]
Consider choice B.
If x=1, then [tex]y=2=2^1;[/tex]
if x=2, then [tex]y=4=2^2;[/tex]
if x=3, then [tex]y=8=2^3;[/tex]
if x=4, then [tex]y=16=2^4.[/tex]
This means that the function [tex]y=2^x[/tex] represents the table B.
ANSWER
See attachment
EXPLANATION
The table that represent a geometric sequence is the one shown in the attachment with y-values
[tex]2,4,8,16,...[/tex]
We can see that, the subsequent term is obtained by multiplying the previous term by 2.
In other words, there is a bit ratio of 2.
Here the table represents a geometric sequence.
In triangle ABC, D is a point on line AB and E is a point on line AC such that DE is parallel to BC. If BC = 20 centimeters, and the area of the trapezoid (trapezium) DBCE is one-fourth the area of triangle ABC, find DE.
Step-by-step Answer:
If trapezium DBCE is one-fourth of the area of the triangle ABC, that means that the area of triange ADE is (1 - 1/4) = three-fourth of ABC.
Since DE is parallel to BC, we can prove that triangles ADE and ABC are similar.
Similar triangles have corresponding sides proportional, and area is proportional to the square of the linear proportions.
From this we can conclude that
(DE/BC)^2 = 3/4
DE/BC = sqrt(3/4) = sqrt(3)/2
DE = sqrt(3)/2 * 20 = 10 sqrt(3) = 17.320508 cm (to 6 decimal places).
On the subject of similar figures/volumes, if we know the ratio of linear dimensions (such as the side of a cube) as k, then the ratio of AREA of similar squares would be k^2.
Example: A square would have a side of 8 (area=8^2=64), and a (similar) square has a side of 10 (area = 10^2= 100). The
ratio of areas = 64/100 = (8^2/10^2) = (8/10)^2
Here 8/10 is the ratio of linear dimensions = k, and the ratio of areas is k^2 = (8/10)^2 = 64/100.
The same works for cubes (or similar volumes) where the volumes would be proportional to k^3.
A function is graphed on the coordinate plane.
what is the value of the function when x = 4
Answer:
1
Step-by-step explanation:
y = mx + b
y = 1/2 x - 1
y = 1/2 (4) - 1
y = 2 - 1
y = 1
When x = 4, the function y = (1/2)x - 1 evaluates to y = 1. This linear equation has a slope of 1/2 and a y-intercept of -1.
To find the value of the function y = (1/2)x - 1 when x = 4, you simply need to substitute x = 4 into the equation and solve for y:
y = (1/2)(4) - 1
y = 2 - 1
y = 1
So, when x = 4, the value of the function y is 1.
In a more general sense, this equation represents a linear function with a slope of 1/2 and a y-intercept of -1. The slope (1/2) represents the rate of change, meaning that for every unit increase in x, y increases by 1/2. The y-intercept (-1) is the value of y when x is 0.
When x = 4, as calculated above, y is 1. This means that if you were to plot this function on a coordinate plane, the point (4, 1) would lie on the graph.
For more question on slope visit:
https://brainly.com/question/16949303
#SPJ2
How do you determine the limit algebraically?
Answer:
- 0.0625
Step-by-step explanation:
Again, I don't know of another way besides Calculus other than letting x = something very tiny.
When you use calculus, the answer approaches - 1/16 = - 0.0625 (I think). So we'll let x = 0.01 and see how that goes.
numerator: 1/(0.01 + 4) - 1/4
(0.24938 - 0.25) / 0.01
- 0.000623 / 0.01 = - 0.0623 which is pretty close considering what I used for x. You could try it with 0.0001 which will get much closer.
Kendra sold 200 shares through her broker on June 8. The price per share was $22.10. The broker charged her a 0.5% commission on the total value. What was Kendra’s return on the trade?
A. $4,397.90
B. $4,420.00
C. $4,596.90
D. $4,620.00
Answer:
A. $4397.9
Explanation:
We are given that Kendra sold 200 shares and that the price per share was $22.1
This means that:
Total value = 200 * 22.1 = $4420
Now, we know that the broker charged 0.5% commission on the total value
This means that:
Broker's charge = 0.5% * 4420 = 0.005 * 4420 = $22.1
Therefore,
Kendra's return = Total value - broker's charge
Kendra's return = 4420 - 22.1 = $4397.9
Hope this helps :)
Answer:
$4,397.90
Step-by-step explanation:
If the mean of six numbers is 41 and if one is removed the mean will be 46 what is the number being removed
Answer:
1 is my answer but I could be wrong
Please help! ASAP!!!
Answer:
Final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].
Step-by-step explanation:
Given expression is [tex](a-\sqrt{2})^8[/tex].
Now we need to find the fourth term of the given expression [tex](a-\sqrt{2})^8[/tex]. So apply the nth term formula using binomial expansion.
exponent n=8
4th term means we use r=4-1=3
x=2, [tex]y=-\sqrt{2}[/tex]
rth term in expansion of [tex](x+y)^n[/tex] is given by formula:
[tex]\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r[/tex]
[tex]=\frac{8!}{\left(8-3\right)!\cdot3!}\cdot a^{\left(8-3\right)}\cdot\left(-\sqrt{2}\right)^3[/tex]
[tex]=\frac{8!}{5!\cdot3!}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]
[tex]=\frac{40320}{120\cdot6}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]
[tex]=56\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]
[tex]=-112a^5\cdot\sqrt{2}[/tex]
[tex]=-112\cdot\sqrt{2}a^5[/tex]
Hence final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].
Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8.
Select one:
a. y = 1/32 x^2
b. y^2 = 8x
c. y^2 = 32x
d. y = 1/8 x^2
The standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is y = 1/32 x², as it is the only option that correctly represents a parabola opening upward with the vertex at the origin and a focus 8 units away.
To find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8, we begin by noting that the vertex of the parabola will be midway between the focus and directrix. Since the focus is 8 units above the x-axis and the directrix is 8 units below the x-axis, the vertex is at the origin (0, 0).
The distance between the vertex and the focus (which is also the distance between the vertex and the directrix) is 8 units; this distance is the value 'p' in the parabola's standard equation.
The parabola opens upward because the focus is above the directrix. The standard form for an upward-opening parabola centered at the origin is y = {1}/{4p}x². In our case, p = 8, so the equation becomes y = {1}/{4(8)}x² which simplifies to y = {1}/{32}x².
Based on the options available, the correct standard form of the equation of the parabola is A. y = {1}/{32}x².
Amber obtained a 30-year, $260,000 loan for her new home. The interest rate is 3.8% and her monthly payment is $1,211.49. How much of the first payment is for principal?
Answer:
$388.16
Step-by-step explanation:
Her monthly interest rate is 3.8%/12, so the amount of interest due on the first payment is ...
$260,000 × 0.038/12 ≈ $823.33
Then the amount applied to the principal is ...
$1211.49 -823.33 = $388.16
Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).
A) y = 2x + 4
B) y = 2x - 8
C) y = -2x + 16
D) y = -12x + 7
Answer:
The answer is D my friends. Good luck.
Step-by-step explanation:
The equation of the line parallel to 2x + 4y = 6 and passing through the point (6, 4) is y = -0.5x + 7.
Explanation:To find an equation of a line parallel to a given line, we need to find a line with the same slope.
First, we need to rewrite the original equation 2x + 4y = 6 in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By rearranging the equation, we get y = -0.5x + 1.5.
Since the new line is parallel to the original line, it will have the same slope.
Therefore, the equation of the line parallel to 2x + 4y = 6 and passing through the point (6, 4) is y = -0.5x + 7.
Margaret is making strawberry milkshakes for the kids party. The recipe calls for of a cup of strawberry syrup to make 8 milkshakes. How many cups of strawberry syrup are needed to make 96 milkshakes.?
Answer:
12
Step-by-step explanation:
96 / 8
Answer:
12 Cups are needed!
Step-by-step explanation:
You find the answer by dividing 96 milkshakes by 8 Milkshakes and find that 12 cups are needed.
:)
Help me find the area of the triangle... ****picture attached
Answer:
60 cm^2
Step-by-step explanation:
The formula for the area of a triangle is ...
A = (1/2)bh
where b is the length of the base, and h is the height. Your triangle shows a base length of 12 cm + 3 cm = 15 cm, and a height of 8 cm. Using these values in the formula, we have ...
A = (1/2)(15 cm)(8 cm) = 60 cm^2
A cell-phone company has noticed that the probability of a customer experiencing a dropped call decreases as the customer approaches a cell-site base station. A company representative approached a cell site at a constant speed and calculated the probability of a dropped call at regular intervals, and the probabilities formed the geometric sequence 0.8, 0.4, 0.2, 0.1, 0.05. If the company representative continues calculating the probability of a dropped call, what will be the next term in the sequence?
Answer:
the answer is 0.00221184
Step-by-step explanation:
as we can see 3rd term is product of first two terms
4th term is product of third and second term
5th term is the product of fourth and third term
the next term in the sequence which is the sixth term will be the product of fifth and fourth term
Answer:
The next term of geometric sequence is 0.025 which is the probability of dropped call.
Step-by-step explanation:
We are given the following information in the question:
The probability of a customer experiencing a dropped call decreases formed the geometric sequence.
The geometric sequence is:
0.8, 0.4, 0.2, 0.1, 0.05
First term = a = 0.8
Common difference = r =[tex]\frac{a_{n}}{a_{n-1}} = \frac{0.4}{0.8} = \frac{1}{2}[/tex]
We have to find the next term of the geometric series to find the next probability.
Next term of sequence =
[tex]a_n = a_{n-1}\times r\\= 0.05\times \displaystyle\frac{1}{2}\\\\= 0.025[/tex]
Hence, the next term of geometric sequence is 0.025 which is the probability of dropped call.
25pts awarded and brainliest awarded, plz help asap!!!!!!
Here is a table of values for y = f(x).
x -2 -1 0 1 2 3 4 5 6
f(x) 5 6 7 8 9 10 11 12 13
Mark the statements that are true
Answer:
B. f(-1)=6
C. The domain of f(x) is the set {-2.-1,0,1,2,3,4,5,6}
Step-by-step explanation:
To find f(5) from the table means, the y-value that corresponds to x=5.
This value is 12.
This implies that:
f(5)=12
Also the y-value that corresponds to -1 is 6.
Hence f(-1)=6
The domain of f(x) are the set of all the x-values.
The domain is : {-2.-1,0,1,2,3,4,5,6}
The range for f(x) is the set of all the corresponding y-values.
From the table, the range is: {5,6,7,8,9,10,11,12,13}
Lucky Jack wins the lottery! He deposits $100,000 in an account that earns 4% interest compounded continuously. How much money is in the account at the end of 5 years?
A) $120,357
B) $122,140
C) $125,620
D) $225,820
Answer:
Option B) $122,140
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=5\ years\\ P=\$100,000\\ r=0.04[/tex]
substitute in the formula above
[tex]A=\$100,000(e)^{0.04*5}=\$122,140.28[/tex]
Round to the nearest dollar
[tex]\$122,140.28=\$122,140[/tex]
Simplify the expression below (X^3)^2
X^(3•2) =X^ 6
Think of an example such as :
(2^3)^2=8^2=64 is the same with
2^(3•2) = 2^6 = 64
Answer= x^6
When two exponents are multiplied together the two exponents multiply.
The dot plot represents an order of varying shirt sizes. Which histogram represents the same data?
Answer: the answer is C
The histogram and dot plot that represent the order of varying shirt sizes are illustrations of charts
How to determine the histogram?The dataset on the dot plot can be represented using the following frequency table
Shirt size Frequency
8 0
10 1
12 3
14 3
16 5
18 4
20 2
22 1
24 1
26 0
Since the options are not given, the next step is to plot and upload the histogram using a graphing tool
See attachment for the histogram that represents the dot plot
Read more about histogram and dot plot at
https://brainly.com/question/15853311
#SPJ5
What is the range of the function represented by these ordered pairs? {(–2, 1), (0, 0), (3, –1), (–1, 7), (5, 7)}
1,0,-1,7,7.
The range always be the Y values
Three friends are starting a food truck and are contributing a total of $140,000 to begin operations. Their investments are in the ratio of 3:4:7. What is the difference in investment between the smallest investor an largest investor?
Answer:
The difference in investment between the smallest investor an largest investor is $40,000
Step-by-step explanation:
Let
x ---> the contribution of the smallest investor
y ---> the contribution of the middle investor
z ---> the contribution of the largest investor
we know that
x+y+z=140,000 -----> equation A
x/y=3/4 -----> y=(4/3)x ----> equation B
x/z=3/7 ----> z=(7/3)x ----> equation C
substitute equation B and equation C in equation A and solve for x
x+(4/3)x+(7/3)x=140,000
(14/3)x=140,000
x=140,000*3/14
x=$30,000
Find the value of y
y=(4/3)x ----> y=(4/3)(30,000)=$40,000
Find the value of z
z=(7/3)x ----> z=(7/3)(30,000)=$70,000
Find the difference in investment between the smallest investor an largest investor
z-x=$70,000-$30,000=$40,000
which function has real zeros at x=-8 and x=5?
Answer: The required function would be [tex]x^2+3x-40[/tex]
Step-by-step explanation:
Since we have given that
There are two real zeroes :
x = -8 and x = 5
So, we need to find the function satisfying the above two zeroes:
Let α = -8 and β = 5
So, it means it is a quadratic equation :
[tex]x^2-(\alpha +\beta)x+\alpha \beta \\\\=x^2-(-8+5)x+-8\times 5\\\\=x^2+3x-40[/tex]
Hence, the required function would be [tex]x^2+3x-40[/tex]
Answer:
The answer is A
Step-by-step explanation:
The length of a train car is 50.6 feet this is baffling 8 feet less than six times the width what is the width
Answer:
the width is 9 23/30 feet ≈ 9.767 ft
Step-by-step explanation:
Let w represent the width of the train car. Then 6 times the width is 6w, and 8 ft less than that is (6w-8). We are told this amount is 50.6 feet, so we have ...
6w -8 = 50.6
6w = 58.6 . . . . . . . add 8; next divide by 6
58.6/6 = w = 586/60 = 293/30 = 9 23/30 . . . . feet
This is a repeating decimal: 9.766666...
The width of the train car is 9 23/30 ft, about 9.77 ft.
Find cos \theta θ if \sin\theta=-\frac{7}{15} sin θ = − 7 15 and falls in quadrant 4
let's recall that on the IV Quadrant the x/cosine is positive and the y/sine is negative, and of course the hypotenuse is just a radius unit and therefore never negative.
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{15}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\bf \pm\sqrt{15^2-(-7)^2}=a\implies \pm\sqrt{176}=a\implies \stackrel{\textit{IV Quadrant}}{+\sqrt{176}=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{\sqrt{176}}}{\stackrel{hypotenuse}{15}}~\hfill[/tex]
Nancy was laid off and applied for unemployment benefits in July. In her state, the weekly unemployment benefit is 55% of the 26-week average of the two highest salaried quarters of the year leading to her application. In April, May, and June, Nancy earned a total of 13,500. In January, Febuary, and March her total income was 12,775. What will Nancy weekly benfits be?
Answer:
$277.91
Step-by-step explanation:
"The 26-week average of the two highest salaried quarters of the year leading to her application" would be the average of $13,500 and $12,775, or
$13,500 + $12,775
---------------------------- = $13137.50
2
Dividing this by 26 weeks (equivalent to 6 months), we get $505.29.
Nancy's weekly employment benefit would be 55% of that, or $277.91.
Answer: $555.82
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A politician wants to see what people in her district think about tax cuts. Which procedure would be a good way of conducting a survey?
Answer:
D
Step-by-step explanation:
C is also possible but it is not purely random and it is not mentioned the mall is in her district.
Answer: D) Mail a questionnaire to random households.
Step-by-step explanation:
A) You are limited to only listeners of the radio show
B) You are limited to only those that are wiling and able to attend the meeting.
C) You are limited to only shoppers at that particular mall.
D) Randomly selecting households is the least biased method of responses from the district.
Alberto has 92 stamps in one large álbum and 38 stamps in anotaré small álbum. How can he use mental math to find how many more stamps are in the large album use drawings to show your answer
Answer:
The answer would be the large album has 54 more stamps than the small album.
Step-by-step explanation:
... 92 - 38 = 54
Do you need a drawing done though?
A conical perfume bottle has a radius of 3.7 centimeters and a height of 5.4 centimeters. Using 3.14 for , approximately how much perfume can the bottle hold? A. 338.78 cubic centimeters B. 112.93 cubic centimeters C. 232.13 cubic centimeters D. 77.38 cubic centimeters
The volume of the conical perfume bottle is 77.38 cubic centimeters of perfume, answer D.
To calculate the volume of a conical perfume bottle, we use the formula for the volume of a cone, which is V = (1/3)
3.14r²h, where r is the radius and h is the height of the cone. Given the radius of 3.7 centimeters and a height of 5.4 centimeters, we calculate:
V = (1/3)
3.14 * (3.7 cm)² * 5.4 cm
= (1/3) * 3.14 * 13.69 cm2 * 5.4 cm
= (1/3) * 3.14 * 73.926 cm3
= 3.14 * 24.642 cm3
= 77.38 cubic centimeters
Therefore, the perfume bottle can hold approximately 77.38 cubic centimeters of perfume, which corresponds to answer choice D.
A logger is spending his afternoon splitting logs for firewood. He can split 11 logs in a hour. If he already has 12 logs split, how many hours can he split 40 logs?
Answer:
If it is 40 total then:
about 3 more hours
Exact answer:
2.545454... hours
If it is 40 more:
about 4 hours
Exact answer:
3.63636363... hours
Answer:
• 3 hours
• 11 hours
• 12 hours
Step-by-step explanation:
Check with substitution in the inequality: 12 + 11h > 40
Of all the baseball caps in a store. 2/3 of the caps are blue. Of all the blue baseball caps. 4/7 are on sale. What fraction of the baseball caps in the store are blue and on sale
19/50 of the baseball caps in the store are blue and on sale.
Let's say there are a total of 100 baseball caps in the store. Then, 2/3 of them are blue, which is:
2/3 x 100 = 66.67 (approximately 67)
So, there are approximately 67 blue baseball caps in the store. Out of these, 4/7 are on sale, which is:
4/7 x 67 = 38 (rounded to the nearest whole number)
Therefore, there are approximately 38 blue baseball caps that are on sale in the store.
The fraction of baseball caps in the store that are blue and on sale is:
38/100 = 19/50
So, 19/50 of the baseball caps in the store are blue and on sale.
for such more question on word problem
https://brainly.com/question/1781657
#SPJ11
To find the fraction of baseball caps in the store that are blue and on sale, multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.
Explanation:To find the fraction of baseball caps in the store that are blue and on sale, we need to multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.
Given that 2/3 of the caps are blue and 4/7 of the blue caps are on sale, we can calculate the fraction of blue caps that are on sale by multiplying 2/3 and 4/7:
2/3 * 4/7 = 8/21
Therefore, 8/21 of the baseball caps in the store are blue and on sale.
Learn more about Fraction of baseball caps that are blue and on sale here:https://brainly.com/question/12656995
#SPJ12