Using the t-distribution, it is found that the 90% confidence interval is of 2.71 hours to 3.29 hours.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 25 - 1 = 24 df, is t = 2.0639.
The other parameters are given as follows:
[tex]\overline{x} = 3, s = \sqrt{0.5} = 0.707, n = 25[/tex]
Hence the bounds of the interval are given as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3 - 2.0639\frac{0.707}{\sqrt{25}} = 2.71[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3 + 2.0639\frac{0.707}{\sqrt{25}} = 3.29[/tex]
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In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision. (2,-1), (3,0.5), (6,1.5), (9,2)
Pease help :((
The solution to the question is arrived at using the knowledge of mathematical models.
What is a mathematical model?A mathematical model is a linguistic and mathematical concepts-based description of a system.
The appropriate model for the given data is:
Because there are discrepancies and no direct equation that can complete all of these points, a Least Square Regression Line is the best option for resolving this problem.
They could be outliers, so we need use a calculator to create a regression line to find the residual value.
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Someone please Help me please
In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
Trigonometric RatioIn the first triangle, we need to use trigonometric ratio to find the missing side in the triangle
Data;
Angle = 45hypothenuse = [tex]8\sqrt{2}[/tex]adjacent = xTo find the adjacent side, we need to use cosine rule on this problem.
[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]
The adjacent side is equal to 8 units
In the second triangle, we also need to use trigonometric ratio, but let's write down our data
angle = 30hypothenuse = 10opposite = ?adjacent = ?We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.
[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]
The adjacent side is equal to 8.660, let's find the opposite side using sine rule
[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]
And lastly, the value of the other angle is
[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]
From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
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A video rental company offers a plan that includes a membership fee of $5 and charges $1 for every DVD borrowed. They also offer a second plan, that costs $47 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?
Answer:
for $5 plan if he rents 47 dvd it will pay 47% as one DVS cost 1 $ .
Step-by-step explanation:
SOMOENE HELP ASAPPPPP
53= 29t < 343
Step-by-step explanation:
Answer:
53 = 343t-29
Step-by-step explanation:
53 is equal to (53 =)
t times 343 (343t)
29 less than the quantity (-29)
Good luck! :)
What is the value of x?
Answer:
108
Step-by-step explanation:
x and 2/3 x are linear pair angles.
Sum of linear pair angles is 180.
x + 2/3 x = 180
3x/3 + 2x/3 = 180
( 3x + 2x )/3 = 180
5x/3 = 180
Cross multiply,
5x = 180 * 3
Divide 5 on both sides,
x = ( 180 * 3 )/5
= 36 * 3
x = 108
Mary and her brother are saving their money to buy a laptop that costs $799. If Mary has $356.00 and her brother has $295.00, do they have enough money together to buy the laptop?
The equation is the formula that relates the circumference of a circle to the radius. this gives us the ability to calculate pi if we physically measure a circle's circumference and radius. solve the equation for to get the formula you would use to perform this activity.
Answer:
π = C/(2r)
Step-by-step explanation:
The equation that relates the circumference of a circle to the radius is ...
C = 2πr
__
We can divide both sides of the equation by 2r to get an expression for π.
[tex]C=2\pi r\\\\\dfrac{C}{2r}=\dfrac{2\pi r}{2r}\\\\\boxed{\pi=\dfrac{C}{2r}}[/tex]
A triangle has a base of 8 cm and a height of 12 cm.
What is the area of the triangle?
Enter your answer in the box.
*box* cm2
Answer: 48 cm^2
Step-by-step explanation:
The equation for the area of a triangle is 1/2(base*height). Plug in the numbers to get an equation of 1/2(8*12). 8*12 = 96. Now divide by 2. 96/2 = 48.
Answer:
48 cm^2
Step-by-step explanation:
a triangle area is hb/2
so 8*12=96
96/2=48 therefore 48 is the answer.
A disk is shaped like a flat circular plate. Its radius is 4.25 inches. To the nearest hundredth, what is the area of the disk? Use 3.14 for π.
Work Shown:
A = pi*r^2
A = 3.14*(4.25)^2
A = 56.71625
A = 56.72
what does (5x3)+(4x2) equal
Answer:
23
Step-by-step explanation:
5 x 3 = 15
4 x 2 = 8
15 + 8
= 23
9. Find the slope of the line between the
coordinates (-6, -13) and (3, -1).
H.
F.
G.
314 43
J.
3/4 4/3
Answer:
The slope is 4/3
Step-by-step explanation:
The solution is in the image
what is 10x+15 if x is 10
The answer would be 115
Step-by-step explanation:
The perimeter of a rectangle is 90 feet. The width is 15 feet. What is the perimeter?
11. Find the equation for the circle with center (−2,4) and passing through (5,−3).
Answer:
In standard form: (x+2)² + (y-4)² = 98
Use the distance formula to find radius:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d = \sqrt{(-2 - 5)^2 + (4-(-3))^2}[/tex]
[tex]\rightarrow \sf d = \sqrt{(-7)^2 + (7)^2}[/tex]
[tex]\rightarrow \sf d = 7\sqrt{2}[/tex]
Equation of circle:
(x-h)² + (y-k)² = r²(x-(-2))² + (y-4)² = (7√2)²(x+2)² + (y-4)² = (7√2)²(x+2)² + (y-4)² = 98What’s the answer? I’m confused
Answer: it would be y/2 if im not mistaken.
Step-by-step explanation: because with x+3/3 the 3 on the top is canceled out leaving x/3 so it would be the same with y+2/2. I hope im right and that this helps. If not i am sorry.
Sandy made several investments. She bought 1000 shares of a company’s stock for $8.60/share, she bought a bond with a face value of $2500 and a coupon rate of 7%, and she invested $5000 into a fund that is expected to grow by 3.5% per year.
The bond Sandy purchased will mature in 10 years. How much interest will she receive semiannually?
How long will it take the fund she invested in to be worth $10,000?
27) Harry made 4 hits in 9 times at-bat. If she keeps the same success level, how many hits should she make in 18 times at bat?
Answer:
8 hits
Step-by-step explanation:
The ratio is :
hits : times-at-bat = 4 : 9Now, we have 18 times at bat.
Multiply both sides of the ratio with 2 :
4 x 2 hits : 9 x 2 times at bat8 hits : 18 times at batHarry should make 8 hits in 18 times at bat.
Evaluate the equation below
Answer:
55
Step-by-step explanation:
we can get the answer by putting it in the calculator
A push-cart vendor is selling sodas at the beach. partway into the day, he raises his
price per bottle by one quarter. after this price increase, the total dollar amount
collected for the day after selling n bottles at the new price is given by the following
equation:
t = 12 + 1.75n
according to this equation, how many bottles did the vendor sell today before raising the
price?
o a
8
ob.
12
c. 18
d. 21
Answer:
[tex]8[/tex].
Step-by-step explanation:
Notice that in equation for the total dollar amount collected ([tex]12+ 1.75\, n[/tex]), every additional bottle sold at the new price brings in [tex]1.75[/tex] dollars:
[tex]\begin{aligned}& 12 + 1.75\, n && \text{$n$ bottles at new price} \\ -\; & 12 + 1.75\, (n+1) && \text{$(n+1)$ bottles at new price} \\ =\; & 1.75\end{aligned}[/tex].
Therefore, the per-bottle price after the [tex]\$0.25[/tex] price increase would be [tex]\$1.75[/tex]. The per-bottle price before the price increase would be [tex]\$1.75 - \$0.25 = \$1.50[/tex].
Also notice that when [tex]n = 0[/tex], the total amount collected was [tex]t = 12 + 1.75\, n = 12[/tex]. In other words, the total amount collected was [tex]\$12[/tex] before any bottle was sold at the new price.
Thus, the vendor had collected [tex]\$12\![/tex] by selling at the initial price of [tex]\$1.50[/tex] per bottle. The number of bottles sold at that price would be:
[tex]\begin{aligned}\frac{12}{1.50} = 8\end{aligned}[/tex].
o Watch help video
A town has a population of 10000 and grows at 5% every year. What will be the
population after 5 years, to the nearest whole number?
Answer:
answers
Step-by-step explanation:
125000 Submit Answer.
Answer:
12763
Step-by-step explanation:
Based on the given conditions, formulate:
10000 x ( 5%+1)⁵
Evaluate the equation/expression: 12762.81563
Find the closest integer: 12763
Find the vertex and the axis of symmetry for the following functions.
a) y = 2x^3 + 4x
b ) y= -x^2+4x-5
Answer:
b
Step-by-step explanation:
its correct
Step-by-step explanation:
a)
y = 2x³ + 4x
a polynomial of 3rd degree cannot have an axis of symmetry.
it can only have a point of symmetry, like in this case.
(0, 0) is the point of symmetry, because due to the fact there is no squared term, any negative x values create exactly the same values (in absolute values) as their positive counterparts - just negative.
the vertex of a polynomial of 3rd degree is the point where the function changes directions.
that point for x³ is the origin, as it is for x. the factors only stretch the graph, but the vertex stays the same.
only if we had a term like (x+a)³ in the polynomial, this would shift the vertex.
so, the point of symmetry and the vertex are the same :
(0, 0).
b)
y = -x² + 4x - 5
the vertex form of a quadratic function is
f(x) = a(x − h)² + k
with (h, k) is the vertex.
x = h is the axis of symmetry.
we use "complete the square" to get it into that form.
-x² + 4x - 5 = -(x² - 4x + 5) = -(x - 2)² - 1
therefore,
y = -(x - 2)² - 1
h = 2, k = -1
the vertex is (2, -1)
the axis of symmetry is x = 2
Can anyone help solve this step by step?
Answer:
85.2 m²
Step-by-step explanation:
Perhaps one of the easiest ways to decompose this composite figure is to consider it as a rectangle with a triangle removed from it.
__
The vertical dimension of the missing triangle is 8-4 = 4 m. The horizontal dimension of the missing triangle is 11.4 -8.4 = 3 m. The overall rectangle, including the missing triangle, is 11.4 m wide and 8 m high.
The area of the figure is ...
area = rectangle area - triangle area
= (11.4 m)(8 m) -1/2(4 m)(3 m) = 91.2 m² -6 m² = 85.2 m²
The area of the shape is 85.2 square meters.
_____
Additional comment
The area of a rectangle is the product of its length and width:
A = LW
The area of a triangle is half the product of its base and height:
A = 1/2bh
Part D
What is the probability of the next wolf caught in the park being unmarked? Write the probability as a fraction, a decimal number, and a percentage.
Animal Total in Park Number Marked
elk 5,625 225
wolf 928 232
cougar 865 173
bear 1,940 679
mountain goat 328 164
deer 350 105
moose 215 86
Answer:
636/928 = 137/200
0.685
68.5%
Step-by-step explanation:
there were v crayons In a box.1/6 of the crayons were new.angie added another 24 new crayons to the box and there are 30 new crayons altogether.how many crayons were there in the box at first
Answer: 36
Step-by-step explanation:
If there are 30 new crayons, all you have to do is subtract the 24 new crayons Angie added, thus being six new crayons. Multiply this by 6 to get 36.
Find the area of the figure. (Sides meet at right angles.)
Answer:
44ft^2
Step-by-step explanation:
Break the shape into 3 rectangles, two 3 by 2's and one 4 by 8. (Get 4 by subtracting 3 from 7 for the left and right most side)
3 x 2 = 6 ft^2
since there's two rectangles you end up 6 + 6 so you get 12 ft^2
then 4 x 8 = 32 ft^2
add 32 and 12, get 44 ft^2
Consider the sequence an = 9(0.4)n. which rule defines sn? sn = 6(0.4n) sn = 9(0.4n) sn = 6(1 – 0.4n) sn = 9(1 – 0.4n)
The rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
How to determine the expression for Sn?The formula of the sequence is given as:
an = 9(0.4)^n
The above means that:
The first term, a = 9Common ratio, r = 0.4The sum Sn is then represented as:
[tex]S_n =\frac{a(1 - r^n )}{1 - r}[/tex]
So, we have:
[tex]S_n =\frac{9 * (1 - r^n )}{1 - 0.4}[/tex]
Evaluate the difference and divide
[tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
Hence, the rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
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Scott rolled a number cube several times and counted how many times he rolled a 3.
What is the theoretical probability of Scott rolling a 3 if his number cube is fair?
Using it's concept, it is found that the theoretical probability of Scott rolling a 3 if his number cube is fair is of [tex]\frac{1}{6}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For a theoretical probability, these number of outcomes are taken before any experiment.
In this problem, there are six numbers, one of which is three, hence the probability is given by:
[tex]p = \frac{1}{6}[/tex].
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3 yards 5 feet 6 inches
X 7=?
F- 32 yards 2 feet
6 inches
G-
33 yards 2 feet
6 inches
H- 33 yards 2 feet
9 inches
J- 34 yards 2 feet
6 inches
K- none of these
3 yards 5 feet 6 inches X 7 is 33.833333 yards. The correct option is K- none of these.
Numbers of yardsFirst step
One yard is 36 inches hence:
3 yards 6 inches=(36 inches×3)+6 inches
3 yards 6 inches=108 inches+6 inches
3 yards 6 inches=114 inches
Second step
5 Feet to inches=5 ft×12
5 feet to inches=60 inches
Third step
Yards=[(114 inches+60 inches)×7]/ 36 inches
Yards=(174 inches×7)/ 36 inches
Yards=1,218 /36 inches
Yards=33.833333
Therefore the correct option is K- none of these.
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please help me to answer
Answer:
7.92 cm²
Step-by-step explanation:
Area of Trapezium :
1/2 x (a + b) x h1/2 x (4.8 + 8.4) x 1.20.6 x 13.27.92 cm²She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width 8.75 inches, length 8.75 inches, height 23 inches.
The hot coffee has a density of 5.8 oz/in3 and the cold coffee has a density of 3.5 oz/ in3
(A) What is the volume of the coffee in each tank?
Show all math work needed to complete this problem.
(B) What is the mass of the coffee in each the tank?
Show all math work needed to complete this problem.
(C) How many tanks can be placed on a table which can support a maximum weight of 800 lb?
Explain why or why not.
Show all math work needed to complete this problem.
Answer:
Part ADimensions of tank:
width = 8.75 inlength = 8.75 inheight = 23 in⇒ Volume of each tank = width × length × height
= 8.75 × 8.75 × 23
= 1760.9375 in³
Part BGiven:
Hot coffee density = 5.8 oz/in³Cold coffee density = 3.5 oz/in³mass = density × volume
⇒ mass of hot coffee = 5.8 oz/in³ × 1760.9375 in³
= 10213.44 oz (nearest hundredth)
⇒ mass of cold coffee = 3.5 oz/in³ × 1760.9375 in³
= 6163.28 oz (nearest hundredth)
Part CConvert the masses of the tanks from ounces to pounds
1 lb = 16 oz
⇒ mass of hot coffee tank = 10213.44 ÷ 16
= 638.34 lb (nearest hundredth)
⇒ mass of cold coffee tank = 6163.28 ÷ 16
= 385.21 lb (nearest hundredth)
If the table can hold a maximum of 800 lb:
hot coffee: 800 lb ÷ 638.34 lb = 1.25 (nearest hundredth)
cold coffee: 800 lb ÷ 385.21 lb = 2.08 (nearest hundredth)
Therefore, either:
1 tank of hot coffee OR2 tanks of cold coffeecan be placed on a table which can support a maximum weight of 800 lb