A car dealership has seven cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start?
A reader of a book wants to estimate the mean word length in the book they are currently reading. they randomly select 19 pages from the book and count the length of 5 words they randomly selected on each of those pages. the table shows the results from the survey. using the sample results estimate the mean word length of any word in the book.
a.5.22 letters
b.5.49 letters
c.5.77 letters
d.5.92 letters
Answer:
B-5.49
Step-by-step explanation:
f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)] The function has real roots and imaginary roots.
Answer:
The function has
2 real roots and
2 imaginary roots.
Abcd is a parallelogram find the measure of a if b is (7x+13)degrees and d d is (8x-8)degrees brainly
The area of a triangle is 40sq inches. If the base of the triangle is 10 inches what is it’s height?
Answer:
Step-by-step explanation: 8 inches
The quotient of a number and 2 is the same as the difference of the number doubled and 3
Michael takes a multiple-choice test with 5 answer choices for each question. If he randomly answers every question what is his expected score
what is the vertex of the parabola
Let's consider the equation of parabola, y = a·(x - α)·(x - β)
where α, β are the x-intercepts.
From the given graph, the y-intercept is (0, -3).
From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.
So the equation of parabola would be now, y = a·(x + 1)·(x - 3)
We can plug the y-intercept (0, -3) in the equation to find value of 'a'.
-3 = a·(0+1)·(0-3)
-3 = -3a
a = 1
So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3
Comparing it with y = ax² + bx + c
The x-coordinate of vertex would be, [tex] x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1 [/tex]
the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.
Hence, vertex would be (1, -4).
A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times. What is the experimental probability of the arrow stopping over Section 3? Section 1: 18 Section 2: 30 Section 3 :32
Answer: [tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
From the given table, The number of times arrow stops over Section 3 = 32
The total number of times spinner spins = 80
Now, the experimental probability of the arrow stopping over Section 3 is given by :-
[tex]P(S-3)=\frac{32}{80}\\\\\Rightarrow P(S-3)=\dfrac{2}{5}[/tex]
Hence, the experimental probability of the arrow stopping over Section 3 is [tex]\dfrac{2}{5}[/tex]
Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 109.7 118.9 134.8 109.6 127.3 115.6 130.4 130.2 111.7 105.5 Assume that bushels per acre. a) Find the 90% confidence interval for the mean yield for this variety of corn. b) Find the 95% confidence interval. c) Find the 99% confidence interval. d) How do the margins of error in (a), (b), and (c) change as the confidence level increases?
a) For a 90% confidence interval: (117.838, 130.056)
b) For a 95% confidence interval: (117.543, 130.352)
c) For a 99% confidence interval: (113.816, 134.078)
d) As the confidence level increases, the margins of error also increase, resulting in wider confidence intervals, indicating greater certainty in the estimation of the true population mean yield.
To find the confidence intervals, we first calculate the sample mean and standard deviation of the yields. Then, we use the t-distribution with degrees of freedom (n-1) to determine the critical values for the given confidence levels. Finally, we use these critical values along with the sample mean and standard deviation to calculate the margins of error and construct the confidence intervals.
a) For a 90% confidence interval:
Sample mean = 123.947
Sample standard deviation = 11.669
Margin of error = t * [tex](s / sqrt(n)) = 1.761 * (11.669 / sqrt(15)) ≈ 6.109[/tex]
90% confidence interval: (123.947 - 6.109, 123.947 + 6.109) ≈ (117.838, 130.056)
b) For a 95% confidence interval:
Margin of error = [tex]2.145 * (11.669 / sqrt(15)) ≈ 7.404[/tex]
95% confidence interval: (117.543, 130.352)
c) For a 99% confidence interval:
Margin of error = [tex]2.947 * (11.669 / sqrt(15)) ≈ 10.131[/tex]
99% confidence interval: (113.816, 134.078)
d) As the confidence level increases, the margin of error also increases because the critical value from the t-distribution becomes larger, resulting in wider confidence intervals. This reflects the increased certainty associated with higher confidence levels.
The margins of error increase as the confidence level increases, indicating wider confidence intervals and greater certainty in the estimation of the true population mean yield.
Jose wants to rewrite 24+9 using the greatest common factor and the distributive property. Which expression should he write?
Answer:
3(8+3)
Step-by-step explanation:
A contractor purchases 7 dozen pairs of padded work gloves for $94.92. He incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct unit price? What is the error?
The correct unit price for the work gloves is $1.13 per pair, and the error in the reported unit price is $12.43 per pair, as the contractor incorrectly reported it as $13.56 per pair.
The question is asking to calculate the correct unit price for the padded work gloves purchased by the contractor and to identify the error in the calculation provided in the expense report.
Firstly, let's determine the total number of pairs of gloves. Since 1 dozen represents 12 items, 7 dozen pairs of gloves will be [tex]7 \times 12 = 84[/tex] pairs of gloves.
Now, to find the correct unit price, we divide the total cost by the total number of pairs:
Unit Price = Total Cost / Total Number of Pairs
Unit Price = $94.92 / 84 pairs
Unit Price = $1.13 per pair
The incorrect unit price was calculated as $13.56 per pair. Therefore, the error in the calculation is:
Error = Incorrect Unit Price - Correct Unit Price
Error = $13.56 - $1.13
Error = $12.43 per pair
The contractor overestimated the unit price by $12.43 per pair.
A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function I(t)=t^2-squrt(t),, and the change in width is given by w(t)=t^2-2t^1/2. Which function gives the change in area of the metal strips?
Answer:
'a(t)=t^4-3t^(5/2)+2t'
When calculating the successive discounts of 15% and 10% on a $100 item, _____. a. take 10% of $85 b. take 10% of $90 c. take 15% of $85 d. take 25% of $100
Answrer
Option (a) is correct .
i.e take 10% of $85
Reason
As given
15% and 10% on a $100 item i.e first applied 15 % discount on $ 100 and than apply 10% discount .
15 % is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Amount becomes when 15 % discount on$100 = 100 - 0.15 × 100
= 100 - 15
= $ 85
Now apply 10 % discount on $ 85.
10 % is written in the decimal form
[tex]= \frac{10}{100}[/tex]
= 0.1
Amount becomes when 15 % discount on$100 = 85- 0.1 × 85
= 85 - 8.5
= $ 76.5
Therefore the option (a) is correct about the successive discounts of 15% and 10% on a $100 item is $76.5 .
please help asap! match equation to the graph
Answer:
B) -7x + 7y= -49
Step-by-step explanation:
Using the general equation for a line
y=mx+b
where m is the slope (positive if the line goes up from left to right and negative is it goes down from left to right)
and b is the point where the line crosses the y-axis
By th graph we can see that the line goes up from left to right, so the slope is positive, and that it crosses the y axis in -7, b= -7 and x is positive.
Solving for y in all the options
A) y = -x
B) y = x - 7
C) y = -x +7
D) y= x+7
the option that describes the line in the graph is B) -7x + 7y= -49 since when clearing for y we get y = x - 7 wich has a positive slope, and has an interception b = -7.
Find the image of z(1,1) after two reflections first across L1 and then across L2
L1: y=2 L2: x-axis
L1: x=3 L2: y=2
Please help asap!!!!!!!!!!18 points
PLEASE MATH HELP WILL GIVE BRAINLIEST!!
The center of a circle is located at (-5, 2), and the radius of the circle is 5 units.
What is the equation of the circle in standard form?
Question 1 options:
(x−5)2 + ( y+2)2 = 10
(x+ 5)2 + (y−2)2 = 25
(x+5)2 + (y−2)2 = 10
(x−5)2 + (y+2)2 = 25
Please help! I'm very confused. 20 points.
An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, where h is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.
Or an angle θ with the point (−20, −21) on its terminating side, what is the value of cosine?
Answer:
The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
Step-by-step explanation:
It is given that an angle θ with the point (−20, −21) on its terminating side.
It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.
According to the Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]hypotenuse^2=(20)^2+(21)^2[/tex]
[tex]hypotenuse^2=400+441[/tex]
[tex]hypotenuse^2=841[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{841}[/tex]
[tex]hypotenuse=29[/tex]
In a right angled triangle,
[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]
[tex]\cos \theta=\frac{20}{29}[/tex]
θ lie in the third quadrant and cosine is negative in third quadrant.
[tex]\cos \theta=-\frac{20}{29}[/tex]
Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
Speed = distance divided by time taken. car 1 travels 10 miles every 5 minutes. car 2 travels 30 miles every 20 minutes. what is the difference of speed between these two cars in mph?
The vertex of this parabola is at (3, -2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expression in the parabola's equation?
Answer:[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]
Step-by-step explanation:
Given
Vertex of Parabola is [tex]\left ( 3,-2\right )[/tex]
and parabola passes through [tex]\left ( 4,3\right )[/tex]
Let us take a parabola of the form
[tex]\left ( y-y_0\right )^2=4a\left ( x-x_0\right )[/tex]
And here [tex]\left ( x_0,y_0\right ) is \left ( 3,-2\right )[/tex]
therefore
[tex]\left ( y+2\right )^2=4a\left ( x-3\right )[/tex]
Now put [tex]\left ( 4,3\right)[/tex] as it lies on parabola
[tex]\left ( 3+2\right )^2=4a\left ( 4-3\right )[/tex]
[tex]a=\frac{25}{4}[/tex]
Thus Equation of parabola is
[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]
If you flip three fair coins, what is the probability that you'll get all three tails?
Let H be the event that head occurs and let T be the event that tail.
Then the complete Sample Space,S for the experiment given in the question is:
S={ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
As we can see the total number of elements in the sample space is 8. Let us represent this by the letter N.
Therefore, N=8
Now, the event of interest to us is TTT and it's occurrence is once. Let represent this by the letter E.
Therefore, E=1
Thus, the probability of the event E occurring is given as:
[tex] P(E)=\frac{E}{N}=\frac{1}{8} [/tex]
[tex] \frac{1}{8} [/tex] is the required answer. This can be represented in percentage too as:
[tex] \frac{1}{8}\times 100=12.5 [/tex]%
Amys class is selling books to raise money for a field trip. If each book sells for $7, how many books will they need to sell to raise $125?
what are the solutions to the equion
plz answer right no it is 14
I️ need to find the answer
How many minutes greater is the software company's median than the bank's median?
Enter your answer in the box.
Answer:
the answer is 10
What is the value of x in the proportion StartFraction 6 x plus 1 over 7 EndFraction equals StartFraction 18 x minus 2 over 14 EndFraction?
A. 0
B. 3
C. two-thirds
D. one-fourteenth
The correct value of x is [tex]\frac{2}{3}[/tex].
To find the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex], follow these steps:
Cross-multiply to eliminate the fractions. Multiply 7 by (18x - 2) and 14 by (6x + 1):
7(18x - 2) = 14(6x + 1)
Expand both sides:
126x - 14 = 84x + 14
Move all terms involving x to one side and constant terms to the other side:
126x - 84x = 14 + 14
Simplify the equation:
42x = 28
Divide both sides by 42 to solve for x:
x = 28 ÷ 42 = [tex]\frac{2}{3}[/tex]
Therefore, the value of x is [tex]\frac{2}{3}[/tex] and the correct answer is option C.
Complete question: What is the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex]?
A. 0
B. 3
C. [tex]\frac{2}{3}[/tex]
D. [tex]\frac{1}{14}[/tex]
I need help to answer this please thank you ?