Answer:
4/3/2/7-8= -7
Step-by-step explanation:
Hi, would be really thankful for an answer
Considering the Central Limit Theorem, it is found that:
a)
The mean is the mean of the sample means.The standard deviation is [tex]\frac{\sigma}{7}[/tex], in which [tex]\sigma[/tex] is the population standard deviation.b) The shape of the distribution is approximately normal.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample means with size n of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].
For the sampling distribution of sample means, the mean and the standard deviation are given as follows:
Mean: [tex]\mu[/tex], that is, the same as the population mean.Standard deviation: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], which is the population standard deviation divided by the square root of the sample size.For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
In this problem, the sample size is greater than 30, hence the shape of the distribution is guaranteed to be approximately normal.
The standard deviation is given as follows:
[tex]s = \frac{\sigma}{\sqrt{49}} = \frac{\sigma}{7}[/tex]
As for the mean, it is the same as the mean of the sample means, you have to calculate all the sample means and then divide by 20.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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A certain element has a half-life of approximately 15 hours. How long would it take
for 500 grams of the element to decay to 299 grams? Leave your answer as an integer
or simplified expression.
Using an exponential decay equation, we will see that after 11 hours the element will decay to 299 grams.
How long takes to decay?We know that we have an element with a half-life T, and it has a decay equation that can be written as:
f(t) = A*e^(-t*ln(2)/T)
Where A is the initial amount of the element, and f(t) is the amount of the element t hours after.
In this case the given values are:
A = 500g
T = 15h
Then the exponential decay is:
f(t) = 500g*e^(-t*ln(2)/15h)
And we want to find the value of t such that f(t) = 299g, then we can solve:
299g = 500g*e^(-t*ln(2)/15h)
299/500 = e^(-t*ln(2)/15h)
If we apply the natural logarithm in both sides we get:
ln(299/500) = -t*ln(2)/15h
-ln(299/500)*15h/ln(2) = t
11 h = t
It will take 11 hours to go from 500 grams to 299 grams.
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A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 35 ft long and 28 ft wide.
Find the area of the garden. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer
Answer:
1287.72 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area of the rectangle is length times width
a = (35)(28) = 980
Area of a circle is [tex]\pi r^{2}[/tex], but this is half of a circle so we will divide the answer by 2
a = [tex]\frac{3.14(14^{2}) }{2}[/tex] = [tex]\frac{3.14 x 196}{2}[/tex] =[tex]\frac{615.44}{2}[/tex] = 307.72
Add the half circle and the rectangle
980 + 307.72 = 1287.72
Find −3 4/9÷(−2 1/3) . Write your answer as a mixed number in simplest form.
The value of the fraction −3 4/9÷(−2 1/3) is 1 10/21.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction will be illustrated as:
= −3 4/9÷(−2 1/3)
Change to improper fraction
= -31 / 9 ÷ - 7/3
= 31/9 × 3/7
= 31 / 21
= 1 10/21
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Find a formula for the quadratic
function whose graph has its vertex
at (−1, 2) and its y-intercept at
y = 3.
Quadratic function whose graph has its vertex
at (−1, 2) and its y-intercept at y = 3 is f(x) = [tex](x+1)^{2}[/tex] + 2
What do you mean by quadratic equation?
A quadratic equation in algebra is any equation that can be transformed in standard form like the following:
[tex]ax^{2} +bx+c[/tex]
Where x stands for an unknown and a, b, and c are known numbers. The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient
It is given that graph of the quadratic funcion has vertex(-1,2) and y-intercept at y=3
Now, using formula, f(x) = a[tex](x-h)^{2}[/tex] + k, where (h,k) is the vertex of the parabola.
Here, vertex of the quadratic function is (-1,2)
So, f(x) = a[tex](x+1)^2[/tex] + 2
Now, we need to solve for a.
y-intercept is given as y=3, which means f(x)= 3 when x=0
Using this we get ,
f(0) = 3
a(1) + 2 = 3
a + 2 = 3
a = 3 - 2
a = 1
Quadratic function become:
f(x) = [tex](x+1)^{2}[/tex] + 2
Therefore, quadratic function whose graph has its vertex
at (−1, 2) and its y-intercept at y = 3 is f(x) = [tex](x+1)^{2}[/tex] + 2
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determaine each quotient 3/4 devided by 1/8
Answer:
6
Step-by-step explanation:
3/4 ÷ 1/8
= 3/4 . 8
= 24/4
= 6
Answer the question below
By just expanding the products, we can see that the expression can be written as:
(x - 1)*(x + 2)*(x + 3) = x³ + 4x² + x - 6
How to rewrite the expression?Here we want to expand the expression:
(x - 1)*(x + 2)*(x + 3)
We can start to expand the first two parts, writing:
(x - 1)*(x + 2)*(x + 3) = [(x - 1)*(x + 2)]*(x + 3)
[x² + (-1)*x + x*2 + (-1)*2]*(x + 3)
[x² - x + 2x - 2]*(x + 3)
[x² + x - 2]*(x + 3)
Now we can finish the expansion:
[x² + x - 2]*(x + 3) = (x²)*x + (x²)*3 + x*x + x*3 + (-2)*x + (-2)*3
= x³ + 3x² + x² + 3x - 2x - 6
= x³ + 4x² + x - 6
That is the polynomial written in standard form.
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a gymnast practices 6 days each week.She practices the same number of ours each day.If she practices 120 hours in a 4 week period how many hours each day does she practice?
Answer: She practices 5 hours a day
Step-by-step explanation: 6 days a week x 4 weeks = 24 days
120 hours of practice / 24 days = 5 hours of practice a day
Answer:
5hrs
Step-by-step explanation:
120 ÷ 4 = 30. 30 ÷ 6 = 5. She practices for 5hrs a week.
6.
The Cookie Jar offered a special deal on Valentine's Day. Buy I dozen cookies
for $6.00 and get 3 cookies free. Mrs. West bought 3 dozen cookies for her
class at school. How many cookies did she get altogether on the special deal?
Answer:
Step-by-step explanation:
It has to be $3.00 because It says Mrs. West bought 3 dozen of cookies and she has $6.00 and the cookies had to be 1$ each so the answer should be $3.00 ( sorry if I'm wrong)
What is the slope of the line through (-2,2) and (3,9)
Answer: The slope is 7/5
Step-by-step explanation:
(-2,2) and (3,9)
The slope formula is [tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
Lets insert our numbers into there!
[tex]m=\frac{9-2}{3- -2}[/tex]
m= 7/5
Hope this helps! <33
Can you solve these two problems please
Answer:
Step-by-step explanation:
Hi Debbie, the tricky part about these types of problem is recognizing that you know the total angle. 180° for the ABCD question and the angles are equal to each other for the TUWXY question , this tip lets you find X for each.
just add the two angle and set equal to 180 in each problem. I'll do the problems below, but , now that you know how, maybe you could try them and check your answer against mine.
The ABCD question
4x+7 + 2x -1 = 180
6x +6 = 180
6x = 174
x = 29
4(29)+7 = 123°
2(29)-1 = 57°
The TUWXY question
6x+13 = 10x-7
20 = 4x
5=x
then
6(5)+13 = 43°
and the next one should be the same
10(5) -7 =43°
check. so there are your answers. :) get it?
A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zero's, 2 one's and 3 two's; another ternary string meeting these conditions is 0021221.
How many ternary strings are there with exactly 3 zero's, 5 one's and 3 two's?
39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.
What is permutation?The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.
Given that, A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zeros, 2 ones and 3 twos
This is just the number of permutations of the set {0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2}. There are 11 elements in the set, so there are 11! = 39,916,880 possible ternary strings with exactly 3 zeros, 5 ones and 3 twos
Hence, 39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.
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26. Use Patterns and Structure Luis is programming
an animation for a countdown timer where
points flash in sequence, one at a time, around
in a circle. He calculates that the coordinates of
the first four points in his sequence are (6, 0),
(5.5, 2.3), (4.2, 4.2), and (2.3, 5.5). He can find
the rest of the coordinates by rotating the first
four points by 90°, 180°, and 270°. What are
the coordinates of the points that complete the
sequence around in a circle?
Answer: ?????
Step-by-step explanation:
There are 1-1/2 pizzas to be shared between 4 friends. What fraction of 1 pizza will each get
The fraction of 1 pizza to be shared with 4 friends are 3/8
What is division?Division is breaking a number up into an equal number of parts.
Given that, there are pizzas 1[tex]\frac{1}{2}[/tex] to be shared between 4 friends,
1[tex]\frac{1}{2}[/tex] = 3/2
For sharing = 3/2÷4 = 3/8
Hence, The fraction of 1 pizza to be shared with 4 friends are 3/8
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The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer:
A. The y-intercept represents the number of mammals when they were originally counted.
B. The line y = 0 is an asymptote of the graph.
C. The y-intercept.is 75.
D. The y-intercept is 120.
E. The asymptote indicates that the number of mammals counted when the study began was 120.
F. The asymptote indicates that as years pass, the number of mammals will approach 0.
G. The line x = 0 is an asymptote of the graph.
The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;
A. The y-intercept represents the number of mammals when they were originally counted was 120
B. The line y = 0 is an asymptote of the graph
D. The y-intercept is 120
F. The asymptote indicates that as years pass, the number of mammals will approach 0
What is an asymptote of a graph?An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.
The points on the graph of the exponential function are;
(0, 120) and (55, 17)
The rate at which the population is decreasing = -3.5%
The output of the graph, y = The number of mammals x years after counting
The key features of the exponential function are;
The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct
The coordinates of the y-intercept is (0, 120)
The y-intercept is therefore the point y = 120
Therefore, option D is correct
The general form of the growth exponential function is presented as follows;
f(x) = a·bˣ + k
r = b - 1
b = 1 + r
Therefore;
b = 1 - 0.035 = 0.965
a = The first term = 120
Plugging in the known values from the graph, we get;
f(0) = 120 = a + k
120 = 120 + k
k = 120 - 120 = 0
k = 0 = The asymptote
Therefore, an asymptote is the line y = 0 option B is therefore correct
The number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity
Therefore as the years pass the number of mammals will approach 0, option F is correct
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PLEASE HELP!! QUICK!
Answer:
(0,-3)
Step-by-step explanation:
Triangles F G H and J K L are shown. Angles G F H and K J L are congruent and angles F H G and J L K are congruent.
To show that ΔFGH ≅ ΔJKL by SAS, what additional information is needed? Check all that apply.
FH ≅ JL and FG ≅ JK
FH ≅ JL and HG ≅ LK
∠G ≅ ∠K and FH ≅ JL
∠G ≅ ∠K and GH ≅ KL
∠G ≅ ∠K and FG ≅ JK
Any of the following information can be used to show that ΔFGH is congruent to ΔJKL by SAS.
How to Show that Two Triangles are Congruent by SAS?The criteria for proving that two triangles are congruent to each other by the SAS congruence postulate are:
The two corresponding sides of both triangles must be congruent to each other.One pair of included corresponding angles in both triangles must also be congruent to each other.In the image given that shows triangle FGH and triangle JKL, we are given the following:
∠F ≅ ∠J and ∠H ≅ ∠L [two pairs of congruent angles]
No two congruent sides are marked in the triangles. Therefore, the additional information that may be needed to prove the triangles are congruent by SAS can be:
a. FH ≅ JL and FG ≅ JK
b. FH ≅ JL and HG ≅ LK
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Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The linear equation that could be used to find the price of a tire patch is of:
4x + 1.9 = 22.2.22.2 - 4x = 1.9.What is a linear equation?The slope-intercept representation of a linear equation is shown by the rule presented as follows:
y = mx + b.
In the context of this problem, the meaning of the variables are given as follows:
Slope m: cost of a single tyre.Intercept b: Amount of Ryan's gift card.The values of these intercept is given as follows:
b = 22.2.
Hence the function is:
y = -mx + 22.2.
He bought four tires, hence x = 4, and had y = 1.9, hence the cost of a tire is found as follows:
-4m + 22.2 = 1.9.
Hence the options are:
4x + 1.9 = 22.2 -> first equation, considering the slope as x.22.2 - 4x = 1.9.Missing InformationThe problem is given by the image shown at the end of the answer.
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Pietro buys 20 candy bars for $6. He
plans to sell all 20 candy bars in 1 day, He
needs to make a profit of $9 per day to
meet his fundraising goal.
How much must he charge for each candy
bar?
Answer:
$0.45
Step-by-step explanation:
6 ÷ 20 = 0.3
Which means each candy bar costs $0.3.
9 ÷ 6 = 1.5
0.3 × 1.5 = 0.45
20 × 0.45 = 9
So he must charge $0.45 for each candy bar.
The entire graph of the function f is shown in the figure below.
Write the domain and range of f using interval notation.
The domain of function f using interval notation is (-3, 3).
The range of function f using interval notation is (-5, 4).
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Additionally, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of a graph to the top.
By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:
Domain = (-3, 3).
Range = (-5, 4).
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The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
The end behavior of a graph is defined as what is going on at the ends of each graph when the function approaches positive or negative infinity.
End behaviour of given graph is, x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞
Since, here a graph is attached.
From graph it is observed that, when x tends to negative side, graph is going to upward direction. and when x tends to positive side then graph is going to downward direction.
So, when x tends negative infinity then y tends to positive infinity.
when x tends to positive infinity then y tends to negative infinity.
Therefore, end behaviour of given graph are,
x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞
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Solve 4 + 2 sinx= 14-8 sinx for 0° ≤ x ≤ 180
x= 90°.
Step-by-step explanation:1. Write the expression.[tex]4 + 2 sin(x)= 14-8 sin(x)[/tex]
2. Subtract "4" from both sides of the equation.[tex]-4+4 + 2 sin(x)= 14-8 sin(x)-4\\ \\2 sin(x)= 10-8 sin(x)[/tex]
3. Add "8sin(x)" to both sides of the equation.[tex]2 sin(x)+8 sin(x)= 10-8 sin(x)+8 sin(x)\\ \\10 sin(x)= 10[/tex]
4. Divide both sides by 10.[tex]\frac{10 sin(x)}{10} = \frac{10}{10} \\ \\sin(x)=1[/tex]
5. Apply the arcsin of sin^-1 to both sides of the equation.[tex]arcsin(sin(x))=arcsin(1)\\ \\x=90[/tex]
6. Conclude.x= 90°.
NO LINKS!! Describe the set of all points P(x, y) in a coordinate plane that satisfy the given condition
Answer:
a) A or first option,b) E or 5th option,c) E or 5th option.Step-by-step explanation:
a) x = - 8Simply check for x-coordinate of - 8, we see only the first option has it, all the others have x = 0 or x = 8 which is impossible to have on the line x = - 8.
It is parallel to the y-axis and x = - 8 for any value of y.
Correct choice is A or 1.
b) y = 8Similar to above, we exclude all the options with a different value of y other than 8.
There are two possible options left:
B or 2- incorrect as y = 0 is parallel to the x-axis, not perpendicular.E or 5 - correct optionc) x ≥ 0Consider line x = 0, this is overlapping with the y-axis.
x ≥ 0 gives us the y-axis (because of equal sign) and all the points to the right from it.
This is matching the description of option E or 5.
Answer:
(a) The line parallel to the y-axis that intersects the x-axis at (-8, 0).
(b) The line parallel to the x-axis that intersects the y-axis at (0, 8).
(c) The set of all points to the right of and on the y-axis.
Step-by-step explanation:
Part (a)
Given condition: x = -8
The equation of a vertical line is x = a.
This line is parallel to the y-axis (since it is vertical) and intersects the x-axis at (a, 0).
Therefore, the description that satisfies the given condition is:
The line parallel to the y-axis that intersects the x-axis at (-8, 0).Part (b)
Given condition: y = 8
The equation of a horizontal line is y = a.
This line is parallel to the x-axis (since it is horizontal) and intersects the y-axis at (0, a).
Therefore, the description that satisfies the given condition is:
The line parallel to the x-axis that intersects the y-axis at (0, 8).Part (c)
Given condition: x ≥ 0
The "≥" symbol means greater than or equal to.
x is greater than zero for all points to the right of the y-axis.
x is equal to zero for all points on the y-axis.
Therefore, the description that satisfies the given condition is:
The set of all points to the right of and on the y-axis.which lines are parallel if m < 4 = m < 5? justify your answer
Answer:
Lines r and s are parallelStep-by-step explanation:
Angles 4 and 5 are congruent and are on the inner side of lines r and s, and opposite side from line l.
If two angles are on the inner sides of two lines and opposite sides of the line intersecting the two lines are equal, then these angles are alternate interior angles.
The two lines are parallel and the intersecting line is the transversal.
Lines r and s are parallel and line l is transversal.
Find the range and standard deviation of the set of data.
11, 10, 5, 13, 16
The range is 11.
(Simplify your answer.)
The standard deviation is ____
(Round to the nearest hundredth as needed.)
Find the standard deviation please
The range of the set of data is 11 and the standard deviation of the set of data is 4.06
What is Standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given, set of data.
11, 10, 5, 13, 16
First of all we will arrange them
5, 10, 11, 13, 16
To find the range we have to;
Range = Biggest number - smallest number
= 16 - 5
Range = 11
Thus, the range of the given set of data is 11
Now, for standard deviation,
By first squaring the discrepancies between the observations and the mean, and then taking the square root of the sum of the squares of the differences divided by the number of observations minus 1, the standard deviation is computed.
Mean = Sum of Observations/Total Observations
Mean = (5 + 10 + 11 + 13 + 16)/5
= 55/5
= 11.
Square of the mean = 11² = 121
Now subtracting the mean from each observation and squaring it gives:
(5 - 11)² = (-6)² = 36
(10 - 11)² = (-1)² = 1
(11 - 11)² = (0)² = 0
(13 - 11)² = (2)² = 4
(16 - 11)² = (5)² = 25
Sum of squares = 36 + 1 + 0 + 4 + 25
= 66
variance = 66 / n-1
= 66 / (5 - 1)
= 66 / 4
= 16.5
Standard deviation = √variance
= √16.5
= 4.06
Thus, the Standard deviation of the set is 4.06
Hence, The range and standard deviation of the set of data is 11 and 4.06 respectively
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2) Business Zoom Corporation makes model cars. Each sells for $29.99. The unit cos
is $14.25. If the company's fixed costs are $314,800, find the number of units they
need to sell to break even.
Answer: Break-even point in units= 20,000
Step-by-step explanation:
Break-even point in units= 20,000
Step-by-step explanation:
Giving the following information:
Selling price per unit= $29.99
Unitary variable cost= $14.25
Fixed costs= $314,800
To calculate the break-even point in units, we need to use the following formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 314,800 / (29.99 - 14.25)
Break-even point in units= 20,000
Answer:
20,000
Step-by-step explanation:
29.99-14.25 (15.74) it the money that they make per unit without accounting for the fixed cost.
314800 = 15.74x Divide both sides by 15.74
20000 = x
Find the two possible values ofX in the GP 72,x,18.
The possible values of X in the GP 72,x,18 is 36.
What is a geometric progression?A geometric progression simply means a sequence that has a common ratio.
From the information, the first term is 72 and the third term is 18
First term a = 72
Third term ar² = 18
Therefore, 72r² = 18
r² = 18/72
r² = 1/4
r = ✓1/4
r = 1/2
Therefore second term will be:
= 72 × 1/2
= 36
Therefore, x is 36.
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what is the difference 5 - 3.12
Answer: There is a difference of 1.88
Step-by-step explanation: Pls brainiest.
Answer:
1.88
Step-by-step explanation:
hopethishelpsya:)
Find the circumference of the circle to the nearest tenth. Use 3.14 for it.
Answer:
Step-by-step explanation:
157m is the answer.
Simplify the expression (4/3)(3/7)
The simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The expression is:
= (4/3)(3/7)
= (4x3)/(3x7)
Cancel 3 from the numerator and denominator
= 4/7
Thus, the simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.
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