The best way to group these ages into six intervals is from 40-44 to 65-69.
What is a Frequency Distribution Table ?A frequency distribution table gives an idea about the data point or interval and its frequency.
The age of the Presidents given as
57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46
The smallest number ( age) is 42 and the largest number (age ) is 69
To make 6 intervals in this gap of 27 , each interval should be of length 5
Therefore the intervals will be
40-44
45-49
50-54
55-59
60-64
65-69
This is the best way to group into intervals.
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Final answer:
The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.
Explanation:
When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.
First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.
This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.
Shelly got 60 questions correct on her math test.If she got 75% how many questions were on the test?
Give a polynomial-time algorithm that takes a sequence of supply values s1, s2, . . . , sn and returns a schedule of minimum cost. for example, suppose r = 1, c = 10, and the sequence of values is
I think that the answer is c can somebody help me out ?
An isosceles triangle has area of 125 ft. If the base is 16 ft, what is the length of each leg? Round your answer to the nearest tenth
Final answer:
To find the length of each leg of an isosceles triangle with an area of 125 ft² and a base of 16 ft, we first calculate the height and then apply the Pythagorean Theorem. The length of each leg is approximately 17.6 ft.
Explanation:
The question asks about finding the length of each leg of an isosceles triangle given the area and the base. To solve this, we use the formula for the area of a triangle, A = 1/2 × base × height, and apply the Pythagorean Theorem since the height creates a right triangle with the leg of the isosceles triangle and half of the base.
First, we find the height using the given area, A = 125 ft² and base, b = 16 ft. The formula rearranges to height = 2A / base, giving us height = 2(125) / 16 = 15.625 ft.
Next, using the Pythagorean Theorem, a² + b² = c², we let a represent half of the base (8 ft), b be the height (15.625 ft), and c be the leg of the triangle. Solving for c, we find c ≈ 17.6 ft, rounded to the nearest tenth.
What can be determined about this data set before finding the range or the interquartile range? 19, 25, 35, 38, 41, 49, 50, 52, 99
The data has an outlier, but the interquartile range will not change. The answer is c
The summation expression in the following series has an absolute value in it. Expand and evaluate the summation notation. What is the sum of the series?
To expand and evaluate the summation notation with an absolute value, we can use the binomial theorem. The expanded form of the series will depend on whether the sum inside the absolute value is positive or negative. Substituting the given values and simplifying the expression will give the sum of the series.
Explanation:A binomial expansion is a way of expressing an algebraic quantity as a sum of an infinite series of terms. In this case, we have an absolute value in the summation expression.
To expand and evaluate the summation notation, we can use the binomial theorem.
The binomial theorem states that (a + b)^n = C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + ... + C(n,n)b^n, where C(n,k) represents the binomial coefficient.
In the given case, we have an expression of the form |a + b|.
To expand this, we can consider two cases: a + b ≥ 0 and a + b < 0. If a + b ≥ 0, then |a + b| = a + b. If a + b < 0, then |a + b| = -(a + b).
Thus, the expanded form of the series will be a + b when a + b ≥ 0, and -(a + b) when a + b < 0.
To evaluate the series, substitute the given values for a and b into the expanded form and simplify the expression.
Hilda has $210 worth of $10 and $12 stock shares. The number of $10 shares is five more than twice the number of $12 shares. How many of each type of share does she have?
Answer:
15 | 10-dollar shares, 5 | 12- dollar shares
Step-by-step explanation:
Write the equation by adding the total values of each type of share.
10(2t+5)+12t=210
We can solve this equation for t to find the number of $12 shares.
10(2t+5)+12t=210
20t+50+12t=210
32t=160
t=5
So, the number of $12 shares is 5. Since the number of $10 shares is 5 more than twice the number of $12 shares, the number of $10 shares is 2(5)+5=15.
Hilda bought 5 $12 shares and 15 $10 shares.
y=0.75(1.05)t Determine whether the function represents a exponential growth or decay.Identify the percent rate of change
The function ff(x) = 0.75(1.05)ˣ is an example of an exponential growth function.
The percent rate of change is 5%
What type of function is the equation
From the question, we have the following parameters that can be used in our computation:
f(x) = 0.75(1.05)ˣ
The function ff(x) = 0.75(1.05)ˣ is an example of an exponential growth function.
In exponential growth functions, the base (in this case, 1.05) is greater than 1, and as x increases, the function increases
Also, we have the percent rate of change to be
Rate = 1.05 - 1
Rate = 0.05
So, we have
Rate = 5%
Hence, the percent rate of change is 5%
Evaluate 2LW + 2HL + 2HW for L = 3,W = 2, and H = 4.
donna received a $70 gift card for a coffee store. she used it in buying some coffee that cost $7.84 per pound. after buying the coffee, she had $30.80 left on her card. how many pounds of coffee did she buy?
The points A(12,7), B(12,−3), C(−2,−3), and D(−2,7) form rectangle ABCD. Which point is halfway between A and B? CLEAR CHECK (12,0) (12,5) (12,2) (12,−2)
What equation results from completing the square and then factoring? x^2 + 24x = 33
Answer:
[tex](x+12)^2=177[/tex]
Step-by-step explanation:
We have been given an equation: [tex]x^2+24x=33[/tex].
To complete the square we change the left hand side of the equation to a perfect square trinomial. For this we add [tex](\frac{b}{2})^2[/tex] to both sides of equation, where b is the coefficient of x.
We can see that coefficient of x for our given equation is 24. So we will add [tex](\frac{24}{2})^2=12^2=144[/tex] to both sides of our equation.
[tex]x^2+24x+144=33+144[/tex]
[tex]x^2+24x+144=177[/tex]
Let us factor left side of our equation as the square of binomial.
[tex](x+12)^2=177[/tex]
Therefore, our resulting equation will be [tex](x+12)^2=177[/tex].
Answer: (x+12)^2=177
Step-by-step explanation:
Kareem lives 4/10 of mile from the mall.Write two equivalent fraction that show what fraction of mile Kareem lives from the mall
The following stem-and-leaf plot represents the scores earned by Mr. Roberts's class on their most recent science test.
What is the median of the scores?
78
80
81
86
Answer:
im pretty sure its 81
Step-by-step explanation:
What’s the answer to the question?
Brigitte fostered 14 dogs this year which is 5 less than last year how many dogs did brigitte foster last year
Answer:
9 DOGS
Step-by-step explanation:
5 LESS= 14-5
=9
complete the pattern and find the rule 87,91,95,99,___,___, ___
Answer:
aₙ = a₁ + (n-1).d
103
107
Step-by-step explanation:
This is an arithmetic sequence because the difference (d) between 2 successive numbers is constant.
d = 91 - 87 = 95 - 91 = 99 - 95 = 4
If the first term is a₁, we can find the n term using the following expression.
aₙ = a₁ + (n-1).d
Here, we want to find the fifth and sixth elements.
a₅ = 87 + (5-1).4 = 103
a₆ = 87 + (6-1).4 = 107
Select all the expressions that have the following quotient
The expression that have the following quotient is:
[tex]\dfrac{-4x^2+20x-25}{-2x+5}[/tex] [tex]\dfrac{-14x^2+35x}{-7x}[/tex] [tex]\dfrac{12x^2-58x+70}{6x-14}[/tex]Step-by-step explanation:1)
[tex]\dfrac{-4x^2+20x-25}{-2x+5}[/tex]
It could also be written as:
[tex]\dfrac{-(5-2x)^2}{5-2x}\\\\\\=-(5-2x)\\\\\\=2x-5[/tex]
Hence, we get the quotient:
[tex]2x-5[/tex]
Option: (1) is correct.
2)
[tex]\dfrac{-14x^2+35x}{-7x}[/tex]
which is simplified as follows:
[tex]\dfrac{-7x(2x-5)}{-7x}\\\\\\=2x-5[/tex]
Option: (2) is correct.
3)
[tex]\dfrac{12x^2-58x+70}{6x-14}[/tex]
which is simplified as follows:
[tex]=\dfrac{2(2x-5)(3x-7)}{2(3x-7)}\\\\\\=2x-5[/tex]
Hence, option: (3) is correct.
4)
[tex]\dfrac{6x^2-10x-4}{3x+1}[/tex]
On simplifying:
[tex]\dfrac{2(3x+1)(x-2)}{3x+1}\\\\\\=2(x-2)\\\\\\=2x-4[/tex]
Hence, option: (4) is incorrect.
5)
[tex]\dfrac{18x-45}{9x}[/tex]
on simplifying:
[tex]\dfrac{9(2x-5)}{9x}\\\\\\=\dfrac{2x-5}{x}[/tex]
Hence, option: (4) is incorrect.
Please answer this question and give give a detailed answer. Brainliest to who ever answers first and gets it correct
Determine whether the lines l1 and l2 are parallel, coincident, skew, or intersecting. if they intersect, find the point of intersection: ℓ1:x1(t)=1−6t,y1(t)=2+9t,z1(t)=−3t ℓ2:x2(u)=2+2u,y2(u)=3−3u,z2(u)=u
To determine whether the lines are parallel, coincident, skew, or intersecting, we first analyze the direction vectors of both lines obtained from the parametric equations. The lines are not parallel or coincident as they're not proportional. They could be intersecting or skew, which we can confirm by finding a potential point of intersection.
Explanation:To determine the relationship between lines ℓ1 and ℓ2, we should analyze the direction vectors of both lines. The coefficients of t or u in the parametric equations for the lines refer to the direction vectors. For ℓ1, the direction vector is (-6, 9, -3). For ℓ2, it's (2, -3, 1).
Lines are parallel if their direction vectors are proportional, and intersect if they pass through a common point and their direction vectors are not proportional. Lines are coincedent if all corresponding points are identical, while skew lines are nonintersecting, nonparallel lines.
Given the direction vectors, we can see they are not proportional. Hence, ℓ1 and ℓ2 are neither parallel nor coincident. They might be intersecting or skew. To distinguish between these two, we need to try to find a point of intersection by equating ℓ1 and ℓ2 and solving for t and u. If a solution exists, the lines intersect at that specific point; if no solution exists, the lines are skew.
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Jennifer bought 28 tickets to the museum for students and adult chaperones.She paid a total of $350.80, which included an $8.00 donation to the museum.Write a system of equations that can be used to determine the number of student tickets, s, and the number of adult tickets, a, Jennifer purchased. Algebraically solve the system of equations to determine the number of student tickets Jennifer purchased. Show or explain your work.
The price for students is 14.50 and the adults are 19.50
Which of the following is an odd function?
g(x) = x2
g(x) = 5x – 1
g(x) = 3
g(x) = 4x
Answer:
g(x) = 4x is an odd function.
Step-by-step explanation:
A function g(x) is odd if it satisfies that, for all x we have g(-x) = -g(x). Then,
[tex]g(x) =x^2[/tex] is not an odd function beacuse only give positive values, then for example if x= 2
[tex]g(-2) =(-2)^2 = 4 \neq -4 = -g(2)[/tex].
g(x) = 5x-1 is not an odd function. I'll also give you a counterexample: for x=1 we have
g(-1) = 5(-1)-1 = -6 ≠ -4 = -(5-1) = -g(1).
g(x) = 3 is not an odd function. I'll also give you a counterexample: for x=1 we have
g(-1) = 3 ≠ -3 = -g(1).
Finally, g(x) = 4x is an odd function because for all x we have g(-x) = -g(x):
g(-x) = 4(-x) = -4x = -g(x).
In triangle XYZ,XY=15,YZ=21, and XZ=27. What is the measure of angle Z to the nearest degree?
Final answer:
Using the Law of Cosines, we find that the cosine of angle Z is approximately 0.6333, and therefore, angle Z in triangle XYZ is approximately 51° when rounded to the nearest degree.
Explanation:
To find the measure of angle Z in triangle XYZ, with sides XY = 15, YZ = 21, and XZ = 27, we can use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. In our case, we can find the cosine of angle Z by the equation:
cos(Z) = (XY² + XZ² - YZ²) / (2 · XY · XZ)
Plugging in the values, we get:
cos(Z) = (15² + 27² - 21²) / (2 · 15 · 27)
Calculating further:
cos(Z) = (225 + 729 - 441) / (810)
cos(Z) = 513 / 810
cos(Z) = 0.6333
The next step is to find the angle whose cosine is 0.6333. We can use a calculator to find the inverse cosine:
Z = cos⁻¹(0.6333)
Hence, the measure of angle Z to the nearest degree is approximately:
Z ≈ 51°
The measure of angle Z is approximately 70 degrees (rounded to the nearest degree).
To find the measure of angle Z in triangle XYZ, you can use the Law of Cosines. The formula is:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos(C) \][/tex]
where:
- c is the side opposite the angle you want to find (in this case, side XZ),
- a and b are the other two sides (XY and YZ),
- C is the angle opposite side c.
In this case, let C be the angle Z, and a = XY = 15, b = YZ = 21, and c = XZ = 27.
[tex]\[ 27^2 = 15^2 + 21^2 - 2(15)(21) \cos(Z) \][/tex]
Now, solve for cos(Z):
[tex]\[ 729 = 225 + 441 - 630 \cos(Z) \][/tex]
[tex]\[ 630 \cos(Z) = 441 - 225 \][/tex]
[tex]\[ 630 \cos(Z) = 216 \][/tex]
[tex]\[ \cos(Z) = \frac{216}{630} \][/tex]
[tex]\[ \cos(Z) \approx 0.343 \][/tex]
Now, find the angle Z:
[tex]\[ Z = \cos^{-1}(0.343) \][/tex]
[tex]\[ Z \approx 70.18 \][/tex]
So, the measure of angle Z is approximately 70 degrees (rounded to the nearest degree).
help please!! just solve for y
susan has a circular koi pond in a square patio with sides measuring 30 feet each. Find the area of the shaded region to the nearest hundredth.use 3.14 for pi
What are the values of a and b?
Answer:
[tex]A= \frac{400}{21} B=\frac{580}{21}[/tex]
Step-by-step explanation:
You just have to remember the rules of the triangles in order to be able to solve this:
The rule of trigonometry that you will have to use is a is similie to 20, B is simile to 29 and 20 is 20.
So you would have to put them like this:
[tex]\frac{21}{20}= \frac{20}{a}= \frac{29}{b}[/tex]
You just have to clear the equations for A and B:
[tex]a=\frac{20*20}{21}=\frac{400}{21}\\ b=\frac{29*20}{21} =\frac{580}{21}[/tex]
So that would be your answer.
The value of 'a' is 400/21 and the value of 'b' is 580/21 and this can be determined by using the properties of trigonometry.
According to the properties of trigonometry:
[tex]\dfrac{21}{20}=\dfrac{20}{a}=\dfrac{29}{b}[/tex] --- (1)
Now, in order to determine the value of 'a' use the above equation:
[tex]\dfrac{21}{20}=\dfrac{20}{a}[/tex]
Cross multiply in the above equation.
[tex]21a = 20\times 20[/tex]
21a = 400
Divide 400 by 21 in order to get the value of a.
[tex]a = \dfrac{400}{21}[/tex]
Now, to determine the value of 'b' again use the equation (1).
[tex]\dfrac{20}{\dfrac{400}{21}}=\dfrac{29}{b}[/tex]
Cross multiply in the above expression.
[tex]20b = 29\times \dfrac{400}{21}[/tex]
[tex]20b = \dfrac{11600}{21}[/tex]
Now, divide on both sides by 20 in the above expression.
[tex]\rm b = \dfrac{11600}{21\times 20}[/tex]
[tex]\rm b = \dfrac{580}{21}[/tex]
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A couple has 12 children, what is the probability that child number 11 is female?
The probability is 1/12.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
Given:
Total children = 12
There is possibility of girl number 11.
So, the probability that child number 11 is female
=1/12.
Hence, the probability is 1/12.
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Final answer:
The probability that the 11th child is female is 50%, assuming an equal chance for the birth of either sex and that the gender of the previous children does not affect this outcome.
Explanation:
The question at hand is a basic probability question in the realm of mathematics. It attempts to find the likelihood of an event that is purely random and independent of previous outcomes. The event in question is the sex of a newborn child, which can either be male or female, generally with equal likelihood.
To determine the probability that child number 11 is female, we assume a 50% chance for either sex, since the likelihood of having a boy or girl is typically equal. The sex of the previous children has no influence on the gender of the next child. Therefore, the probability of child number 11 being female is simply 1/2 or 50%.
It is important to understand that each child's sex is determined independently of their siblings. This is akin to flipping a fair coin where each flip is independent of the previous flips.
A grain distributor can process 14.6 tons of grain an hour.How much can the distributor process in 8.75 hours?
The grain distributor can process 127.75 tons of grain in 8.75 hours.
Explanation:To find out how much the distributor can process in 8.75 hours, you can multiply the amount of grain it can process in one hour by the number of hours. The distributor can process 14.6 tons of grain in an hour, so to find out how much it can process in 8.75 hours, you would multiply 14.6 by 8.75.
14.6 x 8.75 = 127.75
Therefore, the distributor can process 127.75 tons of grain in 8.75 hours.
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Help Please..
On a regional map, one inch represents 68 miles. How many miles apart are two cities that are three inches apart on the map?
Consider the function y = 9 - x2, where x ≥ 3. What is the inverse of the function? What is the domain of the inverse? Show all of your work for full credit.
Answer:
The inverse of the function is [tex]y^{-1}=\sqrt{9-x}[/tex].
The domain of the inverse function is [tex]D:(-\infty,0],\{x|x\in \mathbb{R}\}[/tex]
Step-by-step explanation:
Given : Function [tex]y=9-x^2[/tex] where, [tex]x\geq 3[/tex]
To find : What is the inverse of the function? What is the domain of the inverse?
Solution :
Function [tex]y=9-x^2[/tex]
To find the inverse we interchange the value of x and y,
[tex]x=9-y^2[/tex]
Now, we get the value of y
[tex]y^2=9-x[/tex]
[tex]y=\pm\sqrt{9-x}[/tex]
As [tex]x\geq 3[/tex] so x>0
[tex]y=\sqrt{9-x}[/tex]
The inverse of the function is [tex]y^{-1}=\sqrt{9-x}[/tex].
The domain of the inverse is the range of the original function.
The range is defined as the set of all possible value of y.
As [tex]x\geq 3[/tex]
Squaring both side,
[tex]x^2\geq 9[/tex]
Subtract [tex]x^2[/tex] both side,
[tex]9-x^2\leq 0[/tex]
[tex]y\leq 0[/tex]
The range of the function is [tex]R:(-\infty,0],\{y|y\in \mathbb{R}\}[/tex]
The domain of the inverse function is [tex]D:(-\infty,0],\{x|x\in \mathbb{R}\}[/tex]