Answer:
CI = 28 ± 3.09
Step-by-step explanation:
The sample size, n = 25
The sample mean, m = 28
Standard deviation, s = 7.5
Confidence interval is given as:
CI = Sample mean ± margin of error
We want to find 95% confidence level:
First, let us find the margin of error:
Margin of error = Critical value * standard error
To find the critical value, we need some parameters:
Standard error = [tex]s / \sqrt{n}[/tex]
=> [tex]SE = 7.5 / \sqrt{25}= 7.5 = 5 = 1.5[/tex]
The alpha value, ∝ = 1 - (confidence level / 100) = 1 - 95/100 = 1 - 0.95 = 0.05
Critical probability, p, is given as:
p = 1 - ∝/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975
Now we need the degree of freedom:
df = n - 1 = 25 - 1 = 24
Therefore, the critical value is 2.06 (you can use an online t value calculator).
=> Margin of error = 2.06 * 1.5 = 3.09
Therefore, the confidence interval for the population mean is:
CI = 28 ± 3.09
Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice. URGENT
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I need help with this question please help
Jeanine is selecting various albums to be displayed in the front of her music coffee house. She will be choosing 4 albums for
one part of the display. This part of the display is very prominent and she is really trying to promote jazz. There are five albums
from Diana Kroll, seven albums from Harry Connick Jr. and four albums from Michael Bublé. In how many ways can she choose
four albums for display and at least two albums are from Diana Kroll? Evaluate using both the direct and indirect method.
Gt11.2014
Answer:
The number of ways she can choose four albums for display with at least two from Diana Kroll is from the sixteen albums is 665 ways
Step-by-step explanation:
1) The number of ways she can choose 2 albums of Diana from the 5 Diana Kroll albums is 5!/(2!(5 - 2)!) = 10 ways
Choosing the other 2 albums from the remaining 11 albums gives;
11!/(2!(11 - 2)!) = 55 ways
Total number of ways is then 10 × 55 = 550 ways
Choosing 3 from the 5 Diana Kroll albums is 5!/(3!(5 - 3)!) = 10 ways
Choosing the other 1 album from the remaining 11 albums gives;
11!/(1!(11 - 1)!) = 11 ways
Total number of ways is then 10 × 11 = 110 ways
Choosing 4 from the 5 Diana Kroll albums is 5!/(4!(5 - 4)!) = 5 ways
Choosing the other 0 album from the remaining 11 albums gives;
11!/(0!(11 - 0)!) = 1 way
Total number of ways is then 5 × 1 = 5 ways
Total number of ways = 550 + 110 + 5 = 665 ways
2) In the indirect method, we first find the number of ways to choose 4 albums out of the 16 albums, then we subtract the number of cases where there are 1 and 0 Diana Kroll albums as follows;
16!/(4!(16 - 4)!) = 1820 ways
With 1 Diana Kroll album gives
5!/(1!(5 - 1)!)×11!(3!(11 - 3)!) = 825 ways
With 0 Diana Kroll album gives
5!/(0!(5 - 0)!)×11!(4!(11 - 4)!) = 330 ways
Total number of ways with at least 2 Diana Kroll albums = 1820 - 825 - 330
Total number of ways with at least 2 Diana Kroll albums = 665 ways.
find the equation of the line
Answer: y=1/2x
Step-by-step explanation:
The equation we can use is slope-intercept form. The formula is y=mx+b. The m represents the slope, and b is the y-intercept. The line passes through the y-axis at (0,0). therefore, the y-intercept is 0.
To find the slope, we can take any two points and use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for slope. Let's use (2,1) and (4,2).
[tex]m=\frac{2-1}{4-2} =\frac{1}{2}[/tex]
The slope is 1/2. Our equation is y=1/2x+0 or y=1/2x.
Answer:
y=1/2x+0
Step-by-step explanation:
slope : 1/2
y=mx+b is the equation
y-intercept is 0 therefore the equation becomes:
y=1/2x+0
Find the distance between the two points (-4,8) and (7,8)
Hey there! :)
Answer:
d = 11 units.
Step-by-step explanation:
Use the distance formula:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Plug in the coordinates:
[tex]d = \sqrt{(7 - (-4))^2 + (8-8)^2}[/tex]
[tex]d = \sqrt{(11)^2 + (0)^2}[/tex]
Simplify:
[tex]d = \sqrt{11^{2} }[/tex]
d = 11 units.
Find the total surface area in square inches, of the following 3-
dimensional figure. Enter just a number for your answer.
Answer:
81 in²
Step-by-step explanation:
The 3-dimensional shape given is a square pyramid having a square base, and 4 right triangular side faces that are the same.
The surface area can be calculated by finding the area of the square base and the area of the 4 triangular side faces. Then sum all the areas together.
Or, we can use the following formula below: Base Area + ½(Perimeter of base) × Slant Length
Where,
Base area = s² = 5² = 25 in²
Perimeter of base = 4(s) = 4(5) = 20 in
Slant height = 5.6 in
Surface area = 25 + ½(20) × 5.6
= 25 + 10 × 5.6
= 25 + 56
Surface area = 81 in²
Triangle PQR has coordinates P(–8, 3), Q(–8, 6), and R(–3, 6). If the triangle is translated by using the rule (x, y) right-arrow (x + 4, y minus 6), what are the coordinates of triangle P prime Q prime R prime? (a)P prime (negative 12, 9), Q prime (negative 12, 12), R prime (negative 7, 12) (b)P prime (negative 4, 7), Q prime (negative 14, 0), R prime (1, 10) (c)P prime (negative 4, 9), Q prime (negative 4, 12), R prime (1, 12) (d)P prime (negative 4, negative 3), Q prime (negative 4, 0), R prime (1, 0)
Answer:
d
Step-by-step explanation:
The rule (x, y ) → (x + 4, y - 6 )
means add 4 to the original x- coordinate and subtract 6 from the original y- coordinate, thus
P(- 8, 3 ) → P'(- 8 + 4, 3 - 6 ) → P'(- 4, - 3 )
Q(- 8, 6 ) → Q'(- 8 + 4, 6 - 6 ) → Q'(- 4, 0 )
R(- 3, 6 ) → R'(- 3 + 4, 6 - 6 ) → R'(1, 0 )
Answer:
D
Step-by-step explanation:
evaluate 4^radical sign 8 to the nearest ten thousandth.
Answer:
50.4525
Step-by-step explanation:
4^(√8)
4^(2.82842712475)
= 50.452514
Round up to nearest ten thousandths.
A "necklace" is a circular string with several beads on it. It is allowed to rotate a necklace but not to turn it over. How many different necklaces can be made using 13 different beads? help plz i will give brainlyist to right awnser :3
Answer:
We have 13 different beads to use in our necklace, and the thing that will make a necklace different to others, is the position of the beads.
And because we can not turn the necklaces over, the mirrored necklaces are different (the positions of the beads are mirrored)
For the first bead, we have 13 options, for the second, 12 options, and so on
the total number of combinations is equal to the product of the options for each selection, then we have:
C = 13*12*11*10*9*8*7*6*5*4*3*2*1 combinations:
C = 6,227,020,800.
Now, we are allowed to rotate the necklace, this means that a combination.
a b c d e f g h i j k l m (each letter is equivalent to one of the different beads)
is the same as other ordered as
m a b c d e f g h i j k l
And for each combination, we have 13 rotations, then the actual number of combinations is:
C/13 = 6,227,020,800/13 = 479,001,600
Using arrangements, it is found that 6,227,020,800 different necklaces can be made using 13 different beads.
The beads can be exchanged among the positions to form the necklace, hence, the arrangements formula is used.
This formula gives the number of possible arrangements of n elements, and is defined by:
[tex]A_n = n![/tex]
In this problem, the necklaces are formed by 13 beads, hence [tex]n = 13[/tex] and:
[tex]A_{13} = 13! = 6227020800[/tex]
6,227,020,800 different necklaces can be made using 13 different beads.
A similar problem is given at https://brainly.com/question/24648661
Using the digits 1 to 9, at most one time each, fill in the boxes so that the points make a parallelogram. Mathematically, use parallel line or congruent sides to explain your answer. If there are calculations, include those in your explanation.
Answer:
[tex]\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right[/tex]
Step-by-step explanation:
The coordinates are:
[tex]\left\begin{array}{ccc}A\left( \boxed{3} , \boxed{8} \right)&B\left( \boxed{9} , \boxed{6} \right )\\\\C\left( \boxed{1} , \boxed{4} \right)&D\left( \boxed{7} , \boxed{2} \right )\end{array}\right[/tex]
The parallelogram is attached below.
To verify if these coordinates form a parallelogram, we show that:
AB=CD; and AC=BDUsing Distance Formula
[tex]AB = \sqrt{(6-8)^2+(9-3)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units[/tex]
[tex]CD = \sqrt{(2-4)^2+(7-1)^2} = \sqrt{(-2)^2+(6)^2} = \sqrt{40} $ units[/tex]
[tex]AC = \sqrt{(8-4)^2+(3-1)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units[/tex]
[tex]BD = \sqrt{(6-2)^2+(9-7)^2} = \sqrt{(4)^2+(2)^2} = \sqrt{20} $ units[/tex]
Since AB=CD; and AC=BD, the coordinates A, B, C, and D form the vertex of a parallelogram.
A paper cup is a perfect cylinder that is 6.4 cm tall and 3 cm across. Find the total area of paper needed to make the cup, to the nearest square centimeter.
Hey there! I'm happy to help!
We want to find how much paper we need to make the cup. So, we need to find the surface area of the cylinder, which is basically the "walls and floors" of the cup. So, this is the circle on the bottom and the surrounding stuff that goes up. There is no circular top to this cup, which will be important when finding the total area of paper.
So, first we need to find how much paper we need to make the bottom circle. The formula for the area of a circle is A=πr². This r represents the radius, or the distance from the center of the circle to the edge. We are given that the cup is 3 cm completely across, and the radius is be half of that, so the radius is 1.5 cm. Let's find the area. We will use 3.14 for π.
π×1.5²=7.065
Now, we need to find the area of the walls of the cup. The wall is a rectangle that is basically wrapped around the circle. The height of the rectangle is the height of the cup and the length of the rectangle is the circumference (perimeter) of the bottom circle because the length of the rectangle wraps completely around the circle.
First, let's find the circumference of the circle. The circumference is the diameter (distance across the circle, so 3 cm) multiplied by π. We will use 3.14 for π.
3π=9.42
So, this means that the long side of the rectangle is 9.42 cm, and now we multiply this by the height.
9.42×6.4=60.288
Now, we add the rectangle area and the bottom circle area.
60.288+7.065=67.353
But, they want us to round to the nearest centimetre, so we will just say 67 square centimetres.
An important thing to note is that this is not the area of a normal cylinder (one with a top and a bottom circle) because it is a cup so it does not have a top. If you have a cylinder with a top and a bottom, you would just multiply the area of the circle by two, so then you have the top and bottom. If that were the case, the area of our cylinder would be 74 cm with the numbers we have been given here.
Have a wonderful day!
Can someone please help me I really need help please help me thank you
Answer:
Surface area of the triangular prism = 144 cm²
Step-by-step explanation:
Surface area of a triangular prism = Area of two triangular bases + Area of 3 lateral sides(rectangular sides)
Area of triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(3)(4)[/tex]
= 6 cm²
Area of one rectangular lateral side with sides 3 cm and 11 cm
= Length × width
= 3 × 11
= 33 cm²
Area of the lateral rectangular side with sides 4 cm and 11 cm
= 4 × 11
= 44 cm²
Area of the lateral rectangular side with sides 5 cm and 11 cm
= 5 × 11
= 55 cm²
Total area of lateral sides = 33 + 44 + 55 = 132 cm²
Surface area of the triangular prism = 2(6) + 132
= 144 cm²
Therefore, Surface area of the triangular prism = 144 cm²
An amateur toy maker produces dolls and cars. She can make at most 30 total toys in her spare time in a month. She wants to make at least 4 dolls and 4 cars each month but no more than 10 cars. At the local toy store where she sells her toys, she makes a profit of $25 per doll and $16 per car sold. a) How many of each type of toy should be produced to
maximize her profit? b) What is the maximum profit?
Answer:
$660
Step-by-step explanation:
16*10 +20*25=
160+500=660
Answer:
4 cars, 26 dolls
$714
Step-by-step explanation:
She can make maximum 30 toys
Max 10 cars, then 20 dolls can be made
4 dolls and 4 cars min is the limitation
If she makes 10 cars and 20 dolls, then profit is:
10*$16+20*$25= $660
Since cars bring less profit than dolls, the min number of cars= 4, then max number of dolls= 30 -4= 26,
Then profit is:
4*$16+26*$25= $714
If point P is 4/7 of the distnace frm M to N, what ratio does the point P partiion the directed line segment from M to N
Answer: 4:3.
Step-by-step explanation:
Given: Point P is [tex]\dfrac{4}{7}[/tex] of the distance from M to N.
To find: The ratio in which the point P partition the directed line segment from M to N.
If Point P is between points M and N, then the ratio can be written as
[tex]\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}[/tex]
As per given,
[tex]\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}[/tex]
Hence, P partition the directed line segment from M to N in 4:3.
Help please
What is the value of y in this system of equations?
-6x+2y=-18
-3x-2y=54
Answer:
-6x+2y=-18 = [tex]y = -9 + 3x[/tex]
-3x-2y=54 = [tex]y = -27 - \frac{3x}{2}[/tex]
Step-by-step explanation:
I hope I understood this correctly.
Find m∠V. Struggling in geometry! Help plz :/
Answer:
16 degrees
Step-by-step explanation:
74 + 90 = 164
180-164 = 16
the sum of two different numbers x and y is 70 and the differences when the smaller number is subtracted from the larger number is 30 what is the value of xy
Answer:
1000
Step-by-step explanation:
Lets just say x is the bigger number. We can create two equations.
x + y = 70
x - y = 30
If we add these equations together, we get that:
2x = 100
and that
x=50
Plugging x back into any of the equations gets us that y = 20, so xy = 20*50 = 1000
An equation is formed when two equal expressions. The value of xy will be 1500.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the larger number be represented by x, while the smaller number is represented by y.
Given that the sum of two different numbers x and y is 70. Therefore, the sum of the two numbers can be rewritten as
x + y = 70........ equation 1
Also, when the smaller number is subtracted from the larger number then the difference is 30. Therefore, we can write,
x - y = 30......equation 2
Now, if the two equations are added together,
x + y + x - y = 100
2x = 100
x = 50
Substitute the value of x in any one of the equations, to get the value of y.
x + y = 70
50 + y = 70
y = 20
Therefore, The larger and the smaller number that sums up to 70 and whose difference is 30 are 50 and 20, respectively.
Now, the value of xy can be rewritten as,
xy = 50 × 30
x y = 1500
Learn more about Equation:
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Q3. Ishah spins a fair 5-sided spinner. She then throws a fair coin.
(i) List all the possible outcomes she could get. The first one has been done for you.
(1, H)
(ii) Ishah spins the spinner and tosses the coin.
Work out the probability that she will get a 2 and a head.
Answer:
see below
Step-by-step explanation:
1.
1, H - 2, H - 3, H - 4, H - 5, H
1, T - 2, T - 3, T - 4, T - 5, T
2.
2,H is one out of 10 possible outcomes, so the probability is 1/10
Trey is running for president of the chess club, and he received 8 votes. There are 80 members in the club. What percentage of the club members voted for Trey?
Answer:10
Step-by-step explanation:
8/80=1/10*100=10
A random variable r is normally distributed with a mean of 7 and a standard deviation of 1.5. Find the value of w so that P (8.8
Answer:
The answer is explained below
Step-by-step explanation:
Given that:
mean (μ) = 7 and standard deviation (σ) = 1.5.
The z score is used in statistic used to measure the number of standard deviation by which the raw score is above or below the mean value. It is given by:
[tex]z=\frac{x-\mu}{\sigma}, where\ x\ is\ the \ raw\ score[/tex]
To find the Probability that x < 8.8, we first find the z score using:
[tex]z = \frac{x-\mu}{\sigma}=\frac{8.8-7}{1.5}=1.2[/tex]
From the z tables, P(x < 8.8) = P(z < 1.2) = 0.8849 = 88.49%
?/? of 24 = 16 (answer in fraction)
Answer:
[tex]\boxed{\sf \ \ \ \dfrac{2}{3} \ \ \ }[/tex]
Step-by-step explanation:
hello
24 = 8*3
16 = 8*2
so
[tex]\dfrac{2}{3}*24=\dfrac{2*8*3}{3}=8*2=16[/tex]
so the answer is 2/3
hope this helps
Mr. Ferrier invested $26,000. Some was invested in bonds that made a 5% profit, and the rest was put in stocks that made an 8% profit. How much did mr. Ferrier invest in bonds if his total profit on both types of investments was $1,420
Answer:
bonds=22000
stock=4000
Step-by-step explanation:
let b for bonds , and s for stock
b+s=26000
0.05 b +0.08 s=1420
to solve (by elimination)
1- multiply first equation with 0.05 to eliminate b
0.05 b+0.05 s=1300
0.05b+0.08s=1420
subtract two equations:
0.05b+0.05s-0.05b-0.08s=1300-1420
-0.03s=-120
s=120/0.03=4000
b+s=26000
b=26000-4000=22000
check:0.05(22000)+0.08(4000)=1420
Answer:
$22000
Step-by-step explanation:
x*0.05+(26000-x)*0.08= 1420
0.05x - 0.08x + 2080= 1420
0.03x=2080 -1420
0.03x= 660
x= 660/0.03
x= 22000
$22000 = 5% bonds
$4000 = 8% stocks
Please answer this question now in two minutes
Hey there! :)
Answer:
y = 10/9x + 8/3
Step-by-step explanation:
A line that is perpendicular to y = -9/10x - 10 has a slope that is the negative reciprocal. Therefore:
-9/10 --> 10/9. This is the slope of line q.
Use the formula y = mx + b where:
m = slope
x = x coordinate of point
y = y coordinate of point.
-4 = 10/9(-6) + b
-4 = -60/9 + b
Create a common denominator:
-36/9 = -60/9 + b
24/9 = b
Simplify:
b = 8/3.
Rewrite the equation:
y = 10/9x + 8/3
Use the Distributive Property to write each expression as an equivalent algebraic expression. (7 + a)3 Question 4 options: 3(7a) 21 + 3a 10 + 3a 7 + 3a
Answer:
(B)21+3a
Step-by-step explanation:
An expression is said to be distributive when:
[tex](a+b)c=a \cdot c+b \cdot c[/tex]
Given the algebraic expression: (7 + a)3
Applying the distributive property
[tex](7 + a)3 = 7 \cdot 3+a \cdot 3\\=21+3a[/tex]
An equivalent expression is 21+3a.
The correct option is B
Consider the function. Which statement correctly describes the function’s behavior around its vertical asymptote?
A) As x → –2–, f(x) → ∞ and as x → –2+, f(x) → ∞.
B) As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞.
C) As x → –2–, f(x) → –∞ and as x → –2+, f(x) → –∞.
D) As x → –2–, f(x) → ∞ and as x → –2+, f(x) → –∞.
Answer:
B) As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞.
Step-by-step explanation:
2020 edg.
A function assigns the values. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The statement that correctly describes the function's behavior around its vertical asymptote is As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞. Thus, the correct option is B.
Learn more about Function:
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please help me understand how to do this!
Answer:
x = -72
Step-by-step explanation:
Step 1: Get rid of the fraction by multiplying both sides by 9
-8x = 576
Step 2: Divide both sides by -8 to get x
x = -72
Answer:
x = -72
Step-by-step explanation:
-8x/9 = 64
Multiply each side by -9/8
-8x/9 * -9/8 = 64 *-9/8
x = -72
Which of the following are solutions to the equation below?
Check all that apply.
x2 + 4x-9 = 5x + 3
A. -3
B. 5
| C. 2
D. -4
E. 4
F-7
Answer:
The answers are options A and E
x² + 4x-9 = 5x + 3
Group like terms
x² + 4x - 5x - 9 - 3 = 0
x² - x - 12 = 0
Using factorization method
(x + 3)( x - 4) = 0
x = - 3 x = 4
Hope this helps
Which points are separated by distance of six units?
Answer:
(1,8) and (1,2) are 6 units apart
please help me out friends
Answer:
month 5
Step-by-step explanation:
Find x please help thank you
Answer: x=(7√6)/2
Step-by-step explanation:
To find x, we would have to find the hypotenuse of the 45-45-90 triangle. First, we would have to find the hypotenuse by using the 30-60-90 triangle on top to find it.
For a 30-60-90 triangle, the hypotenuse is 2x in length. the x is the same in all sides. All you would have to do is to plug it in. The leg opposite of 60° is x√3 in length. the leg opposite of 30° is x in length.
Since we know that 7 is opposite of the 30° angle, we know that x is 7. Across fron 60° is the hypotenuse of the 45-45-90 triangle. That leg is x√3. We plug in x=7 and get 7√3.
The hypotenuse of the 45-45-90 triangle is x√2 and the legs are both x. We can set 7√3 equal to x√2 to find x of the missing side.
7√3=x√2 [divide both sides by √2]
x=(7√6)/2
Now, we know x=(7√6)/2.
