The concentration of salt in the tank at the end of 10 minutes is 0.01 pounds per gallon
We can use the formula:
(concentration of salt in tank) * (gallons of water in tank) = (total pounds of salt in tank)
To solve this problem. At the beginning, the tank contains 500 gallons of salt-free water, so the total pounds of salt in the tank is 0. After 10 minutes, 20 gallons of brine have entered the tank, and 20 gallons of the mixture have left the tank. As a result, the amount of water in the tank remains constant at 500 gallons.
The amount of salt that enters the tank in 10 minutes is:
(0.25 lb/gal) * (2 gal/min) * (10 min) = 5 lb
The total pounds of salt in the tank after 10 minutes is:
0 + 5 = 5 lb
Therefore, the concentration of salt in the tank at the end of 10 minutes is
(concentration of salt in tank) * (500 gallons) = 5 lb
Solving for the concentration of salt in the tank, we get:
concentration of salt in tank = 5 lb / 500 gallons
Simplifying this expression, we get:
concentration of salt in tank = 0.01 lb/gal
Therefore, the concentration of salt in the tank at the end of 10 minutes is 0.01 pounds per gallon.
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In Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet. Find the
length of US to the nearest tenth of a foot
If in Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet, then the length of US to the nearest tenth of a foot is approximately 39.4 feet.
In angle STU, we have a right triangle with U=90°, S=31°, and TU=77 feet. To find the length of US, we can use the sine function:
sin(S) = opposite side (US) / hypotenuse (TU)
sin(31°) = US / 77 feet
To find the length of US, multiply both sides by 77 feet:
US = 77 feet * sin(31°)
US ≈ 39.4 feet
Therefore, the length of US to the nearest tenth of a foot is approximately 39.4 feet.
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A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch?
Answer:
To make 3 gallons of punch, you need 2 cups of cranberry juice.
We can set up a proportion to find out how much cranberry juice is needed for 1 gallon of punch:
2 cups / 3 gallons = x cups / 1 gallon
To solve for x, we can cross-multiply:
2 cups * 1 gallon = 3 gallons * x cups
2 cups = 3x
x = 2/3 cup
Therefore, you would need 2/3 cup of cranberry juice to make 1 gallon of punch using this recipe.
A bracelet is now reduced to £420.this is 70% of the original price. what is the original price?
Answer:
.70p = £420, so p = £600
The original price of the bracelet is £600.
The original price of the bracelet was £600.
To find the original price of the bracelet, we need to use the information that the current price is 70% of the original price. We can use algebra to solve for the original price:
Let X be the original price of the bracelet.
70% of X is equal to £420.
We can write this as:
0.7X = £420
To solve for X, we can divide both sides of the equation by 0.7:
X = £420 ÷ 0.7
Evaluating the right-hand side gives us:
X = £600
Therefore, the original price of the bracelet was £600.
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Let f(x) = 2 sqrt(x)/8x^2 + 3x – 9
Evaluate f’(x) at x = 4.
The derivative of the function f(x) = 2 \sqrt(x) / (8x² + 3x - 9) evaluated at x = 4.
To find f'(x), we need to differentiate the given function f(x) using the power rule and the chain rule of differentiation.
First, we can rewrite the function f(x) as:
f(x) = 2x^{1/2} / (8x² + 3x - 9)
Next, we can differentiate f(x) with respect to x:
f'(x) = d/dx [2x^{1/2} / (8x² + 3x - 9)]
Using the quotient rule of differentiation, we have:
f'(x) = [ (8x² + 3x - 9) d/dx [2x^{1/2}] - 2x^{1/2} d/dx [8x² + 3x - 9] ] / (8x² + 3x - 9)²
Applying the power rule of differentiation, we have:
f'(x) = [ (8x² + 3x - 9)(1/2) - 2x{1/2}(16x + 3) ] / (8x² + 3x - 9)²
Now we can evaluate f'(x) at x = 4 by substituting x = 4 into the expression for f'(x):
f'(4) = [ (8(4)² + 3(4) - 9)(1/2) - 2(4)^(1/2)(16(4) + 3) ] / (8(4)² + 3(4) - 9)²
f'(4) = [ (128 + 12 - 9)(1/2) - 2(4)^(1/2)(67) ] / (128 + 12 - 9)^2
f'(4) = [ 131^(1/2) - 2(4)^(1/2)(67) ] / 12167
Therefore, f'(4) = [ 131^(1/2) - 134(2)^(1/2) ] / 12167.
This is the value of the derivative of f(x) at x = 4.
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As a candle burns, its wick gets smaller over time. When first purchased, the wick is 150 mm in length. After 50 minutes, the wick is only 110 mm in length. Find the slope you would use in a linear model of mm per minute. 3 points Construct an equation that models the length of the wick over this time period. Your answer should be in the proper form using correct letters and numbers with no spaces. 2 points Use your linear model to predict the how many minutes it would take to have 74 mm remaining. 3 points
It would take approximately 95 minutes for the wick to have 74 mm remaining.
1) Finding the slope (mm per minute):
The wick was initially 150 mm in length and reduced to 110 mm after 50 minutes. To find the slope, we use the formula:
Slope = (change in length) / (change in time)
Slope = (110 mm - 150 mm) / (50 minutes - 0 minutes)
Slope = (-40 mm) / (50 minutes)
Slope = -0.8 mm/minute
2) Constructing the linear equation:
We now have the slope (-0.8) and the initial length (150 mm) to create a linear equation:
Length (L) = initial length + slope × time (t)
L = 150 - 0.8t
3) Predicting the time to have 74 mm remaining:
To find the time, plug in 74 mm for the length (L) in the equation and solve for t:
74 = 150 - 0.8t
76 = 0.8t
t = 95 minutes
So, it would take approximately 95 minutes for the wick to have 74 mm remaining.
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Sushi corporation bought a machine at the beginning of the year at a cost of $39,000. the estimated useful life was five years and the residual value was $4,000. required: complete a depreciation schedule for the straight-line method. prepare the journal entry to record year 2 depreciation.
Entry debits the Depreciation Expense account for $7,000 and credits the Accumulated Depreciation account for the same amount, reflecting the decrease in the value of the machine over time.
To calculate deprecation using the straight- line system, we need to abate the residual value from the original cost of the machine and also divide the result by the estimated useful life. Using the given values, we have
Cost of machine = $ 39,000
Residual value = $ 4,000
Depreciable cost = $ 35,000($ 39,000-$ 4,000)
Estimated useful life = 5 times
To calculate the periodic deprecation expenditure, we divide the depreciable cost by the estimated useful life
Periodic deprecation expenditure = $ 7,000($ 35,000 ÷ 5)
Depreciation Expense $7,000
Accumulated Depreciation $7,000
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The journal entry is as given in figure:
Use the equations to find ∂z/∂x and ∂z/∂y. ez = 5xyz
The partial derivative of z with respect to x is 5xy + 5xz, and the partial derivative of z with respect to y is 5xz + 5yz.
To find the partial derivatives of z with respect to x and y, we use the chain rule. The chain rule allows us to find the rate of change of a function with respect to one of its independent variables while holding all other independent variables constant.
Using the chain rule, we can find the partial derivatives of z with respect to x and y as follows:
∂z/∂x = 5(yz) + 5x(1)(z)
∂z/∂x = 5xy + 5xz
∂z/∂y = 5(xz) + 5y(1)(z)
∂z/∂y = 5xz + 5yz
Therefore, the partial derivative of z with respect to x is 5xy + 5xz, and the partial derivative of z with respect to y is 5xz + 5yz.
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Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
The dot plot that most accurately displays Miss Little's class data is illustrated below.
To create a dot plot, we first need to determine the range of the data, which is the difference between the highest and lowest values. In this case, the range is from 8 to 16. We then draw a number line that spans the range, and mark each data point along the line with a dot.
Let's take a look at the first data set: 13, 14, 9, 12, 16, 11, and 10. The range is from 9 to 16, so we draw a number line from 9 to 16. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 13, one dot above 14, two dots above 9, one dot above 12, one dot above 16, one dot above 11, and one dot above 10.
We repeat this process for the second data set: 9, 8, 10, 10, 11, 15, and 10. The range is from 8 to 15, so we draw a number line from 8 to 15. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 9, one dot above 8, three dots above 10, one dot above 11, one dot above 15, and zero dots above 14.
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Complete Question:
Miss. Little wants to know how many pairs of shoes each of her students owns. She decides to ask each of her students to write the number of pairs of shoes that he or she owns. This data is displayed in the provided chart. Plot the dot plot that most accurately displays Miss Little's class data.
13 14 9 12 16 11 10
9 8 10 10 11 15 10
Shelby was in the next stall, and she needed 150 mL of a solution that was 30% glycerin. The two solutions available were 10% glycerin and 40% glycerin. How many milliliters of each should Shelby use?
Taking the data into consideration, Shelby should use 50 mL of the 10% glycerin solution and 100 mL of the 40% glycerin solution, as explained below.
How to find the amountsLet x be the amount of 10% glycerin solution and y be the amount of 40% glycerin solution that Shelby needs to use. We know that Shelby needs a total of 150 mL of the 30% glycerin solution, so we can write:
x + y = 150 (equation 1)
We also know that the concentration of glycerin in the 10% solution is 10%, and the concentration of glycerin in the 40% solution is 40%. So, the amount of glycerin in x mL of the 10% solution is 0.1x, and the amount of glycerin in y mL of the 40% solution is 0.4y. The total amount of glycerin in the 150 mL of 30% solution is 0.3(150) = 45 mL. So, we can write:
0.1x + 0.4y = 45 (equation 2)
We now have two equations with two variables. We can use substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.1, we get:
0.1x + 0.1y = 15 (equation 3)
Subtracting equation 3 from equation 2, we get:
0.3y = 30
y = 100
Substituting y = 100 into equation 1, we get:
x + 100 = 150
x = 50
Therefore, Shelby needs to use 50 mL of the 10% glycerin solution and 100 mL of the 40% glycerin solution.
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50 POINTS ASAP Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of five eighths to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(5.8, −3), B′(1.6, −1.5), C′(−1.6, 3), D′(2.5, 3)
A′(−16, 24), B′(−8, 8), C′(16, −24), D′(16, 16)
A′(2.5, −3.75), B′(1.25, −1.25), C′(−2.5, 1.25), D′(−2.5, −2.5)
A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)
Answer:
A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)
Step-by-step explanation:
in the described situation you only need to multiply the coordinates by the scale factor (in our case the given 5/8)
A (-4, 6) turns into
A' (-4×5/8, 6×5/8) = A' (-2.4, 3.75)
and therefore we know already here that all the other answer options are wrong.
When solving the equation 6x² - 2x = -3 with the quadratic formula.
If a = 6, what are the values of b and c?
b =
C =
A/
A student takes a measured volume of 3. 00 m hcl to prepare a 50. 0 ml sample of 1. 80 m hcl. What volume of 3. 00 m hcl did the student use to make the sample?.
The student used 30.0 mL of 3.00 M HCl to make the 50.0 mL sample of 1.80 M HCl.
To find the volume of 3.00 M HCl needed to make a 50.0 mL sample of 1.80 M HCl, we can use the equation:
M₁V₁ = M₂V₂
Where M₁ is the initial concentration, V₁ is the initial volume, M₂ is the final concentration, and V₂ is the final volume.
We are given M₁ = 3.00 M, M₂ = 1.80 M, and V₂ = 50.0 mL. We can rearrange the equation to solve for V₁:
V₁ = (M₂V₂) / M₁
V₁ = (1.80 M * 50.0 mL) / 3.00 M
V₁ = 30.0 mL
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Last question :) btw if u can’t tell the equation there is 6x+68
Answer:
The answer for x is 2
z is 100°
Step-by-step explanation:
80=6x+68
6x=80-68
6x=12
divide both sides by 6
6x/6=12/6
x=2
z=?(empty space)
?(empty space)=z
80+z+z+6x+68=360
Note:6x+68=80
80+80+2z=360
160+2z=360
2z=360-160
2z=200
divide both sides by 2
2z/2=200/2
z=100°
If (arc)mEA=112* and m
If angle of arc EA is 112 degrees then value of arc IV is 36 degrees by outside angles theorem
Given that Arc EA measure is One hundred twelve degrees
By Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs
(112-x)/2=38
112-x=38×2
112-x=76
112-76=x
36 degrees = angle IV or x
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What is the meaning of a relative frequency of 0. 56
A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.
In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.
To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.
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thank you !!!!!!!! (Choose ALL answers that are correct)
Answer:
a and b
Step-by-step explanation:
What is the equation, in slope-intercept form, of the line that passes through
(0, 5) and has a slope of -1? (6 points)
Oy=-x-5
Oy=x+5
Oy=-x+5
Oy=x-5
Answer:
C) y = - x + 5---------------------------
The given point (0, 5) represents the y-intercept and we have a slope of -1.
It translates as:
m = - 1, b = 5 in the slope-intercept equation of y = mx + bBy substituting we get equation:
y = - x + 5This is option C.
4 km 20) Determine the distance across the lake? 6 km Lake 6
hope this helps you
please help i need this asap
All the value of angles are,
⇒ ∠a = 118°
⇒ ∠b = 62°
⇒ ∠q = 84°
⇒ ∠v = 84°
Given that;
Two parallel lines t₁ and t₂ are shown in image.
Here, we have;
Apply the definition of corresponding angles,
∠d = 180 - 62
∠d = 118°
Hence, By definition of vertically opposite angles,
⇒ ∠a = 118°
And,
∠b = 180 - 118°
∠b = 62°
Apply the definition of corresponding angles,
∠q = 180 - 96
∠q = 84°
Hence, By definition of vertically opposite angles,
⇒ ∠v = 84°
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Given the center, a vertex, and one focus, find an equation for the hyperbola:
center: (-5, 2); vertex (-10, 2); one focus (-5-√29,2).
The equation of the hyperbola is -(x + 5)²/71 + (y - 2)² = -71
How to calculate the valueWe can also find the distance between the center and the given focus, which is the distance between (-5, 2) and (-5 - √29, 2):
d = |-5 - (-5 - √29)| = √29
Substituting in the known values, we get:
c² = a² + b²
(√29)² = (10)² + b²
29 = 100 + b²
b² = -71
(x - h)²/a² - (y - k)²/b² = 1
where (h, k) is the center of the hyperbola.
Substituting in the known values, we get:
(x + 5)²/100 - (y - 2)²/-71 = 1
Multiplying both sides by -71, we get:
-(x + 5)²/71 + (y - 2)²/1 = -71/1
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9. define a relation r on the integers, ∀m, n ∈ z, mean if m n is even. is r a partial order relation? prove or give counterexample.
No, the relation r is not a partial order relation.
To prove this, we need to show that r is not reflexive, not antisymmetric, or not transitive.
r is reflexive if ∀a∈Z, a a holds, which means that any integer is related to itself. This is true for r since a a = 2 × a = even.r is antisymmetric if whenever a b and b a, then a = b. This is not true for r since, for example, 2 6 and 6 2, but 2 ≠ 6.r is transitive if whenever a b and b c, then a c. This is not true for r since, for example, 2 6 and 6 4, but 2 is not related to 4.Since r fails to satisfy the antisymmetric property, it is not a partial order relation.
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2. A social media company claims that over 1 million people log onto their app daily. To test this claim, you record the number of people who log onto the app for 65 days. The mean number of people to log in and use the social media app was discovered to be 998,946 users a day, with a standard deviation of 23,876. 23. Test the hypothesis using a 1% level of significance.
The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the t-value (-1.732) is less than the critical value (-2.429).
Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.
Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.
Level of significance = 1%
We can use a one-sample t-test to test the hypothesis.
t = (X - μ) / (s / √n)
where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Substituting the values, we get
t = (998,946 - 1,000,000) / (23,876 / √65)
t = -1.732
Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.
Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.
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3. let f be a differentiable function on an open interval i and assume that f has no local minima nor local maxima on i. prove that f is either increasing or decreasing on i.
Shown that if f has no local minima nor local maxima on i, then f is either increasing or decreasing on i.
Since f has no local minima nor local maxima on i, it means that for any point x in i, either f is increasing or decreasing in a small interval around x. In other words, either f'(x) > 0 or f'(x) < 0 for all x in i.
Now suppose there exist two points a and b in i such that a < b and f(a) < f(b). We want to show that f is increasing on i.
Consider the interval [a,b]. By the Mean Value Theorem, there exists a point c in (a,b) such that f'(c) = (f(b) - f(a))/(b - a). Since f(a) < f(b), we have (f(b) - f(a))/(b - a) > 0, which implies f'(c) > 0. Since f'(x) > 0 for all x in i, it follows that f is increasing on [a,c] and on [c,b]. Therefore, f is increasing on i.
A similar argument can be made if f(a) > f(b), which would imply that f is decreasing on i.
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An experiment involving learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available in environment I is 420 minutes, and the maximum amount of time available in environment II is 600 minutes. The white mice must spend 10 minutes in environment I and 25 minutes in environment II, and the rabbits must spend 12 minutes in environment I and 15 minutes in environment II. Find the maximum possible number of animals that can be used in the experiment and find the number of white mice and the number of rabbits that can be used.
We find that the maximum possible number of animals is 37, with 17 white mice and 20 rabbits.
Let's use the following variables:
x be the number of white mice
Let y be the number of rabbits
Based on the given information, we can create the following system of linear inequalities:
10x + 12y ≤ 420 (maximum time available in environment I)
25x + 15y ≤ 600 (maximum time available in environment II)
We also have the constraints that x and y must be non-negative integers.
To solve this problem, we can use a graphing approach. We can graph each inequality on the same coordinate plane and shade the region that satisfies all the constraints. The feasible region will be the region that is shaded.
However, since x and y must be integers, we need to find the corner points of the feasible region and test each one to see which one gives us the maximum value of x + y.
To find the corner points, we can solve each inequality for one variable and then substitute into the other inequality:
For the first inequality: 12y ≤ 420 - 10x, so y ≤ (420 - 10x)/12
For the second inequality: 15y ≤ 600 - 25x, so y ≤ (600 - 25x)/15
Since y must be a non-negative integer, we can use the floor function to round down to the nearest integer:
For the first inequality: y ≤ ⌊(420 - 10x)/12⌋
For the second inequality: y ≤ ⌊(600 - 25x)/15⌋
We can then plot these two expressions on the same graph and find the points where they intersect. We can then test each point to see if it satisfies all the constraints and if it gives us the maximum value of x + y.
After doing all the calculations, we find that the maximum possible number of animals is 37, with 17 white mice and 20 rabbits.
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Shannon's net worth is $872. 17 and her liabilities are $15,997. If she pays off a credit card with a balance of $7,698, what is her new net worth?
Answer:
To calculate Shannon's new net worth after paying off her credit card, we need to subtract the credit card balance from her total liabilities, and then subtract the result from her net worth:
New liabilities = $15,997 - $7,698 = $8,299
New net worth = $872.17 - $8,299 = -$7,426.83
Based on these calculations, Shannon's new net worth would be -$7,426.83 after paying off her credit card. This indicates that her liabilities still exceed her assets, and she would need to continue working towards reducing her debt and increasing her net worth over time.
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8-73.
For each diagram below, write and solve an equation for x
Answer:
a.x=100 equation: 540=(125·2)+90+(2x)
b. x=3 equation: 6x+18=2x+30
Step-by-step explanation:
a. We know that the interior angles of a pentagon have to equal 540 degrees.
So:
540=125+125+90 (hence the square) + x + x
simplify:
540=340+2x
simplify:
200=2x
x=100
b. Using the alternate exterior angles theorem we can say:
6x+18=2x+30
simplify:
4x+18=30
4x=12
x=3
145 student are in the auditorium. Of the students in the auditorium, about 86% of the students play a sport. About 45% of the students are in the school play. How many students play a sport? How many students are in the play? Round your answer to the nearest whole
About 125 students play a sport and about 65 students are in the play.
To find the number of students who play a sport and those who are in the play, we need to use the given percentages and round the answers to the nearest whole.
Find the number of students who play a sport:
Multiply the total number of students (145) by the percentage of students who play a sport (86%).
145 × 0.86 = 124.7
Round the answer to the nearest whole number:
Approximately 125 students play a sport.
Find the number of students who are in the play:
Multiply the total number of students (145) by the percentage of students who are in the play (45%).
145 × 0.45 = 65.25
Round the answer to the nearest whole number:
Approximately 65 students are in the play.
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In ABC, the bisector of A divides BC into segment BD with a length of
28 units and segment DC with a length of 24 units. If AB -31. 5 units, what
could be the length of AC ?
To find the length of AC in triangle ABC, we will use the Angle Bisector Theorem and the given information:
In triangle ABC, the bisector of angle A divides BC into segments BD and DC, with lengths of 28 units and 24 units, respectively. Given that AB has a length of 31.5 units, we want to determine the possible length of AC.
Step 1: Apply the Angle Bisector Theorem, which states that the ratio of the lengths of the sides is equal to the ratio of the lengths of the segments created by the angle bisector. In this case, we have:
AB / AC = BD / DC
Step 2: Plug in the known values:
31.5 / AC = 28 / 24
Step 3: Simplify the ratio on the right side:
31.5 / AC = 7 / 6
Step 4: Cross-multiply to solve for AC:
6 * 31.5 = 7 * AC
Step 5: Calculate the result:
189 = 7 * AC
Step 6: Divide both sides by 7 to find AC:
AC = 189 / 7
Step 7: Calculate the value of AC:
AC = 27 units
So, the length of AC in triangle ABC could be 27 units.
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What is the volume of the prism, measured in cubic inches
Answer:
360 cubes
Step-by-step explanation:
In May, the cost for a child is not changed. The cost for an adult is reduced by p % to $22.10. (i) Calculate p.
The cost for an adult is reduced by approximately 26.33% to $22.10.
How to solveThe original cost for an adult ticket (X) = $30
The reduced cost for an adult ticket = $22.10
We need to find the percentage decrease (p) from the original cost to the reduced cost:
p = ((Original cost - Reduced cost) / Original cost) * 100
p = (($30 - $22.10) / $30) * 100
p = ($7.90 / $30) * 100
p ≈ 26.33 %
The fee for an adult has notably decreased by approximately 26.33%, now costing a mere $22.10.
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In May, the cost for a child is not changed. The cost for an adult is reduced by p % to $22.10. If the original cost of an adult ticket is $X, (i) calculate p, given that the original cost for an adult ticket is $30.
