Answer:
B. $424.000
Step-by-step explanation:
The function a(t)=424(1+0.06)
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 28 tires surveyed, the mean lifespan was 46,300 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Answer:
[tex]z=\frac{46300-50000}{\frac{9800}{\sqrt{28}}}=-1.998[/tex]
Now we can calculate the p value using the alternative hypothesis with this probability:
[tex]p_v =P(z<-1.998)=0.0229[/tex]
The p value for this case is significantly lower than the value of [tex]\alpha=0.05[/tex] so then we can reject the null hypothesis at this signficance level and we have enough evidence to conclude that the true mean for the deluxe tire is less than 50000 and the claim is not correct.
Step-by-step explanation:
Information given
[tex]\bar X=46300[/tex] represent the sample mean for the lifespans
[tex]\sigma=9800[/tex] represent the population standard deviation
[tex]n=28[/tex] sample size
[tex]\mu_o =50000[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
The idea for this case is verify if the deluxe tire averages at least 50,000, so then the system of hypothesis are:
Null hypothesis:[tex]\mu \geq 50000[/tex]
Alternative hypothesis:[tex]\mu < 50000[/tex]
We know the population deviation so then the correct test stattistic would be:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{46300-50000}{\frac{9800}{\sqrt{28}}}=-1.998[/tex]
Now we can calculate the p value using the alternative hypothesis with this probability:
[tex]p_v =P(z<-1.998)=0.0229[/tex]
The p value for this case is significantly lower than the value of [tex]\alpha=0.05[/tex] so then we can reject the null hypothesis at this signficance level and we have enough evidence to conclude that the true mean for the deluxe tire is less than 50000 and the claim is not correct.
(5+2×3)−4+(5x5) ? Highly appreciate it. :)
Answer:
32
Step-by-step explanation:
Answer: 32
Step-by-step explanation:
Giving brainliest for CORRECT awnser.
Answer:
C
Step-by-step explanation:
Answer:
C. (2x+3)(x+5)
Step-by-step explanation:
We need to use FOIL for this
First
Outer
Inner
Last
Let's see the answers of our options:
A. (2x+1)(x+15) = 2x²+30x+x+15 = 2x²+31x+15
B. (2x+15)(x+1) = 2x²+2x+15x+15 = 2x²+17x+15
C. (2x+3)(x+5) = 2x²+10x+3x+15 = 2x²+13x+15
D. (2x+5)(x+3) = 2x²+6x+5x+15 = 2x²+11x+15
Only option C simplifies to 2x²+13x+15
Maggie is rock climbing. After reaching the summit, she descends 14 feet in 2 1/3 minutes. If she continues at this rate, where will Maggie be in relation to the summit after 8 minutes?
Answer:
about 27.42
Step-by-step explanation:
Assume that the probability of a driver getting into an accident is 5.7% and
that the average cost of an accident is $24,500. If the driver's insurance
premium is $1686.50, what is the overhead cost for the insurance company
to insure the driver?
A. $256
B. $190
C. $290
D. $260
Answer:
C. $290
Step-by-step explanation:
The expected cost is:
E = 1686.50 − (0.057) (24500)
E = 290
What’s the correct answer for this?
Answer: a
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
It would still be 10° because dilation doesn't change angles
Shown below is a regular pentagon inscribed in a circle. Calculate the area of the shaded region. Round your answer to the nearest tenth.
Answer:
S(a) = 27,5036 squared units
Step-by-step explanation:
Shaded area is :
S(a) = Area of the circle - area of the regular pentagon (1)
A(c) = area of the circle
A(c) = π*(r)² ⇒ A(c) = π*(6)² ⇒ A(c) = 36*π ⇒ A(c) = 113,0976 squared units
Area of a regular pentagon:
a) If we draw a straight line between the center and each vertex we get 5 triangles, and if we draw the apothem for each side, we get 10 triangles. We will calculate the area of one of these triangles
The first 5 triangles has a central angle equal to 72⁰ according to:
360/5 = 72
When we divide these triangles in two triangles by means of the apothem, each central angle will be of 36⁰, then
sin 36⁰ = 0,58778 and cos 36⁰ = 0,809017 and sin 36⁰ = x/6 here x is half of the side of the regular pentagon. Then
0,58778 = x/6
x = 6*0,58778
x = 3,52668 units of length
and cos 36⁰ = a/6 where a is the apothem, then
0,809017 = a / 6 ⇒ a = 6*0,809017
a = 4,8541 units of length
Now we are in conditon to calculate area of the triangles as:
A(t) = (1/2)*b*h
A(t) = (1/2)*x*a ⇒ A(t) = 0,5* 3,52668*4,8541
A(t) = 8,5594 squared units
Finally we have 10 of these triangles, then
Area of regular pentagon is : 10*A(t) squared units
A(p) = 85,594 squared units
Now plugging these values in equation (1) we get the shaded area
S(a) = 113,0976 - 85,594
S(a) = 27,5036 squared units
There are 5 slices of pepperoni pizza, 1 slice of sausage pizzá, and 3 slices of cheese pizza left at the pizza party. Without looking, Amy took a slice of pizza, ate it, and then took another slice. What is the probability of Amy eating two slices of cheese pizza?
Answer:
3/8
Step-by-step explanation:
add 5+1+3=9
and there is 3 cheese pizza so its 3 over 8.
Answer:
3/9
Step-by-step explanation:
A car travel 65kms from A to B in 70 minutes and 80 km from B to C in 75 minutes.
Find the average speed in km/h of the car for the whole journey?
Answer:
60 km/h
Step-by-step explanation:
The car has traveled a total distance of 65+80 = 145 km in 70+75 = 145 minutes. Then the average speed is ...
speed = distance/time = (145 km)/(145 min)·(60 min/h) = 60 km/h
The average speed for the journey is 60 km/h.
Tuli is 10 years younger than Emily. The product of their
ages 2 years ago was 39. Let the present age of Emily
be A. Which of the following quadratic equations does A
satisfy?
Answer:
a² - 14a - 15 = 0 (quadratic equation)
Emily's age = 15 years
Tuli's age = 15 - 10 = 5 years
Step-by-step explanation:
let
Emily age = a
Tuli age = a - 10
Two years ago their ages will be as follows.
Emily's age = a - 2
Tuli's age = a - 10 - 2 = a - 12
The product of their ages 2 years ago is 39.
(a - 2)(a - 12) = 39
a² - 12a - 2a + 24 - 39 = 0
a² - 14a - 15 = 0 (quadratic equation)
To get a
a² + a - 15a - 15 = 0
a(a + 1) - 15(a + 1)
(a + 1)(a - 15)
a = -1 or 15
we can only use 15 as it is positive.
SOLVE 3/4 +(1/3/1/6) -(1/2)
Answer:9/4
Step-by-step explanation:
3/4 + (1/3/1/6) - (1/2)
3/4 + (1/3 ➗ 1/6) - 1/2
3/4 + (1/3 x 6/1) - 1/2
3/4 + ((1x6)/(3x1)) - 1/2
3/4 + (6/3) - 1/2
3/4 + 2 - 1/2
(3+8-2)/4
9/4
Writing Percents as Fractions
a. Write 35% as a fraction in simplest form.
35% =
35
100
Write as a fraction with
a denominator of 100.
7
20
Simplity.
Answer:
Answers are below
Step-by-step explanation:
Percent means "out of 100" so 35% is 35/100. We can simplify this fraction by dividing the numerator and denominator by 5. 35/100 / 5 = 7/20.
7/20 multiply the numerator and denominator by 5.
7/20 x 5 = 35/100
If this answer is correct, please make me Brainliest!
Answer:
b and c
Step-by-step explanation:
Uta invests an amount into a compound interest investment account that pays 6% a year. After six years, she withdraws her
total balance of $500. Using the formula A - P(1 + r), how much money did Uta initially invest?
$180.00
$320.00
$352.48
$471.70
Answer:
$352.48
Step-by-step explanation:
500 = P(1+6/100)^6
500 = P(1.141851912)
P = 500 / 1.1418519112 = 352.48
Write a recursive formula to describe the sequence: 1, 3, 7, 13...
Answer:
f(n) = f(n - 1) + 2(n - 1) for n [tex]\geq[/tex] 1
Step-by-step explanation:
The volume of a cone is 3x* cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
O 3x
6x
370x2
O 90X2
Mark this and retum
Save and Exit
Next
Submit
Answer:
The radius of a cone is [tex]\dfrac{3}{\sqrt{\pi} }\ \text{units}[/tex].
Step-by-step explanation:
The formula of the volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]
r is radius of cone
h is height of cone
We have,
Volume of a cone is 3x cubic units and height is x units. Putting the values of volume and height such that,
[tex]r=\sqrt{\dfrac{3V}{\pi h}}\\\\r=\sqrt{\dfrac{3\times 3x}{\pi x}} \\\\r=\sqrt{\dfrac{3\times 3}{\pi}}\\\\r=\sqrt{\dfrac{9}{\pi}}\\\\r=\dfrac{3}{\sqrt{\pi} }\ \text{units}[/tex]
So, the radius of a cone is [tex]\dfrac{3}{\sqrt{\pi} }\ \text{units}[/tex].
How do you describe the translation (x, y) → (x + 3, y - 7) in words?
Answer:
You move right 3, and down 7
Find the value of each unknown variable in the given figures ?
10) a. 130
Step-by-step explanation:
[tex]180 - 50 = 130[/tex]
Write parametric equations of the line 2x - y = 3.
a. X = 1, y = 2t - 2
c.
X = 1, y = 3t-2
b. X= 1, y = 2t-3
d.
1
1
X = 1,y= =
2
1.9 -
3
Please select the best answer from the choices provided
A
OB
С
OD
Find the arc length of a partial circle with a radius of 5
Will mark brainlist! pleaseeee
Answer:23.55
Step-by-step explanation:
radius=r=5
Φ=360-90
Φ=270
π=3.14
Length of arc=Φ/360 x 2 x π x r
length of arc=270/360 x 2 x 3.14 x 5
Length of arc=0.75 x 2 x 3.14 x 5
Length of arc=23.55
Answer:
23.55 units
Step-by-step explanation:
Hope this helps!
The driveway in front of the brown house is 35 feet long and the driveway in front of the red house is 7 yards, 9 feet long. Which house has the long driveway and by how much? *
Brown house driveway; larger by 30 feet
Red house driveway; larger by 7 feet
Brown house driveway; larger by 5 feet
They are both equal.
Answer:
Brown house driveway; larger by 5 feet
Step-by-step explanation:
Lets convert yds to ft
We know 3 ft = 1yd
3*7 = 21
so 7yds = 21 ft
Add the 9 ft
7yds 9ft = 21+9 = 30 ft
The house with the 35 ft driveway is longer by (35-30) or 5 ft
A ball is thrown straight up from a cliff. The function f(x)= -4.9t^ + 17t +19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is the height reached? Round your answer to one decimal place.
Answer:
33.7 m at 1.7 seconds
Step-by-step explanation:
For quadratic ax^2+bx+c, the line of symmetry (x-coordinate of the vertex) is ...
-b/(2a)
For your quadratic, the vertex (highest point) is reached at time ...
t = -(17)/(2(-4.9)) = 17/9.8 ≈ 1.7 . . . . seconds
__
The height at that time is ...
f(17/9.8) = (-4.9(17/9.8) +17)(17/9.8) +19 = 289/19.6 +19 ≈ 33.7 . . . meters
_____
Comment on the function evaluation
We have used the "Horner form" of the function to make evaluation easier.
f(t) = (-4.9t +17)t +19
f a triangle has a side length of 10, 12 and 15 units respectively, what type of triangle is it acute right obtuse or no solution
Answer:
Acute.
Step-by-step explanation:
Using the Triangle Inequality Theorem you know that the sum of the lengths of two sides of a triangle are greater than the length of the third side.
Using this we can narrow it down that this DOES have a solution, since 10+12>15.
Now, we can determine if this triangle is a right triangle using the Pythagorean Theorem. C is the longest length.
If c^2= a^2+b^2, then it is a right triangle.
If c^2< a^2+b^2 then it is an acute triangle.
If c^2>a^2+b^2 then it is an obtuse triangle.
We can now substitute. (A and B are interchangeable, but C is the longest length.
A=10
B=12
C=15
A^2=100
B^2=144
C^2=255
We can now figure out that this triangle is acute because A^2+ B^2 (244) < C^2 (255).
Hope this helps!
A sector with an area of 11/2*pi cm^2 has radius of 3 cm. What is the central angle measure of a sector in degrees?
190
200
210
220
Answer:
Step-by-step explanation:
Area of sector = angle/360 * pi * r^2
5.5pi = angle/360 * pi * 9
5.5 = angle/360 * 9
angle = (5.5 * 360)/9 = 40 * 5.5 = 220
Compute the amount of interest earned in the following simple interest problem. A deposit of $4,500 at 5% for 3 years:
$67.50
$6.75
$675.00
$6,750.00
Answer:
$675.00
Step-by-step explanation:
4500 x 0.05 x 3 = 675
3/4 x 1/4
next problme: 3/5 x 1/5
100 pts
Answer:
0.1875 and 0.12
Step-by-step explanation:
3/4x1/4 is 0.1875. 3/5 x 1/5 is 0.12
Answer:
1)0.1875
2)0.12
Step-by-step explanation:
Calculate the volume of the pyramid.
4cm
Base = 35cm
Enter your math answer
Answer:
V = 46.67cm²
Step-by-step explanation:
[tex]V=\frac{lwh}{3}[/tex] Use this equation to find the volume of the pyramid
[tex]V=\frac{35*4}{3}[/tex] Multiply in the numerator
[tex]V=\frac{140}{3}[/tex] Divide
V = 46.67cm²
If this answer is correct, please make me Brainliest!
Consider that point A is reflected across the x-axis. What is the distance between point A and the point of its reflection?
Answer:
It would be 2 x the absolute value of the y coordinate.
Step-by-step explanation:
Example:
(5,-3)
Absolute value of y-coordinate is 3 and distance would equal 2 x 3 = 6 units apart.
you know I'm ballin usual like Kobe
Answer:
miss him :(
Step-by-step explanation:
Answer:
:( RIP
Step-by-step explanation:
Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rolling any number from 1 to 5 are equal, but the probability of rolling a 6 is twice the probability of rolling a 1. What are the probabilities of the 6 outcomes? What is the probability that the first roll will be an odd number and the second roll will be an even number?
Answer:
Probabilities:
1-5:1/7
6: 2/7
Probability of even number: 4/7
Probability of odd number: 3/7
Step-by-step explanation:
We are told that the probability in each throw is as follows. Probability of getting 1 to 5 is the same and the probability of 6 is twice the probability of getting 1. Let us call c the probability of having a 1. So, the probability of having 2,3,4,5 is also c. In this case, the probability of having 6 is 2*c. Since all of this outcomes are mutually exclusively, then we must have the following
[tex] c+ c + c+ c +c + 2c = 1= 7c[/tex](since the probabilities of mutually exclusive events that cover all outcomes of the experiment must add to 1)
This implies that [tex]c = \frac{1}{7}[/tex]. Then, the probability of having a 6 is 2/7 and to have any other number is 1/7.
Each roll is independent of each other, so the probability of having an odd or even number doesn't depend of the other trials.
To calculate the probability of having an even number, we add the probabilties of getting a 2,4,6. In this case, that is 1/7+1/7+2/7 = 4/7. To calculate the probability of an odd number we add the probabilities of 1,3,5 which 1/7+1/7+1/7 = 3/7.
The design for a playground is represented on the coordinate plane below, where the units are in yards.
A fence will be built around the perimeter of the entire playground.
How many yards of fencing will be needed to build the fence?
Answer:
The perimeter of the field is 21 yards
Step-by-step explanation:
See attachment 1 for the coordinates plane.
The question is best solved using an attachment.
To calculate the perimeter of the fence, we simply add the sides of the rectangle.
Attachment 2 is a labelled diagram of attachment 1.
From 2, we have that
Perimeter = A + B + C + D + E + F
Where A to F represent the length of each sides of the fence
From coordinates geometry,
A = 5
B = 4
C = 6½
D = 1½
E = 1½
F = 2½
So,
Perimeter = 5 + 4 + 6½ + 1½ + 1½ + 2½
Perimeter = 21
Hence, the perimeter of the field is 21 yards