Work Shown:
area = length*width
length = area/width
length = 3162/51
length = 62 meters
Find the compound ratio of 2:3 and 5:4
The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.
How to determine a compound ratio
Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:
For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).
If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:
r = (2 · 5) : (3 · 4)
r = 10 : 12
Finally, we simplify the resulting expression:
r = 5 : 6
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The perimeter of a rectangle is 64 feet. The length is two more than double the
width. Find the dimensions of the rectangle.
(Remember Perimeter of rectangle = 2L+ 2w)
Answer:
To solve this problem, we can set up the following equation:
2L + 2W = 64
We are told that the length of the rectangle is two more than double the width, so we can write the following equation:
L = 2W + 2
Substituting this equation into the first equation, we get:
2(2W + 2) + 2W = 64
Simplifying this equation, we get:
6W + 4 = 64
Subtracting 4 from both sides, we get:
6W = 60
Dividing both sides by 6, we get:
W = 10
The width of the rectangle is 10 feet.
To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:
L = 2(10) + 2
= 20 + 2
= 22
The length of the rectangle is 22 feet.
Therefore, the dimensions of the rectangle are 10 feet by 22 feet.
Step-by-step explanation:
which fractions, when converted, result in a repeating decimal? select all that apply 1/8 1/6 3/12 8/9 2 and 4/5 4 and 3/11
Answer:
B. 1/6
D. 3/12
F. 4 3/11
PLEASE MARK BRAINLIEST
A _____ is a flat surface that has no thickness.
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 27 weeks. Assume that the length of unemployment is normally distributed with population mean of 27 weeks and the population standard deviation of 2 weeks. Suppose you would like to select a random sample of 39 unemployed individuals for a follow-up study.
Required:
a. What is the distribution of X?
b. What is the distribution of xÌ?
c. What is the probability that d. For 36 unemployed individuals, find the probability that the average time that they found the next job is less than one randomly selected individual found a job less than 27 weeks?
Answer:
X ~ N(27, 4) ;
xbar ~ N(27, 0.1026) ;
0.5 ;
0.5
Step-by-step explanation:
Probability distribution of X : N(μ, σ²)
μ = 27 ; σ = 2
X ~ N(μ, σ²) = X ~ N(27, 2²) ;X ~ N(27, 4)
Distribution is approximately normal ; μ = xbar ; xbar = 27
(Standard Error)² = (σ/√n)²= (2/√39)² = 0.1026
xbar ~ N(μ, σ²) = xbar ~ N(27, 2²) ; xbar ~ N(27, 0.1026)
Probability that a randomly selected individual found a job in less than 27 weeks :
P(X < 27) :
Obtain the Zscore :
Z = (x - μ) / σ
Z = (27 - 27) / 2 = 0/2
Z = 0
P(Z < 0) = 0.5
D.) n = 36
P(X < 27) :
Obtain the Zscore :
Z = (x - μ) / σ/√n
Z = (27 - 27) / (2/√36) = 0/0.33333
Z = 0
P(Z < 0) = 0.5
Can someone help me with 18 and 20 please
Answer:
both are b
Step-by-step explanation:
the point is equal to -2 because there is a point on -2 and with 20 it b because 2 time 10 is 20 +26 makes 46 which makes 43 less than 46
Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214? Explain.
There are 3,024 different ways 1,214 can be shown.
What is permutation?Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given 1,214
since there are 4 places in the digit,
so 4 values less than 10 can be solved by
9, 8, 7, and 6
so by permutation to find ⁹P₄ = 9!/(9 - 4)!
= (9 x 8 x 7 x 6 x5!)/5!
⁹P₄ = 3,024
Hence there are 3,024 different ways.
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A certain forest covers an area of 4000 km². Suppose that each year this area decreases by 4.25%. What will the area be after 15 years?
The area of the forest after 15 years will be 2189.4
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
i = The initial area of the forest = 4200km
r = Per year decrease is = 4.25%
n = Number of years = 15
The required formula is
The area of forest will be
A = i (1-r)^n
A = 4200(1-0.425)^15
A= 2189.4
Hence, the area of the forest will be 2189.4
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New repost of my question
Answer:
Step-by-step explanation:
???
What is the surface area of the cylinder with height 8 mi and radius 6 mi? Round your answer to the nearest thousandth.
Answer:ANSWER would either be 120π or about 376.8
Step-by-step explanation:
A=2πrh+2πr2
A=2π*6*8+2π*6*2
A=96π+24π
A= 120π
or
A≈376.8
ANSWER would either be 120π or about 376.8
Answer: the real answer is 527.788 the top answer is wrong I did it and it said it was wrong
Step-by-step explanation:
Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem.
g(x) = x3 + x2-x-1:(-1,1)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. Rolle's Theorem applies and the point(s) guaranteed to exist is/are x =
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
B. Rolle's Theorem does not apply.
Answer:
I have attached the answers
What is the equation of the least squares regression line for the data set?
The equation of the least squares regression line for the data set is (b) ŷ = -2.984x + 112.38
How to determine the equation of the least squares regression line for the data setFrom the question, we have the following parameters that can be used in our computation:
Volunteer 15 11 22 35 18 41 27 18
Trees 77 99 4 11 44 14 2 90
Using a graphing calculator, we have the following calculation summary
Sum of X = 187Sum of Y = 341Mean X = 23.375Mean Y = 42.625Sum of squares (SSX) = 741.875Sum of products (SP) = -2213.875The regression equation is represented as
ŷ = bX + a
Where
b = SP/SSX = -2213.88/741.88 = -2.98416
a = MY - bMX = 42.63 - (-2.98*23.38) = 112.37978
So, we have
ŷ = -2.98416X + 112.37978
Approximate
ŷ = -2.984x + 112.38
Hence, the equation is ŷ = -2.984x + 112.38
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A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On time Delayed Total
Domestic 96 412
International 76
Total 147
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or
negative? (4 points)
Answer:
A.
domestic: 316 / 96 / 412
international: 76 / 51 / 127
total: 392 / 147 / 539
B. 51 its the smallest number
C. I don't know what association means but 76.2% of domestic flights land on time and 63% of international flights land on time so id say its positive
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
c = 52 yards
Step-by-step explanation:
You have to use the Pythagorean theorem to solve this question.
[tex]a^2+b^2=c^2[/tex]
The hypotenuse is longest side of a triangle.
Lets substitute in our values:
[tex]20^2+48^2=c^2[/tex]
Lets simplify this to:
[tex]400 + 2304 = 2704[/tex]
Now we need to find the square root of 2704:
[tex]\sqrt{2704}=52[/tex]
Therefore, the hypotenuse is 52 yards long.
I need help right away!!
Answer:
i think its c though im not sure
Step-by-step explanation:
Can someone please help asap
Answer:
the answer is 38
Step-by-step explanation:
because one of the angles is 90 and the other one is 45, so the other angle is 45 too
so.. this is an isosceles triangle
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed.
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
26.794 yd = _________km.
By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
What is the value of 1meter in terms of centimeter ?
1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .
Given,
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
we know that ,
1yard = 0.0009144 km
so ,
26.794 yard = 26.794*0.0009144 km
= 0.024500
Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
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area of a parallelogram help wanted ty
The area of the parallelogram is 72 square units. Option B
How to determine the area of the parallelogramThe formula for calculating the area of a parallelogram is expressed as;
A = bh
Given that;
A is the area of the parallelogramb is the base of the parallelogramh is the height of the parallelogramFrom the information given, we have that;
The base of the parallelogram = x + yThe height of the parallelogram = hNow, substitute the values
x + y = 8 + 4
add the values
x + y = base = 12 units
h = 6 units
Now, substitute the values into the formula, we get;
Area, A = 12(6)
multiply the values
Area, A = 72 square units
Hence, the value is 72 square units
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Simplify: 9- 4x + 2x + 8x° +1+ 6x?
Answer:
10+12x
Step-by-step explanation:
9−4x+2x+8x+1+6x
(9+1)+(−4x+2x+8x+6x)
10+12x
Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results: Exam Image Exam Image We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic
Answer:
[tex]t = 31.29[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Stick} & {25.8} & {26.9} & {26.2} & {25.3} & {26.7}& {26.1} \ \\ {Liquid} & {16.9} & {17.4} & {16.8} & {16.2} & {17.3}& {16.8} \ \end{array}[/tex]
Required
Determine the test statistic
Let the dataset of stick be A and Liquid be B.
We start by calculating the mean of each dataset;
[tex]\bar x =\frac{\sum x}{n}[/tex]
n, in both datasets in 6
For A
[tex]\bar x_A =\frac{25.8+26.9+26.2+25.3+26.7+26.1}{6}[/tex]
[tex]\bar x_A =\frac{157}{6}[/tex]
[tex]\bar x_A =26.17[/tex]
For B
[tex]\bar x_B =\frac{16.9+17.4+16.8+16.2+17.3+16.8}{6}[/tex]
[tex]\bar x_B =\frac{101.4}{6}[/tex]
[tex]\bar x_B =16.9[/tex]
Next, calculate the sample standard deviation
This is calculated using:
[tex]s = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
For A
[tex]s_A = \sqrt{\frac{\sum(x - \bar x_A)^2}{n-1}}[/tex]
[tex]s_A = \sqrt{\frac{(25.8-26.17)^2+(26.9-26.17)^2+(26.2-26.17)^2+(25.3-26.17)^2+(26.7-26.17)^2+(26.1-26.17)^2}{6-1}}[/tex]
[tex]s_A = \sqrt{\frac{1.7134}{5}}[/tex]
[tex]s_A = \sqrt{0.34268}[/tex]
[tex]s_A = 0.5854[/tex]
For B
[tex]s_B = \sqrt{\frac{\sum(x - \bar x_B)^2}{n-1}}[/tex]
[tex]s_B = \sqrt{\frac{(16.9 - 16.9)^2+(17.4- 16.9)^2+(16.8- 16.9)^2+(16.2- 16.9)^2+(17.3- 16.9)^2+(16.8- 16.9)^2}{6-1}}[/tex]
[tex]s_B = \sqrt{\frac{0.92}{5}}[/tex]
[tex]s_B = \sqrt{0.184}[/tex]
[tex]s_B = 0.4290[/tex]
Calculate the pooled variance
[tex]S_p^2 = \frac{(n_A - 1)*s_A^2 + (n_B - 1)*s_B^2}{(n_A+n_B-2)}[/tex]
[tex]S_p^2 = \frac{(6 - 1)*0.5854^2 + (6 - 1)*0.4290^2}{(6+6-2)}[/tex]
[tex]S_p^2 = \frac{2.6336708}{10}[/tex]
[tex]S_p^2 = 0.2634[/tex]
Lastly, calculate the test statistic using:
[tex]t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_B)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]
We set
[tex]\mu_A = \mu_B[/tex]
So, we have:
[tex]t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_A)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]
[tex]t = \frac{(\bar x_A - \bar x_B) }{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]
The equation becomes
[tex]t = \frac{(26.17 - 16.9) }{\sqrt{0.2634/6 +0.2634/6}}[/tex]
[tex]t = \frac{9.27}{\sqrt{0.0878}}[/tex]
[tex]t = \frac{9.27}{0.2963}[/tex]
[tex]t = 31.29[/tex]
The test statistic is 31.29
Work out the cost of 12kg of potatoes and 1 1/2kg of carrots
Answer:
The cost is #15.90
Step-by-step explanation:
See comment for complete question
Given
[tex]P \to Potato[/tex]
[tex]C \to Carrot[/tex]
[tex]3P + 2C = 5.08[/tex]
[tex]P = 1.24[/tex]
Required
[tex]12P + 1\frac{1}{2}C = ??[/tex]
First, we solve for C
Substitute [tex]P = 1.24[/tex] in [tex]3P + 2C = 5.08[/tex]
[tex]3 * 1.24 + 2C = 5.08[/tex]
[tex]3.72 + 2C = 5.08[/tex]
Collect like terms
[tex]2C = 5.08 - 3.72[/tex]
[tex]2C = 1.36[/tex]
Solve for C
[tex]C = \frac{1.36}{2}[/tex]
[tex]C = 0.68[/tex]
So, we have:
[tex]P = 1.24[/tex]
[tex]C = 0.68[/tex]
[tex]12P + 1\frac{1}{2}C = ??[/tex] becomes
[tex]12P + 1\frac{1}{2}C = 12*1.24 + 1\frac{1}{2}*0.68[/tex]
[tex]12P + 1\frac{1}{2}C = 14.88 + 1.02[/tex]
[tex]12P + 1\frac{1}{2}C = 15.90[/tex]
For what value of x does 4^x =(1/8)^x+5
9514 1404 393
Answer:
(b) -3
Step-by-step explanation:
It can work well to rewrite the equation as powers of 2.
[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\\\\(2^2)^x=(2^{-3})^{x+5}\qquad\text{as powers of 2}\\\\2x=-3(x+5)\qquad\text{equate exponents}\\\\5x=-15\qquad\text{add $3x$}\\\\\boxed{x=-3}\qquad\text{divide by 5}[/tex]
__
Check
4^-3 = (1/8)^(-3+5) ⇒ 1/64 = (1/8)^2 . . . . true
Pls help i only have 2 minuets left
Answer:
14, 3!
Step-by-step explanation:
It is very complicated to explain.
Write in standard form 0.0003251
Answer:
Step-by-step explanation:
The answer is 3.2510 x 10^-4
please explain step by step in full process
questions
Given L || M find the value of unknown angles in each of the following figures
Answer:
x = 120°
y = 60°
Step-by-step explanation:
✔️since, lines l and m, area parallel, therefore,
x = 120° (they are corresponding angles having matching corners. Thus, corresponding angles are congruent to each other)
✔️x + y = 180° (linear pair angles)
Plug in the value of x
120 + y = 180
Subtract 120 from each side of the equation
y = 180 - 120
y = 60°
Help please ????????????
Answer:
700 i think-
Step-by-step explanation:
A line is parallel to y=2x-8 and intersects the point (-4,-1) what is the equation of this parallel line?
Answer:
y = 2x + 7
Step-by-step explanation:
y + 1 = 2 ( x + 4 )
y = 2x + 8 - 1
y = 2x + 7
Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, April 26, 2014, in Charleston, South Carolina, high tide occurred at 6:30 am (6.5 hours) and low tide occurred at 12:24 pm (12.4 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 5.86 feet, and the height of the water at low tide was − 0.38 foot.
(a) Approximately when will the next high tide occur?
(b) Find a sinusoidal function of the form
y = A sin(ωx – ϕ) + B
that models the data.
(c) Use the function found in part (b) to predict the height of the water at 3 pm on April 26, 2014.
Answer:
(a) The next tide will occur at 6:55pm
(b) [tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]
(c) The height is: 2.904ft
Step-by-step explanation:
Given
[tex]T_1 = 12hr:25min[/tex] --- difference between high tides'
Solving (a): The next time a high tide will occur
From the question, we have that:
[tex]High =6:30am[/tex] --- The time a high tide occur
The next time it will occur is the sum of High and T1
i.e.
[tex]Next = High + T_1[/tex]
[tex]Next = 6:30am + 12hr : 25min[/tex]
Add the minutes
[tex]Next = 6:55am + 12hr[/tex]
Add the hours
[tex]Next = 6:55pm[/tex]
Solving (b): The sinusoidal function
Given
[tex]High\ Tide = 5.86[/tex]
[tex]Low\ Tide = -0.38[/tex]
[tex]T = 12hr:25min[/tex] -- difference between consecutive tides
[tex]Shift = 6.5hr[/tex]
The sinusoidal function is represented as:
[tex]y = A\cos(w(x - C)) + B[/tex]
Where
[tex]A = Amplitude[/tex]
[tex]A = \frac{1}{2}(High\ Tide - Low\ Tide)[/tex]
[tex]A = \frac{1}{2}(5.86 - -0.38)[/tex]
[tex]A = \frac{1}{2}(6.24)[/tex]
[tex]A = 3.12[/tex]
[tex]B = Mean[/tex]
[tex]B = \frac{1}{2}(High\ Tide + Low\ Tide)[/tex]
[tex]B = \frac{1}{2}(5.86 - 0.38)[/tex]
[tex]B = \frac{1}{2}(5.48)[/tex]
[tex]B = 2.74[/tex]
[tex]w = Period[/tex]
[tex]w = \frac{2\pi}{T}[/tex]
[tex]w = \frac{2\pi}{12:25}[/tex]
Convert to hours
[tex]w = \frac{2\pi}{12\frac{25}{60}}[/tex]
Simplify
[tex]w = \frac{2\pi}{12\frac{5}{12}}[/tex]
As improper fraction
[tex]w = \frac{2\pi}{\frac{149}{12}}[/tex]
Rewrite as:
[tex]w = \frac{2\pi*12}{149}[/tex]
[tex]w = \frac{24\pi}{149}[/tex]
[tex]C = shift[/tex]
[tex]C=6.5[/tex]
So, we have:
[tex]y = A\cos(w(x - C)) + B[/tex]
[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]
Solving (c): The height at 3pm
At 3pm, the value of x is:
[tex]x=3:00pm - 6:30am[/tex]
[tex]x=9.5hrs[/tex]
So, we have:
[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]
[tex]y = 3.12 \cos(\frac{24\pi}{149}(9.5 - 6.5)) + 2.74[/tex]
[tex]y = 3.12 \cos(\frac{24\pi}{149}(3)) + 2.74[/tex]
[tex]y = 3.12 \cos(\frac{72\pi}{149}) + 2.74[/tex]
[tex]y = 3.12 *0.0527 + 2.74[/tex]
[tex]y = 2.904ft[/tex]
pls help, last question. the one circled in red
On solving the provided question, we can say that - in the linear equation y = 1/2x + 5, slope, m = 1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
in the linear equation =>
y = +1/2x + 5
on comparing with y = mx +c
slope, m = 1/2
and, c= +5
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what line
no association
nonlinear association
positive linear association
negative linear association
I believe that is a negative linear association.