The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
What is meant by absolute maximum and absolute minimum values?
A function's absolute maximum point is the point at which it can reach its highest value. A similar absolute minimum point is where the function's least possible value is obtained.
Given: [tex]f(x)=xe^{\frac{-x2}{32} }[/tex]
Differentiate the function,
[tex]f'(x)=e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }[/tex]
[tex]e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=0[/tex]
[tex]\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=e^{\frac{-x^{2} }{32} }[/tex]
[tex]\frac{x^{2} }{16} =1[/tex]
[tex]x^{2} =16[/tex]
[tex]x=[/tex] ±[tex]4[/tex]
The interval is given as: [-2,8]
This means that the value of x = -4, is out of the interval.
So, we have the following critical points:
x = (-2, 4, 8)
⇒ f(x) at x = -2
[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-(-2)^{2} }{32} }[/tex]
[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-4}{32} }[/tex]
[tex]f(-2)=-1.765[/tex]
⇒ f(x) at x = 4
[tex]f(4)=4[/tex] × [tex]e^{\frac{-(4)^{2} }{32} }[/tex]
[tex]f(4)=4[/tex] × [tex]e^{\frac{-16}{32} }[/tex]
[tex]f(4)=2.426[/tex]
⇒ f(x) at x = 8
[tex]f(8)=8[/tex] × [tex]e^{\frac{-(8)^{2} }{32} }[/tex]
[tex]f(8)=8[/tex] × [tex]e^{\frac{-64}{32} }[/tex]
[tex]f(8)=1.083[/tex]
Hence, by comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
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prove that if a decimal number is divisible by 3 if and only if the sum of its digits is divisible by three
if a decimal number is divisible by 3 if and only if the sum of its digits is divisible by three is evident and proved below.
Let n be a decimal number.
Assume n is divisible by 3.
lets consider n in terms of its digits as
n = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0
where m is the number of digits in n and d_1, d_2, ..., d_m are its digits.
Substituting n = 3k into the above equation, we get
3k = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0
Subtracting 3k from both sides of the equation, we get
0 = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0 - 3k
Adding 3k to both sides of the equation, we get
3k = d_1 * 10^(m-1) + d
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Solve the system of two linear equations by the method of elimination (also called addition method). For a dependent system, give the answer in the form of an ordered pair in terms of x. (If there is no solution, enter NO SOLUTION.) x - y = -15 -3x + 3y = 45 (x, y) =?
x - y = -15 -3x + 3y = 45 (x, y) = the system of two linear equations using the method of elimination ( 5, 45).
x - y = -15
-3x + 3y = 45
written as
3x - 3y = -15
+3x + 3y = 45
6x = 30
x = 5
Substitute x = 5 into either of the linear equations to find y.
x - y = -15
5 - y = -15
y = 45
Therefore, the solution is (5, 45).
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How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
a) The line belongs to the plane.
b) The line does not belong to the plane.
How to verify if a line belongs or not to a plane?The equation of a line has the format given as follows:
[tex]\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}[/tex]
The equation of a plane has the format given as follows:
Ax + By + Cz + D = 0.
The line will belong to the plane if these two conditions are satisfied:
[tex]Ax_1 + By_1 + Cz_1 + D = 0[/tex]aA + bB + cC = 0.In standard format, the line for item a is given as follows:
[tex]\frac{x - 1}{4} = \frac{y + 2}{9.5} = \frac{z - 3}{1}[/tex]
Then the conditions are tested as follows:
3(1) - 2(-2) + 7(3) - 28 = 0.4 x 3 - 2 x 9.5 + 1 x 7 = 0.The two conditions are satisfied, hence the line belongs to the plane.
For item b, we have that:
(-2)(-6) + 1(8) - 5(-3) + 1 = 36.
First condition already not satisfied, hence the second does not need to be tested, meaning that the line does not belong to the plane.
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In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars. Five of the points are labeled A, B, C, D, and E, respectively.
E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven (thousands) Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven?
Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.
"Information available from the question",
In the question:
In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars.
Five of the points are labeled A, B, C, D, and E, respectively.
E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven
To find the which point is the most influential with respect to a regression of trade-in value versus miles driven?
Now, According to the question:
According to the points of labeled:
The correct answer is :
To see the figure.
Hence, Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.
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Sample Response: First, I would write the rate as a fraction. Then I would divide the numerator by the denominator. Which key phrases did you use in your response? Find an equivalent ratio that compares a quantity to exactly one unit of another quantity. Write the rate as a fraction. Divide the numerator by the denominator.
The key phase that we see in our response is "Divide the numerator by the denominator" (option C).
What is a key phrase?A key phrase refers to a phrase that contains words that define the most important part of a text. A key phrase serves as a summary of a paragraph or larger text.
In this case, the key phrase would serve to establish what was the mathematical procedure that we carried out to solve a mathematical problem. According to the above, it can be inferred that the key phrase must contain the most precise information to describe this procedure.
Based on the above, the correct answer is "Divide the numerator by the denominator" because it exactly describes the procedure that was performed.
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which expression can be used to find 20 percent of 92?; which expression gives the best estimate of 45 percent of 76?; what is 50 percent of 62? 0.31 3.1 31 310; what is 60 percent of 92?; which expression can be used to find 12 percent of $98?; which expression can be used to find 38 percent of 22?; which correctly explains how to estimate 55 percent of 64?; 20% of 190
The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.
Given that,
Finding the expression that can be utilised to find
20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.
What is percentage?From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.
Take
20% of 92
Multiply 20%×92
=18.4
45% of 76
Multiply 45% ×76
=34.2
50% of 62
Multiply 50%×62
=31
60% of 92
Multiply 60%×92
=55.2
12% of 98
Multiply 12%×98
=11.76
Therefore,
The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 191.3
Step-by-step explanation:
In 2005: x=2005-1998=7
y=123.1(1.065)^7
= 191.3
Which angle has a positive sine and a negative cosine?
The angle with a positive sine and negative cosine among the options is [tex]\frac{3\pi }{4}[/tex]
What is an obtuse angle?
Obtuse angle is any angle greater than 90°: Straight angle is an angle measured equal to 180°: Zero angle is an angle measured equal to 0°: Complementary angles are angles whose measures have a sum equal to 90°:
All obtuse angles usually have positive sine and negative cosine.
Amongst all the options [tex]\frac{3\pi }{4}[/tex] is the only obtuse angle . which if you convert to degrees
using π rad = 180 degrees, 3/4 x 180 you get 135°
In conclusion [tex]\frac{3\pi }{4}[/tex] is the angle with a positive sine and negative cosine.
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3.79 divided by 4 answer
Answer:
0.9475
Hope this Helps!
a one sided confidence interval bounding the high side is desired for the true average stray-load loss (in watts) for a certain induction motor when the line current is held at 10 amps for a speed of 1500 rpm. assume that the stray-load loss population is normally distributed with standard deviation = 2. Compute a one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71. Give your answer accurate to three decimal pointsPlease show steps with out excel or calculators I use tables only
using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.
The standard normal distribution table is used to calculate the critical value for this problem.
The critical value at 99% confidence level is 2.576.
The formula for the one-sided confidence interval is given by:
Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n))Therefore, the one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71 is:
Upper Bound = 71 + (2.576 * 2/sqrt(86))
Upper Bound = 71 + (1.41)
Upper Bound = 72.41
The one-sided 99% Confidence Interval for mu when n = 86 and X_Bar =71 is calculated by using the standard normal distribution table to find the critical value of 2.576, and then using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.
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question a newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. the editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. which of the following methods will achieve the desired sampling design?
Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.
The correct option is (B).
Now, According to the question:
Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.
Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)
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The complete question is this:
A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?
(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.
(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.
(C) Select one voting district at random, and then select a random sample of 500 from the selected voting district.
(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.
(E) Select the first 500 city residents who attend the next high school football game.
(See Example 12) A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. In how many ways can the executive committee be formed?
Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.
a. The number is ⁴²P₅ = 42!/37!
=42×41×40×39× 38 ×37!/37!
=102080160 ways.
b. The number is ⁴²C₅ = 42!/ 5! × 37!
=42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!
= 850668 ways.
If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.
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You have been given the task of organizing a poll regarding an upcoming election. The object is to estimate the proportion of the country that will vote to keep the current government in power. You have been told to collect a sample and find a 95% confidence interval for the proportion. This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74. a) Calculate the minimum sample size that is required in this survey. Give your answer as a whole number. Someone working on your team reports that the information suggesting that the proportion of people that will vote to keep the current government is equal to 0.74 is out of date. In fact, some recent events in politics mean that there is no safe guess at what the proportion might be. b) Based on this new information, calculate the minimum sample size that is required in this survey. Give your answer as a whole number.
The confidence interval for the task of organizing the poll for the upcoming elections be,
(222.117 , 257.883)
Given, You have been given the task of organizing a poll regarding an upcoming election.
The object is to estimate the proportion of the country that will vote to keep the current government in power.
You have been told to collect a sample and find a 95% confidence interval for the proportion.
This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.
We have to find the confidence interval,
Subtract 1 from your sample size. 10 – 1 = 9.
Subtract the confidence level from 1, then divide by two.
(1 – .95) / 2 = .025
For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.
Divide your sample standard deviation by the square root of your sample size.
25 / √(10) = 7.90569415
Now, Multiply 2.262 × 7.90569415 = 17.8826802
For the lower end of the range
240 – 17.8826802 = 222.117
For the upper end of the range
240 + 17.8826802 = 257.883
Hence, the confidence interval be (222.117 , 257.883)
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Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 171 in. Find the dimensions of the cylindrical package of greatest volume that may be sent via priority mail. (Hint: The length plus the girth is 2r + l.)
r =
l =
volume =
If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.
Given that,
The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.
We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.
We know that,
Let
Length= Breadth =x
Height=y
Volume can be written as
V=x²y
Now,
Combined length and girth is
7x+y=171
y=171-7x
V(x)=x²(171-7x)
V(x)=171x²-7x³
Differentiating with respect to x.
V'(x)=343x-21x²
The maximum value
V'(x)=0
343x-21x²=0
7x(49-3x)=0
x=0
and
49-3x=0
3x=49
x=49/3
Once again differentiating with respect to x.
V''(x)=343-42x
V''(x)=343-42(0)=343>0(min)
V''(x)=343-42(49/3)=-343<0(max)
The maximum volume is
Vmax=V(49/3)=(49/3)(171-7(49/3))
Vmax=925
Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.
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Write the following expression using the fewest possible terms.
(−3x − 12) + (16 + 8x)
5x + 4
5x + (−4)
11x + 28
11x + (−4)
Therefore option a) 5x+4 is the simplified form of the equation.
What is equation?Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.
Here,
Given:
=>(−3x − 12) + (16 + 8x)
=> -3x-12+16+8x
=> 5x+4
So 5x+4 is the simplified form of the equation
Therefore option a) 5x+4 is the simplified form of the equation
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cost per pound ($) ingredient beginning ending quantity (pounds) per 100 pounds of product a 2.50 3.95 25 b 8.75 9.90 15 c 0.99 0.95 50
The relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.
In the given question we have to compute the price relatives for the three ingredients A, B and C.
Now finding the relative price using the formula.
Relative Price(RP) = Ending Cost(E)/Beginning Cost(B) *100
Now from the given table;
Ingredient Beginning(B) Ending(E) E/B E/B*100
A 2.50 3.95 1.58 158
B 8.75 9.90 1.131 131.1
C 0.99 0.95 0.96 96
Hence, the relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.
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The right question is
A chemical company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. (Round your answers to the nearest integer.)
Cost per Pound ($)
Ingredient Beginning Ending Quantity (pounds) per 100
Pounds of Product
A 2.50 3.95 25
B 8.75 9.90 15
C 0.99 0.95 70
Compute the price relatives for the three ingredients.
Item Price Relative
A
B
C
Julia's frogs are 2/5 of the amount of Rimma's frogs. If Rimma gives 1 /2 of her frogs to Julia, what will be the ratio of Julia's frogs to Rimma's frogs?
The Ratio of Julia’s frogs to Rimma’s frogs will be 9:5
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Ratio = [tex]\frac{1^{st} element}{2^{nd} d element}[/tex]
Let Rimma’s frog = x
So, Julia's frog = [tex]\frac{2x}{5}[/tex]
Rimma gives [tex]\frac{1}{2}[/tex] of her frog to Julia
Therefore, rimma left with [tex]\frac{x}{2}[/tex]
Ratio = [tex]\frac{Julia's frog}{Rimma's frog}[/tex]
[tex]=\frac{\frac{2x}{5} +\frac{x}{2} }{\frac{x}{2} } \\=\frac{\frac{9x}{10} }{\frac{x}{2} }\\=\frac{9}{5}[/tex]
Therefore, ratio will be 9:5
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f ( x ) = − 2 x − 3 find f( 2 )
Answer:
The answer is (-7)
Step-by-step explanation:
f(x) = -2x - 3, if f(2)
f(2) = -2(2) - 3 = -4 - 3 = (-7)
Thus, The answer is (-7)
Enter the letter only!
(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph thus option (B) will be correct.
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.
As per the given coordinates,
The coordinate is the representation of horizontal and vertical distinctions.
The (3,1) is the point that is 3 grid right or horizontal and 1 unit up or vertical from the origin.
Hence "(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph".
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NO LINKS!! Please help me with these graphs. (NOT Multiple choice)
a. Show the end behavior
b. Shape the graph near the near x-intercepts.
1. p(x)= 2/3(3x - 6)(x + 2) (x - 3)^2
2. p(x) = (x - 3)^2 (x + 2) (2x + 7)^2
3. p(x) = (x - 5)(x + 2) (x - 1) - 30
Answer:
[tex]\begin{aligned}\textsf{1.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{2.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{3.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]
Step-by-step explanation:
Root Multiplicity
Odd multiplicity → the graph will cross the x-axis at the root.
Even multiplicity → the graph will touch the x-axis at the root (but will not cross the x-axis).
Question 1Given function:
[tex]p(x)= \dfrac{2}{3}(3x - 6)(x + 2)(x - 3)^2[/tex]
Therefore:
Degree: 4 (even)Leading coefficient: positiveEnd behaviors:
[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty[/tex]
[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]
The x-intercepts of a function are when f(x)=0.
Therefore, the x-intercepts are:
x = -2 with multiplicity 1x = 2 with multiplicity 1x = 3 with multiplicity 2Therefore, the graph of the given function has 3 turning points.
Begins in quadrant IICrosses the x-axis at x = -2Crosses the x-axis at x = 2Touches the x-axis at x = 3Ends in quadrant IQuestion 2Given function:
[tex]p(x)=(x - 3)^2 (x + 2) (2x + 7)^2[/tex]
Therefore:
Degree: 5 (odd)Leading coefficient: positiveEnd behaviors:
[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]
[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]
The x-intercepts of a function are when f(x)=0. Therefore, the x-intercepts are:
x = -3.5 with multiplicity 2x = -1 with multiplicity 1x = 3 with multiplicity 2Therefore, the graph of the given function has 4 turning points.
Begins in quadrant IIITouches the x-axis at x = -3.5Crosses the x-axis at x = -2Touches the x-axis at x = 3Ends in quadrant IQuestion 3Given function:
[tex]p(x)=(x - 5)(x + 2)(x - 1)-30[/tex]
Therefore:
Degree: 3 (odd)Leading coefficient: positiveEnd behaviors:
[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]
[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]
The graph has 2 turning points.
Begins in quadrant IIITurning points at x ≈ -0.7 and x ≈ 3.4Crosses the x-axis at x ≈ 5.8Ends in quadrant IBritney is buying a shirt and a hat at the mall. The shirt costs $31.18, and the hat costs $18.32. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
The change she should receive is $50.50 and we can find it by using simple cost and price calculations.
What is selling price?
Selling price is the amount of money that a seller charges for a product or service. It is the amount of money that a buyer pays for a product or service. The selling price is determined by a variety of factors, such as the cost of production, the perceived value of the product or service, the market demand for the product or service, competitive pricing in the market, and the profit desired by the seller. The selling price may also be affected by the availability of financing options for buyers, taxes, and other applicable fees. The selling price is an important factor in marketing and promoting a product or service. It must be set at the right level to attract buyers and ensure that the seller can make a profit.
Selling price for a shirt = $31.18
Selling price for a hat = $18.32
Total amount she have = $100
Total selling price (for both) = $49.50
So, the remaining amount = $100 - $49.50
= $50.50
So, the change she should receive = $50.50
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Please answer the question about nets
Answer:
Side h and side
A teacher prepares 12 assignments for her 2 students.
How many different ways can the assignments be assigned if and only if one assignment assigned to each student?
The ways the assignments can be assigned to the students with the condition is 66 ways
How to determine the ways the assignments can be assigned to the students?From the question, we have the following parameters that can be used in our computation:
Total number of questions, n = 12
Total numbers of students, r = 2
The number of ways the assignments can be assigned to the students is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 12 and r = 2
Substitute the known values in the above equation
Total = ¹²C₂
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 12!/10! * 2!
Evaluate
Total = 66
Hence, the number of ways is 66
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How far away is the ball from Amaya when it is at its maximum height?
The distance of the ball away from Amaya at Maximum height is; 18 feet
What is the maximum height of the projectile?Given the projectile equation as;
y = -0.02(x - 18)² + 12 to model the horizontal distance of a ball from Amaya's position.
We want to find out how far away is the ball from Amaya when it is at its maximum height.
The model takes the form of a parabolic equation and as such, the maximum height is obtained at the Vertex :
The general vertex form of the equation of a parabola is;
y = a(x - h)² + k
With maximum height obtained at the Vertex (h, k)
From the model given, we can say that;
Coordinate at the Vertex : (h, k) = (18, 12)
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Complete question is;
Amaya is standing 30 ft from a volleyball net. The net is 8 ft high. Amaya serves the ball. The path of the ball is modeled by the equation y = -0.02(x - 18)² + 12, where x is the ball's horizontal distance in feet from Amaya's position and y is the distance in feet from the ground to the ball. a. How far away is the ball from Amaya when it is at its maximum height?
Which of the following is not a regular polygon? A) equilateral triangle
B) square
C) rectangle
D) None of these
Answer: D.) None of these
Step-by-step explanation: A polygon is regular when all angles are equal and all sides are equal (otherwise it is "irregular").
Find two numbers m and n such that m+n =5 and mn=4
what is 1.35 as a fraction; what is 175 as a decimal; 13 as a decimal; 0.13 as a decimal; 1.35 as a decimal; 15.5% as a decimal; 1 3/5 as a decimal; 1.35 as a fraction in simplest form
1.35 as a fraction in simplest form is written as 27/20.
A fraction, which is expressed in the form p/q, where p and q are both integers, denotes a portion of a whole.
To convert 1.35 to a fraction, do the following:
Write the decimal number split by 1 first as follows:
1.35/1
Since the numerator has two digits after the decimal point, we must multiply the numerator and denominator by 102 to get 100, removing the decimal point.
1.35 × 100/ 1 × 100 = 135/100
Because 135 and 100 have 5 in common, we may simplify the fraction to show the same amount: 135 5/100 5 = 27/20.
We can also phrase 1.35 as an improper fraction since the numerator exceeds the denominator.
Therefore, 1.35 as a fraction in simplest form is written as 27/20.
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please help i need it!
thank you!!
Determine which integer in the solution set will make the equation true.
3p + 13 = 22
S: {−1, 1, 3, 4}
−1
1
3
4
The integer in the solution set that will make the equation true is (c) 3
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
3p + 13 = 22
Subtract 13 from both sides of the expression
So, we have the following representation
3p = 9
Divide both sides of the equation by 3
p = 3
Hence, the solution is p = 3
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Please help! It’s really hard
The area of the entire floor is: C. 140 square feet.
How to Find the Area of a Composite Figure?The entire floor of the building given is composed of a trapezoid, rectangle, and a triangle.
Therefore, the area of the entire floor = area of the trapezoid + area of the rectangle + area of the triangle.
The formula are:
Area of entire floor = 1/2(a + b)h + (l × w) + 1/2(b)(h)
The variables are:
Base (a) = 4 ft
Base (b) = 8 ft
Height of trapezoid (h) = 6 ft
Length of rectangle (l) = 10 ft
Width of rectangle (w) = 8 ft
Base of triangle = 6 ft
Height of triangle (h) = 8 ft
Area of entire floor = 1/2(4 + 8)6 + (10 × 8) + 1/2(6)(8)
Area of entire floor = 36 + 80 + 24 = 140 square feet.
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