An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²
Here, we have,
According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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Round 2,561 to the nearest hundred.
Answer:
2,600.
Step-by-step explanation:
Rounding 2,561 to the nearest hundred means rounding it to the nearest multiple of 100.
To do this, we need to look at the digit in the tens place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the hundreds place, which is 25, by 1.
Therefore, rounding 2,561 to the nearest hundred gives us 2,600.
Hurry pls (Time limit)
Give me the domain and range
Tell me if the graph is a function or not.
The answer choices are below
The graph is a function: yes.
The domain of this function is: all real numbers.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.
Range = {-∞, ∞}, y|y ∈ R, or all real numbers.
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Find the area of the rhombus below.
The area of the rhombus is derived to be 70 square units
How to calculate for the area of the rhombusIn calculating for the area of a rhombus, we multiply the length of its two diagonals and divide the result by two
For the given rhombus, we have diagonals:
5 + 5 = 10 and 7 + 7 = 14
thus;
Area of the rhombus = (10 × 14)/2
Area of the rhombus = 140/2
Area of the rhombus = 70 square units.
Therefore, the area of the rhombus is derived to be 70 square units.
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geometry please help fast
questions 1 and 2
Daran has a change jar that contains $0.80 in pennies and nickels. He has 10 more nickels than pennies. How many of each type of coin does he have?
Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. In 1996, the average LOS for non-heart patients was 4.6 days. A random sample of 20 hospitals in one state had a mean LOS for non-heart patients in 2000 of 3.8 days and a standard deviation of 1.2 days. How large a sample of hospitals would we need to be 99 percent confident that the sample mean is within 0.5 days of the population mean? Select one: a. 48 b. 7 c. 3 d. 32 e. 96
The sample of hospitals would we need to be 99 percent confident that the sample mean is within 0.5 days of the population mean is A. 48
How to calculate the sampleWe want to find the sample size (n) that would give us a confidence interval of 0.5 days, so we can rearrange the formula to solve for n:
n = (z*σ/CI)^2
Plugging in the given values:
z = 2.576 (for 99% confidence level)
σ = 1.2 days
CI = 0.5 days
n = (2.576 × 1.2/0.5)²
n ≈ 48
Therefore, the correct option is A.
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Which of these fractions is largest A: 6 as a fraction of 30 B: 30 centimetres as a fraction of 2 metres C: 16 pence as a fraction of £1 ? You must show your working.
Answer:
A: 6 as a fraction of 30 = 6/30 = 1/5
B: 30 centimetres as a fraction of 2 metres = 30/200 = 3/20
C: 16 pence as a fraction of £1 = 16/100 = 4/25
To compare these fractions, we need to express them with a common denominator. The smallest common multiple of 5, 20, and 25 is 100. So we can convert each fraction to have a denominator of 100:
A: 1/5 = 20/100
B: 3/20 = 15/100
C: 4/25 = 16/100
Now we can see that the largest fraction is C: 16 pence as a fraction of £1, which is 16/100 or 16%.
Step-by-step explanation:
Mark Brainliest!!
Simplify √ x + 3√ 3x − 5√ x.
Answer: -4rootx+3root3x
Step-by-step explanation:
think of the expression under the radicals as like terms, you can only add those that are the exact same 1-5=-4(rootx) can't do anything with the middle
710 divided by 9
what is the answer please help
Answer:
78.8888888889 or just round to 79
Step-by-step explanation:
Your welcome. Can you please mark me brainliest please? :)
Answer:
78.8888888889
Step-by-step explanation:
Find the probability the student is a sophomore.
Answer:
I believe the answer is 30%
You are 28-year-old healthy male and interested in purchasing life insurance. Using the table, determine what the annual premium for a Whole Life insurance police, given that the face value of the policy is $162,253. If need be, round your answer to the nearest cent.
The annual premium for a Whole Life insurance policy, for the healthy male, would be A. $ 2, 881.61
How to find the annual premium ?From the given table, a 28 year old male would have to pay $ 17. 76 for each $ 1,000 of coverage of Whole Life Insurance.
For a policy that is worth $ 162, 253 therefore, the annual premium would therefore be:
= Amount per thousand / 1, 000 x Policy coverage
= 17. 76 / 1, 000 x 162, 253
= 0.01776 x 162, 253
= $ 2, 881.61
In conclusion, the annual premium is $ 2, 881.61 .
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A pilot wants to fly on a bearing of 60.8. By flying due east he finds that a 59 mph wind blowing from the south puts him on course. Find ground speed of the plane
Answer:
68
Step-by-step explanation:
We can use vector addition to solve this problem. Let's consider two vectors: the velocity of the plane relative to the ground, which we want to find, and the velocity of the wind relative to the ground, which we know is due south with a magnitude of 59 mph.
Let's call the ground speed of the plane "v" and the angle between the plane's velocity and the due east direction "θ". The bearing of 60.8 is the angle between the plane's velocity and due north, so the angle between the plane's velocity and due east is (90 - 60.8) = 29.2 degrees.
Now we can use trigonometry to find the components of the plane's velocity relative to the ground:
v(cosθ, sinθ) = (v cosθ, v sinθ)
The plane's velocity relative to the wind is due east, so its x-component is v cosθ = 59 mph. Therefore, we can solve for v:
v = 59 / cosθ
v = 59 / cos(29.2) ≈ 67.55 mph
So the ground speed of the plane is approximately 67.55 mph. Round it up to 68.
r(t) =
t2 − 36
i − j + ln(t − 1)k
(a)
Find the domain of r.
The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
The given vector function can be correctly expressed as:
r(t) = (t-2)i / (t+2) + sintj + ln(36-t²)k²
The domain of the given function can be determined by finding the domain of each respective component.
(t-2)i / (t+2)
Not defined, t = -2
Thus, the domain of the first component of the vector = (-∞, 2) ∪ (2, ∞)
The 2nd component = sin t
No restriction on t,
The 3rd component of the function is ㏑(36 - t²)
we know,
Natural number is defined for +ve numbers,
i.e.
36 - t² > 0
(6 + t) (6 - t) > 0
thus, it satisfies the inequality -6 < t < 6
The third domain = (-6,6)
Hence, the domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
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Will give Brainliest and points!!!!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
How to calculate or determine the rate of change or slope of a line?In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 24)/(6 - 0)
Slope (m) = -24/6
Slope (m) = -4.
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Given ⊙K with secants NS and NR, which expression represents PS?
An expression that represent PS include the following: C. (NP + NQ + QR)/NR - NR.
What is the Tangent Secant Theorem?In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.
By applying the Tangent Secant Theorem to this circle, we have the following:
NP × PS = NQ × QR
PS = (NQ × QR)/NP
In terms of line segment NR, the expression can be rewritten as follows;
(NP + NQ + QR)/NR - NR
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1
2
32
1 point
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
The value of the median for this data set would be type your answer....
1 point
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
The value of the mode for this data set would be type your answer.....
1 point
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
The value of the mean for this data set would be type your answer....
(Input only a number)
(Input only a number)
(Input only a number)
AnswerAnswer:
55
60
57.27
Step-by-step explanation:
rearrange the values in order:
40, 45, 45, 50, 50, 55, 60, 60, 60, 95, 100
1. median is the middle number when we put all the numbers in order, and it is 55 for this list.
2. mode is the number that appears the most, and in this list, it's 45 and 60.
3. mean is the average of all the scores in the list, and it's 57.27 for this list.
chatgpt
PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
415.67 = (1/3)(13.4)(11.7)h
415.67 = 52.26h
h = about 7.95 feet
birth weights for a simple random sample of 195 boys were recorded. the mean weight calculated for this sample was 3.04 kilograms and the standard deviation was 0.71 kilograms
Answer:
The sample mean birth weight for the 195 boys is 3.04 kilograms and the sample standard deviation is 0.71 kilograms.
Step-by-step explanation:
Sera is solving a number puzzle that involves three integers e, f, and g where e is negative. The product of e and f is-12. The product of e and g is 6. The product of f and g is -8. What are the values for e, f, and g?
The values for e, f, and g are -3, 4 and -2 respectively.
What are the values for e, f, and g?e × f = -12
e × g = 6
f × g = -8
From (1)
ef = -12
e = -12/f
From (3)
fg = -8
g = -8/f
Substitute e and g into (2)
e × g = 6
-12/f × -8/f = 6
96/f² = 6
cross product
96 = f² × 6
96 = 6f²
divide both sides by 6
f² = 96/6
f² = 16
find the square root of both sides
f = √16
f = 4
Hence,
e × f = -12
e × 4 = -12
4e = -12
e = -12/4
e = -3
e × g = 6
-3 × g = 6
-3g = 6
g = 6/-3
g = -2
f × g = -8
4 × -2 = -8
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Question content area top
Part 1
The length of a rectangular park is six times its width. The park is surrounded by a 3-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.
The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).
Given that:
Width, W = x
Length, L = 6x
Path width, d = 3
The rectangle's area will be given as,
Area of the rectangle = L × W square units
The quadratic function to represent the total area of the park and the path will be given as,
A = (x + 2 · 3) (6x + 2 · 3)
A = (x + 6)(6x + 6)
A = 6(x + 6)(x + 1)
A = 6(x² + 7x + 6)
The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).
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Select the correct answer.
A glass case is in the shape of a rectangular prism. The volume of the case is cubic foot. How many cubic blocks with a side length of foot would
be required to find the volume of the glass case?
OA 2
OB 3
OC. 4
D. 5
Reset
From the question that we have, the solution that we have gotten is that 4 cubic blocks with a side length of foot would be required to find the volume of the glass case
How to solve the problemWe have been given that a glass case is in shape of a rectangular prism.
The volume of a single cubic block is:
We have
Volume of block
= (1/5) * (1/5) * (1/5)
= 1/125 cubic feet
Next we will now have to divide the volume of the glass case by the volume of a single cubic block:
V olume of case / Volume of the block =
(4/125) / (1/125)
= 4
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A glass case is in the shape of a rectangular prism. The volume of the case is cubic 4/125 foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case?
14) -1 -10a < -1 or 10 + 3a ≤-5
The solution to the inequality is:
0 < a or a ≤ -5
How to solve the inequality?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.
We have: -1 -10a < -1 or 10 + 3a ≤ -5 and we want to solve for the variable "a".
-1 -10a < -1 or 10 + 3a ≤ -5
-10a < -1 + 1 or 3a ≤ -5 - 10
-10a < 0 or 3a ≤ -15
a < 0/(-10) or a ≤ -15/3
a > 0 or a ≤ -5
Since a a > 0 is the same as 0 < a. We can say:
0 < a or a ≤ -5
Thus, 0 < a ≤ -5
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
The area of the composite figure is 13 ft².
How to find the area of a composite figure?The figure is a composite figure. The are of the composite figure is the sum of the individual areas.
The composite figure can be divided into two shapes namely rectangle and triangle.
Therefore,
area of the composite figure = area of the rectangle + area of the triangle
Hence,
area of the rectangle = 4.5 × 2
area of the rectangle = 9 ft²
area of the triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × 4 × 2
area of the triangle = 8 / 2
area of the triangle = 4 ft²
Therefore,
area of the composite figure = 9 + 4
area of the composite figure = 13 ft²
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please help me with this.
According to the figure,
a. angle LCQ is 45 degrees
b. the major arc are KPR and QRPK
c. congruent minor arcs are LQ and QR
d. the three arcs that form a semicircle are RP, LQ ,and QR
What are major arcs?A major arc designates a segment of an arch with a measurement which surpasses 180 degrees.
Geometrically, the circle, a closed curve, exhibits all its points uniformly spaced from a central focal point named the center of the circle.
The arc is regarded as major when it comprises a superior portion of the circular geometry, extending beyond half of the total circumference.
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The average student at Rio Hondo takes 9.1 units per semester (SD = 1.2). Some people believe that students in transfer level math will be more likely to be on track to graduate quickly. Five students from PSY 190 were taking 12, 14, 6, 6, and 16 units. Conduct the steps of hypothesis testing to determine whether students in PSY 190 take more units compared to the average Rio Hondo student.
The critical value from the given data is 2.776.
Hypothesis Testing:
Step 1: State the null and alternative hypotheses.
Null Hypothesis (H0): The average number of units taken by students in PSY 190 is equal to the average number of units taken by Rio Hondo students.
Alternative Hypothesis (H1): The average number of units taken by students in PSY 190 is greater than the average number of units taken by Rio Hondo students.
Step 2: Calculate a test statistic.
To calculate a test statistic, we will use a one-sample t-test. The t-test will allow us to compare the average of the PSY 190 students to the average of all Rio Hondo students. The test statistic will be calculated as follows:
t = (x - μ) / (s/√n)
Where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
In this case, x = 10.6, μ = 9.1, s = 5.1, and n = 5.
Plugging these values into the equation, we get:
t = (10.6 - 9.1) / (5.1/√5) = 1.78
Step 3: Determine the critical value.
To determine the critical value, we need to determine the degrees of freedom, which is equal to n-1 = 4. We can then look up the critical value in a t-table with α = 0.05 and 4 degrees of freedom. The critical value is 2.776.
Step 4: Compare the test statistic to the critical value.
Since the test statistic (1.78) is less than the critical value (2.776), we fail to reject the null hypothesis.
Therefore, the critical value from the given data is 2.776.
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san
3
Mia is the new CEO of a sales company. In her first year, the company made $475,000 in sales. In each of
the following years, her sales are expected to increase at a rate of 1796. If this trend continues, what will be
her company's sales in year 14?
A $6,201,709
B $5,129,458
C $3,656,872
D
$2,935,294
The company sales in year 14, given the rate of increase and the amount made in sales would be C $3,656,872.
How to find the sales ?In the first year, the sales of the company were $ 475, 000 and this sales is scheduled or predicted to grow at 17 %.
This means that the company sales in year 14 would be :
= Initial sales x ( 1 + rate ) ^ number of years
Initial sales = $ 475, 000
Rate = 17 %
Number of years = 14 years
The company sales in year 14 is:
= 475, 000 x ( 1 + 17 %) ¹⁴
= $3, 656, 872
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#3 i
Cylinder A and Cylinder B are similar. Find the surface area of Cylinder B. Give your answer in terms of pi.
The volume of the small cylinder is 36π
What are similar shapes?Similar figures are two figures having the same shape. The two cylinders are similar but of different radius and height.
The height of the big cylinder is calculated as
V = πr²h
h = V/ πr²
h = 144π/π36
h = 144/36
h = 4 cm
Therefore the scale factor = 4/2
area factor =( 4/2)² = 16/4
therefore the volume of the cylinder is;
16/4 = 144π/ x
16x = 144π × 4
16x = 576
dividing both sides by 16
x = 576/16
x = 36π
therefore the volume of the small cylinder is 36π.
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Jason has three T-shirts of different colors. He shares his T-shirts with his two brothers. How many ways can all three boys trade shirts and not wear the same color twice? A. one B. two C. three D. six
Answer: 6
Step-by-step explanation:
There are six possible ways that the three boys can initially choose shirts: ABC, ACB, BAC, BCA, CAB, CBA.
Use the information given in the figure to find the length RU. If applicable, round your answer to the nearest whole number.
Answer:7
Step-by-step explanation:
use the Pythagoras theorem to find su (40^2-32^2) take the square root =24 use this to solve for ru. (25^2-24^2=49) square root of 49 is
The ratio of the volume of cone A to the volume of cone B is 27:8
Cone A and cone B are mathematically similar.
The surface area of cone A is 297 cm²
Show that the surface area of cone B is 132 cm²