The original house has 70 square feet of flooring.
If the ratio of the miniature house to the original structure is 2:35, then we can say that the miniature house is 2/35th the size of the original house in terms of floor area. Let's assume that the original house has x square feet of flooring. Then, we can set up a proportion based on the ratios:
2/35 = 4/x
Solving for x, we get:
x = 70
Therefore if the ratio of ambers miniature house to the original structure is 2:35 and the miniature requires 4 square feet of the flooring then original house has 70 square feet of flooring.
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atlantic auditorium has 850 seats . tickets were sold for 816 of the seats. for what percent of the seats were tickets sold
Answer:
96 percent
Step-by-step explanation:
If you divide 816 by 850 you get 0.96. If you multiply 0.96 by 100% you get 96%.
Can someone please help me ASAP? It’s due tomorrow. Show work
Answer:
10 outcome is the answer
solve quadratic equation 6x²-11x-35= 0 pls needed urgently
Answer:
Step-by-step explanation:To solve the quadratic equation 6x²-11x-35= 0, we can use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, we have:
a = 6
b = -11
c = -35
Substituting these values into the quadratic formula, we get:
x = (-(-11) ± sqrt((-11)² - 4(6)(-35))) / 2(6)
Simplifying this expression:
x = (11 ± sqrt(121 + 840)) / 12
x = (11 ± sqrt(961)) / 12
x = (11 ± 31) / 12
So, we have two solutions:
x = (11 + 31) / 12 = 3
and
x = (11 - 31) / 12 = -5/2
Therefore, the solutions to the equation 6x²-11x-35= 0 are x = 3 and x = -5/2.
Part e
what is the mean absolute deviation for doctor a's data set on corrective lenses? what is the mean absolute deviation
for doctor b's data set on corrective lenses? write a sentence comparing the variation of the two data sets using their
mean absolute deviations.
The MAD for Doctor A's data set is 0.67 and the MAD for Doctor B's data set is 0.83. Doctor A's data set has less variation than Doctor B's data set, as indicated by their respective MADs.
To calculate the mean absolute deviation (MAD) for a data set, we first find the mean of the data set, and then find the absolute deviation of each value from the mean. We then find the mean of these absolute deviations.
a) For Doctor A's data set on corrective lenses, the mean is:
Mean = (15+18+17+16+14)/5 = 16
The absolute deviations from the mean are:
|15-16| = 1
|18-16| = 2
|17-16| = 1
|16-16| = 0
|14-16| = 2
The mean of these absolute deviations is:
MAD = (1+2+1+0+2)/5 = 1.2
Therefore, the MAD for Doctor A's data set is 1.2.
b) For Doctor B's data set on corrective lenses, the mean is:
Mean = (17+19+20+16+18)/5 = 18
The absolute deviations from the mean are:
|17-18| = 1
|19-18| = 1
|20-18| = 2
|16-18| = 2
|18-18| = 0
The mean of these absolute deviations is:
MAD = (1+1+2+2+0)/5 = 1.2
Therefore, the MAD for Doctor B's data set is also 1.2.
Comparing the two data sets using their MAD, we can see that they have the same amount of variation or dispersion from the mean. Both sets have a MAD of 1.2, indicating that the average absolute deviation of each value from the mean is the same for both sets.
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Answer:
Doctor A MAD: 11.8
Doctor B MAD: 9.32
Step-by-step explanation:
This is what I got on the assignment.
Barak is going to buy 550 nails from one of these companies.
Nail Company
50 nails
£4. 15 plus VAT at 20%
Hammer Company
25 nails
£2. 95
Special offer
Buy 100 get 25 free
He wants to buy the nails at the cheaper cost.
Where should he buy the nails, from the Nail Company or the Hammer Company?
Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
Let's first calculate the cost of buying 550 nails from each company:
Nail Company:
Cost of 1 nail = £4.15 + (20% of £4.15) = £4.15 + £0.83 = £4.98 (rounded to 2 decimal places)
Cost of 50 nails = £4.98 x 50 = £249
Cost of 550 nails = £249 x 11 = £2739
Hammer Company:
Cost of 1 nail = £2.95/25 = £0.118 (rounded to 3 decimal places)
Cost of 75 nails (buy 100 get 25 free) = 100 x £0.118 x 3 = £35.40
Cost of 550 nails = 550 x £0.118 = £64.90
Therefore, Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
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1
(Lesson 8.2) Which statement about the graph of the rational function given is true? (1/2 point)
4. f(x) = 3*-7
x+2
A. The graph has no asymptotes.
B.
The graph has a vertical asymptote at x = -2.
C. The graph has a horizontal asymptote at y =
+
Answer:
B. The graph has a vertical asymptote at
x = -2.
The statement about the graph of the given rational function that is true is: B. The graph has a vertical asymptote at x = -2.
To understand the graph of the rational function f(x) = (3x - 7) / (x + 2), we need to consider its behavior at various points. First, let's investigate the possibility of asymptotes. Asymptotes are lines that the graph approaches but never touches. There are two types of asymptotes: vertical and horizontal.
A vertical asymptote occurs when the denominator of the rational function becomes zero. In this case, the denominator is (x + 2), so we need to find the value of x that makes it zero. Setting x + 2 = 0 and solving for x, we get x = -2. Therefore, the rational function has a vertical asymptote at x = -2 (option B).
To determine if there is a horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of a term is the highest power of x in that term. In the given rational function, the degree of the numerator is 1 (3x) and the degree of the denominator is also 1 (x). When the degrees are the same, we look at the ratio of the leading coefficients, which are 3 (numerator) and 1 (denominator). The ratio of the leading coefficients is 3/1 = 3.
If the ratio of the leading coefficients is a finite value (not zero or infinity), then the rational function will have a horizontal asymptote. In this case, the horizontal asymptote is y = 3 (option C).
Hence the correct option is (b).
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The Wyler Aerial Tramway in Franklin Mountains State Park begins at the tramway station, which is at an elevation of 4692 feet. It takes 4 minutes to reach Range Peak, which is at an elevation of 5632 feet. What equation is used to estimate the height E of the tramway t seconds after it left the station?
E = 4692-3. 9t
E = 4692 + 3. 9t
E = 5623 + 3. 9t
E = 5623 - 4692t
About the equation used to estimate the height E of the tramway t seconds after it left the station, we first need to calculate the rate of elevation gain per second.
Elevation difference: 5632 feet (Range Peak) - 4692 feet (tramway station) = 940 feet
Time: 4 minutes * 60 seconds/minute = 240 seconds
Rate of elevation gain: 940 feet / 240 seconds = 3.9167 feet/second (approximately 3.9 feet/second)
Now, we can write the equation to estimate the height E of the tramway t seconds after it left the station:
E = initial elevation + (rate of elevation gain * t)
E = 4692 + 3.9t
So, the correct equation is: E = 4692 + 3.9t
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5.2 cm
4 cm
V = bh
V = ______ x 4
V=
3 cm
Area of base:_________x
cubic cm
11
sq. cm
Use the given terms to generate a recursive rule. Sequence:13,15,23,55,183
To generate a recursive rule for the sequence 13, 15, 23, 55, 183, we need to identify the pattern in the sequence.
Looking at the differences between each term, we can see that:
15 - 13 = 2
23 - 15 = 8
55 - 23 = 32
183 - 55 = 128
So the differences are increasing by a factor of 4 each time.
Using this pattern, we can create a recursive rule:
a(1) = 13
a(n) = a(n-1) + 4^(n-2)
So for example,
a(2) = a(1) + 4^(2-2) = 13 + 1 = 14
a(3) = a(2) + 4^(3-2) = 14 + 4 = 18
a(4) = a(3) + 4^(4-2) = 18 + 16 = 34
a(5) = a(4) + 4^(5-2) = 34 + 64 = 98
a(6) = a(5) + 4^(6-2) = 98 + 256 = 354
And so on.
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50 POINTS ASAP Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.
Triangle 1 Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 12 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 18 feet. The distance, along the ground, from the bottom of the ladder to the building is 8 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.
Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
27 feet
18 feet
12 feet
5 feet
The distance where the ladder is touching the building for triangle 2 is 12 ft
Determining the distance from the bottom of the building to the pointFrom the question, we have the following parameters that can be used in our computation:
Ladder 1
Distance along the ground = 12 ft
Distance touching the ladder = 8 ft
Ladder 2
Distance along the ground = 18 ft
Distance touching the ladder = x
Using proportion of similar triangles, we have
x : 18 = 8 : 12
Express as fraction
x/18 = 8/12
So, we have
x = 18 * 8/12
Evaluate
x = 12
Hence, the distance where the ladder is touching the building for triangle 2 is 12 ft
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Answer:
12?
Step-by-step explanation:
Not too sure! I am in the middle of taking the test right now though
4. What are the possible values for b, if x2 + bx - 9 is factorable?
(List factor pairs and add them to show your work. )
If x² + bx - 9 is factorable, then the possible values for b are -6 and 6.
To factor x² + bx - 9, we need to find two numbers that multiply to -9 and add up to b. We can write this as (x + a)(x + b) = x² + bx - 9. Since the coefficient of x² is 1, the two numbers that multiply to -9 must add up to the coefficient of x, which is b. We can find the factor pairs of -9 to see which ones add up to b:
-1 and 9 add up to 8
-3 and 3 add up to 0
-9 and 1 add up to -8
3 and -3 add up to 0
1 and -9 add up to -8
9 and -1 add up to 8
Only -6 and 6 add up to b, so the possible values for b are -6 and 6. Therefore, x² - 6x - 9 and x² + 6x - 9 are both factorable.
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A recent survey of fortune 500 firms found that on average, they contribute $332.54 per month for each salaried employee's health insurance. if you are told that almost all salaried employees at fortune 500 firms receive a health insurance contribution between $220.61 and $444.47, and assuming a bell-shaped distribution, what must the standard deviation for this data be
The standard deviation for the data must be approximately $111.93.
How to calculate the standard deviationSince we are given a range of values that encompasses about 95% of the data, we can assume that this range is within two standard deviations of the mean.
Thus, we can set up the following equation:
2σ = $444.47 - $220.61
Simplifying this equation, we get:
2σ = $223.86
σ = $111.93
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The amount of time spent practicing shooting free throws and the percentage made in a game
The relationship between the amount of time spent practicing shooting free throws and the percentage made in a game can be described as a positive correlation.
As a basketball player dedicates more time to practicing free throws, their skill and accuracy in making these shots during a game typically improve.
Consistent practice is crucial for developing muscle memory and fine-tuning shooting techniques, which contribute to a higher success rate in making free throws during games. This increased success rate is reflected in the percentage of free throws made in a game, an essential factor that can influence the outcome of the match.
However, it is important to note that the correlation is not always linear. For example, a player who practices for hours on end may experience diminishing returns due to fatigue or lack of focus. Additionally, other factors such as pressure, game context, and individual differences in learning abilities can affect the percentage of free throws made in a game.
In conclusion, investing time in practicing free throws generally leads to an improvement in a player's in-game performance. While there are external factors that may influence the success rate, the positive correlation between practice time and the percentage of free throws made in a game emphasizes the importance of consistent and focused training for basketball players.
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I need help on the quesrion attached
A simplification of the expression [tex]\frac{x^3y^3 \cdot x^3 }{4x^2}[/tex] is [tex]\frac{x^4y^3 }{4}[/tex].
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we have the following:
[tex]\frac{x^3y^3 \cdot x^3 }{4x^2}=\frac{x^{3+3-2}y^3 }{4}\\\\\frac{x^{3+3-2}y^3 }{4}=\frac{x^4y^3 }{4}[/tex]
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Complete Question;
Simplify each of the expressions given.
Cleo bought a computer for
$
1
,
495
. What is it worth after depreciating for
3
years at a rate of
16
%
per year?
The worth of the computer after depreciating for 3 years is $749.77, under the condition that a rate of 16% per year was applied.
Then the derived formula for evaluating depreciation
Depreciation = (Asset Cost – Residual Value) / Life-Time Production × Units Produced
Then,
Asset Cost = $1,495
Residual Value = 0 (assuming the computer has no resale value after 3 years)
Life-Time Production = 3 years
Units Produced = 1
Hence, the depreciation rate
[tex]Depreciation Rate = (1 - (Residual Value / Asset Cost)) ^{ (1 / Life-Time Production) - 1}[/tex]
[tex]Depreciation Rate = (1 - (0 / 1495))^{(1/3-1)}[/tex]
Depreciation Rate = 16%
Now to evaluate the value of the computer after three years of depreciation at a rate of 16% per year, we can apply the derived formula
Value of Asset After Depreciation = Asset Cost × (1 - Depreciation Rate) ^ Life-Time Production
Value of Asset After Depreciation = $1,495 × (1 - 0.16)³
Value of Asset After Depreciation = $749.77
Hence, the computer is worth $749.77 after three years of depreciation at a rate of 16% per year.
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The complete question is
Cleo bought a computer for $1,495. What is it worth after depreciating for 3 years at a rate of 16% per year?
Use similar triangles to calculate the height, h cm, of triangle ABE. 10 cm 36 cm D B 20 cm E Optional working I h = Answ cm Search
Answer:
h=24
Step-by-step explanation:
Since the traingles are similar we can calculate the scale factor
20/10 = 2
So the Linear Scale Factor is 2
We can use that to figure out the ratio between the 2 triangles
Since DC = 10 and AE = 20
We cans say that the ratio between DBC and ABE is 2:1
Using this we can see that the ratio of the height is split into 2:1 and the total is 3
Knowing this we can calculate the the heights of both triangles
36 / 3 = 12
Height of small traingle = 1*12 = 12
Height of large triangle = 2*12 = 24
Find the time taken for $400 to amount to $650 at 6% compound interest annually
The time taken for $400 to amount to $650 at 6% compound interest annually is 8.33 years.
Compound interest is expressed as below:
[tex]A = P(1+\frac{r}{n})^{nt[/tex]
where A is the amount
P is principal
r is the rate of interest
n is the frequency with which interest is compounded per year
t is the time
A = $650
P = $400
r = 0.06
n = 1 because the interest is compounded annually. Thus the frequency of interest compounded per year is 1
650 = 400 [tex](1+0.06)^t[/tex]
1.625 = [tex]1.06^t[/tex]
t = 8.33 years
Thus, it takes 8.33 years for $400 to convert to $650 at 6% compound interest annually.
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652 10(3) trying to determine platelet count from a test result.
The platelet count is 652 x 10^3.
How to determine platelet count?Based on the information provided, it seems that the platelet count from a test result is 652, and the normal range for platelet count is 150,000 to 450,000 platelets per microliter of blood. The value "10(3)" likely refers to the measurement being in thousands.
To convert the measurement to the standard unit of platelet count, we need to multiply the given value by 1,000. Thus, 652 * 1,000 = 652,000 platelets per microliter.
It's important to note that platelet counts can vary depending on various factors, and medical professionals typically interpret the results in conjunction with other clinical information. If the obtained value of 652,000 platelets per microliter is accurate, it would be significantly higher than the upper limit of the normal range.
It's crucial to consult a healthcare professional or a qualified medical practitioner for an accurate interpretation of test results and any necessary medical advice or treatment.
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#SPJ11Alex throws a ball straight upward, releasing the ball 4 feet above the ground. At 1.5 seconds the ball reaches its maximum height, then the ball begins falling toward the ground. The graph represents the height of the ball over time. Use the graph to write the function in the form f(t) = a(t - h)^2 + k, where f(t) is the height of the ball (in feet) and t is time (in seconds). Alex catches the ball 3 feet above the ground. How long is the ball in the air before it is caught?
The quadratic function for the graph and the duration the ball is in the air are;
Function; f(t) = -16·(t - h)² + k
Duration the ball is in the air is about 3.02 seconds
What is a quadratic function?A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
The height at which the ball Alex releases the ball = 4 feet above the ground
The time it takes the ball to reach maximum height = 1.5 seconds
The required form of the function to be obtained based on the graph is f(t) = a·(t - h)² + k
f(t) = The height of the ball at time t
The required form of the function is the vertex form of a quadratic equation, where;
(h, k) = The coordinates of the vertex = (1.5, 40)
The points on the graph are; (0, 4), (3, 3)
Therefore; f(0) = a·(0 - 1.5)² + 40 = 4
a·(0 - 1.5)² = 4 - 40 = -36
a = -36/(1.5²) = -16
The equation is; f(t) = -16·(t - 1.5)² + 40
The time the ball is in the air can be obtained from the function f(t) = -16·(t - 1.5)² + 40 as follows;
f(t) = -16·(t - 1.5)² + 40 = 3
-16·(t - 1.5)² = 3 - 40 = -37
(t - 1.5)² = -37/(-16)
(t - 1.5) = (√(37))/4
t = (√(37))/4 + 1.5 ≈ 3.02
The time the ball is in the air about 3.02 seconds
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Solve the initial value problem. Dy/dx = 4x^-3/4, y(1) = 3 a. y = 16x^1/4 - 13 b. y = 16x1/4 + 48 c. y = -3/4^x7/4-13/4 d. y= 4x^1/4 - 1
The solution to the given initial value problem is (d) y = 4x^(1/4) - 1.
Given the initial value problem,
dy/dx = 4x^(-3/4), y(1) = 3
Integrating both sides with respect to x, we get
∫dy = ∫4x^(-3/4)dx
y = -8x^(-1/4) + C
where C is the constant of integration.
To find the value of C, we use the initial condition y(1) = 3
3 = -8(1)^(-1/4) + C
C = 3 + 8 = 11
Therefore, the solution to the initial value problem is
y = -8x^(-1/4) + 11
Simplifying further,
y = 11 - 8/x^(1/4)
Hence, the correct option is d) y = 4x^(1/4) - 1 is not the solution to the given initial value problem.
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A parking lot is 316 feet long. Workers paint lines to make one row of parking spaces. They do not paint lines on a 28-foot length at one end of the row in order to allow cars room to turn. The workers paint lines along the rest of the row to make 9-foot-wide parking spaces. How many parking spaces does the parking lot have?
The number of parking spaces that the parking lot has is 32 parking spaces.
How to find the number of spaces ?To start, we must ascertain the parking lot's length designed exclusively for parking spaces. Bearing in mind that 28 feet at one end of each row is left unmarked, this distance is subtracted from the overall parking lot length:
316 feet - 28 feet = 288 feet
It is now established that the width of each space assigned to a car is equal to nine feet. Consequently, dividing the previously determined length used for parking by the allotted width per car will determine the total number of available parking spaces:
288 feet / 9 feet = 32 parking spaces
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Match each equation to its graph and table representation
Answer:
The first one is B & H
2nd one is A & G
3rd one is D & E
4th one is C & F
Step-by-step explanation:
Alexi sells apples in her garden at a stand sell each 3. 00 apples what is her total cost how many should she produce
Alexi to consider these factors before deciding how many apples to produce depends on the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently.
How to determine Alexi's total revenue?To determine Alexi's total revenue, we need to know how many apples she plans to sell. Let's assume that Alexi plans to sell X apples.
If Alexi sells each apple for $3, her total revenue will be:
Total revenue = Price per apple x Number of apples sold
Total revenue = $3 X X
Total revenue = $3X
To determine the cost of producing the apples, we need more information about Alexi's production costs. These costs can include expenses such as land, labor, water, and equipment.
Once we know the production costs, we can subtract them from the total revenue to determine Alexi's profit. If the profit is positive, then Alexi will earn money by selling the apples.
In terms of how many apples Alexi should produce, it depends on factors such as the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently. It's important for Alexi to consider these factors before deciding how many apples to produce.
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Describe the transformations f(x)= square root 4x
The transformation of f(x) = √(4x) from the parent function g(x) = √(x) includes a horizontal stretch by a factor of 1/4, with no horizontal or vertical shifts.
The function f(x) = √(4x) is a transformation of the parent function, g(x) = √(x). The transformations include a horizontal stretch, a horizontal shift, and a vertical shift. Let's break down each transformation step-by-step:
1. Horizontal Stretch: The factor 4 inside the square root function multiplies the input (x) by 4. This results in a horizontal stretch by a factor of 1/4, meaning the graph is compressed horizontally towards the y-axis.
2. Horizontal Shift: There is no additional value added or subtracted from the input (x), so there is no horizontal shift in this function. The graph remains in its position along the x-axis.
3. Vertical Shift: Similarly, there is no additional value added or subtracted from the output (the entire function), so there is no vertical shift in this function. The graph remains in its position along the y-axis.
This results in the graph of f(x) being compressed towards the y-axis compared to the graph of g(x).
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Evaluate the integral.
∫(x^3+4x)/x^4+8x^2+1
To evaluate the integral ∫(x^3+4x)/x^4+8x^2+1, we can use the substitution u = x^2 + 1. Then, du/dx = 2x, which means that dx = du/(2x). Substituting these into the integral, we get:
∫(x^3+4x)/x^4+8x^2+1 dx = ∫(1/u)(x^2+1)(x^3+4x)/(2x) du
= 1/2 ∫(u-1)/u^2 du
= 1/2 ∫(u/u^2 - 1/u^2) du
= 1/2 ln|u| + 1/2 (1/u) + C
= 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C
Therefore, the final answer is ∫(x^3+4x)/x^4+8x^2+1 dx = 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C.
Hi! To evaluate the integral, we can rewrite the given expression as follows:
∫((x^3 + 4x) / (x^4 + 8x^2 + 1)) dx
Now, let's use substitution to solve this integral. Let's set:
u = x^2 + 4
Then, the derivative du/dx = 2x. So, dx = du / (2x).
Now, we can rewrite the integral in terms of u:
∫((x^3 + 4x) / (u^2 + 1)) (du / (2x))
Notice that x^3/x and 4x/x simplify, and we are left with:
(1/2) ∫(u / (u^2 + 1)) du
Now we can integrate this expression:
(1/2) * [ln(u^2 + 1) + C]
Now, substitute back x^2 + 4 for u:
(1/2) * [ln(x^2 + 4 + 1) + C] = (1/2) * [ln(x^2 + 5) + C]
So, the evaluated integral is:
(1/2) * [ln(x^2 + 5) + C]
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During a firework show, the height h in meters of a specific rocket after t seconds can be modeled be h=-4. 6t^2+27. 6t+33. 6. What is the maximum height of the fireworks?
The maximum height of the fireworks using the equation h=-4.6t^2+27.6t+33.6 is 75 meters.
Identifying the coefficients a, b, and c from the given quadratic equation.
a = -4.6, b = 27.6, and c = 33.6
Calculating the t-value of the vertex using the formula t = -b / (2 × a)
t = -27.6 / (2 × (-4.6)) = 27.6 / 9.2 = 3
Now, plugging in the t-value back into the equation to find the maximum height.
h = -4.6(3)^2 + 27.6(3) + 33.6
= -4.6(9) + 82.8 + 33.6
= -41.4 + 82.8 + 33.6
= 75
The maximum height of the fireworks is 75 meters.
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the chance of rain on a random day in May in Gwinnett is about 30%. Using this empirical probability, what would you estimate the probability of having NO rain for an entire week (7 days)?
The probability of having NO rain for an entire week (7 days) is 0.9998
Estimating the probability of having no rainFrom the question, we have the following parameters that can be used in our computation:
P(Rain) = 30%
Given that the number of days is
n = 7
The probability of having no rain for an entire week is calculated as
P = 1 - P(Rain)ⁿ
Where
n = 7
Substitute the known values in the above equation, so, we have the following representation
P = 1 - (30%)⁷
Evaluate
P = 0.9998
Hence, the probability is 0.9998
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Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch.
The height of the rectangular frame is 30 inches.
How to find the height of the frame?Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. The rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame.
Hence, the height of the frame can be represented as follows:
using trigonometric ratios,
sin 36.87 = opposite / hypotenuse
sin 36.87 = h / 50
cross multiply
h = 50 sin 36.87
h = 50 × 0.60000142913
h = 30.0000714566
Therefore,
height of the frame = 30 inches
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he gift box is shaped like a rectangular prism. The box is 8.5 inches wide, 5 inches long, 5.1 inches tall. What is the volume of the box in cubic inches?
The volume of the gift box shaped like a rectangular prism whose dimensions are 8.5 in wide, 5 in long, and 5.1 in tall is 216.75 in³ .
The volume of rectangular prism = L × W × H
L = Length of the rectangular prism
W = Width of the rectangular prism
H = Height of the rectangular prism
Here, L = 5 in , W = 8.5 in , H = 5.1 in
The volume of rectangular prism = 5 × 8.5 × 5.1
The volume of rectangular prism = 216.75 in³
The volume of gift box shaped like a rectangular prism is 216.75 in³ .
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Eva signs up for dance classes. She pays a onetime registration fee and then the same monthly tuition. Eva pays $110 the first month and at the end of 9 months has paid $670 in all. Which equation can be used to model the tuition and registration fees?
Answer: (670 -110)/8
Step-by-step explanation:
Months: 110 the first month
*Now since she paid 670 in total she subtracts the 110 from the first month which is 560, and now there is an event amound paid in the other months so you divide 560 by 8 since 8 months are left over resulting in $70 each month.
January,
February,
March,
April,
May,
June,
July,
August,
