Answer: 9.7 seconds
Step-by-step explanation:
\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)
HELP QUICK
(question in picture)
Answer:
Step-by-step explanation:
There’s a total of 10+16+20+18 = 64 candies.
There’s 10 red candies.
10 / 64 = 0.15625
Rounded: 0.2
K-7d use k=9 and d=-2
Answer:
-5
Step-by-step explanation:
substitute in the values. 9-7(-2)
-7*-2=14
9-(14)
9-14=
-5
PLEASE HELP ME I REALLY NEED TO GET MY GRADE UP I INCLUDED THE GRAPH WITH THE QUESTION!!!
Graph f(x) = -2/3x -3
Use the line tool and select two points to graph the line.
Answer: To graph the function f(x) = -2/3x -3, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing the given function with the slope-intercept form, we can see that the slope of the function is -2/3 and the y-intercept is -3.
To graph the function, we can start by plotting the y-intercept, which is -3, on the y-axis. Then, we can use the slope to find additional points on the line.
The slope of -2/3 means that for every unit we move to the right along the x-axis, we need to move down by 2/3 units along the y-axis. So, starting from the y-intercept at (-3,0), we can move 3 units to the right along the x-axis and 2 units down along the y-axis to get the point (-0.6,-2). We can repeat this process to get more points on the line, or we can simply draw a straight line through the two points we have found.
Putting it all together, the graph of f(x) = -2/3x -3 looks like:
|
|
|
-2 | ●
|
|
-3 | ●
|______________
-3 -0.6 x
The ● symbols indicate the two points we found, and the line connecting them represents the graph of the function.
Step-by-step explanation:
Using suitable identity, find the value of 87^3+ 13^3/
87^2 −87 ×13 + 13^2
The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.
We will first calculate the numerator:
As (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :
\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))
= 100(\(87^2\) - 87 * 13 + \(13^2\))
Now, calculate the denominator:
\(87^2 - 87 * 13 + 13^2\)
As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):
\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)
\(= 74^2\)
So by solving the equation further:
\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)
As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:
\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)
So, the value of the given expression is 100.
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Factor completely x3 − 2x2 − 8x 16. (x 2)(x2 8) (x − 2)(x2 8) (x 2)(x2 − 8) (x − 2)(x2 − 8).
Answer:
D) (x - 2)(x² - 8)
Step-by-step explanation:
Separate the polynomial into two groups of two terms and factor out the common value from each group. If the values factored out from each group are the same, then you can use the grouping method. The factors will be the outside terms and the common factor.
x³ - 2x² + -8x + 16
= x²(x - 2) + -8(x - 2)
= (x² - 8)(x - 2)
Answer:
D
Step-by-step explanation:
Good luck :D
Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range.
explanation is ideal but not essential :)
Considering the absolute value function, it is found that:
The vertex is at (-3,0).The domain is all real values.The range is [0, ∞).Absolute value functionThe absolute value function of vertex at point (h,k) is defined according to the following rule:
f(x) = |x - h| + k.
In the context of this problem, the function is given as follows:
g(x) = |x + 3|.
Hence the coefficients are:
h = -3, k = 0.
Meaning that the coordinates of the vertex are given by:
(-3,0).
The domain is the input values of the function, and since the absolute value function has no restriction, it is composed by all real values.
The range of the function is the set containing the output values of the function, and since the function has no vertical shift, it is the non-negative numbers.
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You live on a triangular piece of land with a base of 121 yards and a height of 80 yards. The area of your land is
square yards.
fill in the blanks
Answer:
the area of the land is 4,840
Step-by-step explanation:
the equation for finding the area of a triangle is base x hight divided by 2
Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers. How many seats were on each type of flight?
The number of the small seats is 30 while the number of the big seats is 94.
What is the number of seats on each of the flights?We know that from the question, Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers.
Now;
Let the number of small seats be x and the number of large seats be y
It follows that;
3x + 5y = 560 ----- (1)
5x + 2y = 338 ------(2)
If you multiply (1) by 5 and (2) by 3 we have;
15x + 25y = 2800 ------ (3)
15x + 6y = 1014 -----------(4)
19 y = 1786
y = 1786/19
= 94
Substitute y = 94 into (1)
3x + 5(94) = 560
x = 560 - 5(94)/3
x = 30
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According to the general equation for conditional probability, if P(An B) = 4
and P(B) = ?, what is P(ALB)?
O
A.
40
49
B.
24
49
O
16
49
Help please
Answer:
B
Step-by-step explanation:
2(x + 1) = -2
Dont understand how to do this?
Answer:
x = -2
Step-by-step explanation:
2(x + 1) = -2
Divide both sides by 2.
x + 1 = \(\frac{-2}{2}\)
Divide −2 by 2 to get −1.
x + 1 = -1
Subtract 1 from both sides.
x = -1 - 1
Subtract 1 from −1 to get −2.
x = -2
Hope it helps and have a great day! =D
~sunshine~
Answer:
x= -2
Step-by-step explanation:
2 is distributed into the parentheses so 2 times x and 2 times 1 will give you 2x+2=-2
then because you want to have x alone you subtract 2 from each side to keep the equation even and true but putting 2x by itself
2x= -4
then you divide by 2 on both sides
x= -2
Help meh pwease <3 Have a great day y’all!
The first thing you would do is add all the numbers to get the total budget : $1500
Next you would calculate the present to get : 24.2% or just 24% if your rounding
find the
volume or air
4m
by
5m which is only 3m
high
Answer:
volume of cuboid=l×w×h
volume of cuboid=4×5×3=60cm³
a newsletter publisher believes that 71% 71 % of their readers own a rolls royce. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.02 0.02 level of significance, the testing firm fails to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.
The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.
In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.
A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.
The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by \(H_0\):
p = 0.71 (71%) and
the alternate hypothesis is represented by \(H_a\):
p ≠ 0.71 (71%).
Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.
The test statistic for a sample proportion can be calculated by
z = (p - P) / √(P(1 - P) / n)
Where 'p' denotes the sample proportion,
P denotes the population proportion, and
n denotes the sample size.
A two-tailed test is used because the alternate hypothesis is written as \(H_a\):
p ≠ 0.71 (71%).
At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.
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What is the measurement shown on the dial indicator? A. +0.006 B. +0.060 C. +0.005 D. +0.600
A dial indicator is an instrument used to accurately measure small distances. A probe or stylus is applied to the object to be measured and the instrument gives a reading in decimal inches. The correct answer is +0.005.
The measurement shown on the dial indicator is +0.005. The concept of a dial indicator is quite interesting. A dial indicator is an instrument used to accurately measure small distances.
The object is located between the measuring surfaces of the indicator and a probe or stylus is applied to the object to be measured. As the probe moves over the object, the instrument gives a reading in decimal inches.
Therefore, the correct answer to this question is option C: +0.005.
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Sketch the graphs y=1/3x+2
Answer:
mark a dot 2 on the y axis and from there go up one right 3 until you can anymore then go back to the two and go down one left 2
Step-by-step explanation:
(1) If the nullspace of a 4 times 6 matrix A is 3-dimensional, what is the dimension of the column space of A? (2) If the nullspace of an 8 times 5 matrix A is 5-dimensional, what is the dimension of the row space of A?
1. If the nullspace of a 4 times 6 matrix A is 3-dimensional, the dimension of the column space of A is 3.
2. If the nullspace of an 8 times 5 matrix A is 5-dimensional, the dimension of the row space of A is 5.
(1) By the Rank-Nullity Theorem, the dimension of the nullspace and the dimension of the column space add up to the number of columns in the matrix. Therefore, if the nullspace of a 4 x 6 matrix A is 3-dimensional, then the dimension of the column space of A is 6 - 3 = 3.
(2) By the Rank-Nullity Theorem, the dimension of the nullspace and the dimension of the row space add up to the number of columns in the matrix. Therefore, if the nullspace of an 8 x 5 matrix A is 5-dimensional, then the dimension of the row space of A is 5 = 5.
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(a) Omar changed 800 rands into dollars when the rate was $1 = 6.25 rands.
(i)
How many dollars did Omar receive?
Answer:$128
Step-by-step explanation:
If $1=6.25 rands then we must divide 800 by 6.25
a number increased by 13 is at most -15
Answer:
-28 is the number
Step-by-step explanation:
-28 + 13 = -15
Enter the correct number. If it is a fraction, enter it in this form- example: 1/2
The absolute value of the slope of line A is \(|-11| = 11.\) The absolute value of the slope of line B is \(|-5| = 5.\) Since 11 > 5, line A is steeper than line B.
What are signs of slope indicates?The sign of the slope indicates the direction of the line; a positive slope means the line is increasing from left to right, while a negative slope means the line is decreasing from left to right. A slope of zero indicates a horizontal line.
The slope of a line represents its steepness. The absolute value of the slope indicates the degree of steepness, regardless of whether the slope is positive or negative.
The absolute value of the slope of line A is |-11| = 11.
The absolute value of the slope of line B is |-5| = 5.
Therefore, Since 11 > 5, line A is steeper than line B.
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what is the answer to 7(n+4)=21
Answer:
n=-1
Step-by-step explanation:
distribute the 7 to n+4 to get 7n + 28 = 21. subtract 28 from both sides to get 7n = -7. divide both sides by 7 to get n=-1
you could also divide everything by 7 at the beginning to get n+4=3, then subtract 4 from both sides to get n=-1
Hey there!
7(n + 4) = 21
7(n) + 7(4) = 21
7n + 28 = 21
SUBTRACT 28 to BOTH SIDES
7n + 28 - 28 = 21 - 28
CANCEL out: 28 - 28 because it gives you 0
KEEP: 21 - 28 because it helps solve for the n-value
NEW EQUATION: 7n = 21 - 28
SIMPLIFY IT
7n = -7
DIVIDE 7 to BOTH SIDES
7n/7 = -7/7
CANCEL out: 7/7 because that gives you 1
KEEP: -7/7 because it gives you the value of the n-value
NEW EQUATION: n = -7/7
SIMPLIFY IT!
n = -1
Therefore, your answer should be: n = -1
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Using the data below and the SES forecast α=0.3 , what is the error for the 3rd week? Week 1,2,3,4. Time Series Value 22.00 7.00 10.00 13.00
The error for the 3rd week, using SES forecast with α=0.3, is -0.1.
To calculate the error for the 3rd week using SES (Simple Exponential Smoothing) forecast, we first need to calculate the forecasted value for the 3rd week. The forecasted value is calculated using the formula:
\(F_t = α * A_{t-1 }+ (1 - α) * F_{t-1}\)
Where:
\(F_t\) is the forecasted value for week t
\(A_{t-1}\) is the actual value for the previous week (week t-1)
\(F_{t-1}\) is the forecasted value for the previous week (week t-1)
α is the smoothing factor
Given the time series values for weeks 1, 2, 3, and 4 as 22.00, 7.00, 10.00, and 13.00 respectively, and α=0.3, we can calculate the forecasted value for the 3rd week as follows:
F₃ = 0.3 * 7.00 + (1 - 0.3) * 10.00
= 2.1 + 7
= 9.1
The error for the 3rd week is then calculated as the difference between the actual value and the forecasted value:
Error₃ = Actual Value₃ - Forecasted Value₃
= 10.00 - 9.10
= -0.1
Therefore, the error for the 3rd week, using SES forecast with α=0.3, is -0.1.
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whats the slope of (10,8) and (-15, 18)
Answer:
\(m=-\frac{2}{5}\)
Step-by-step explanation:
If f is one-to-one and f(13) = 15, then f-¹(15) = (f(13))-¹ =
If f is one-to-one and f(13) = 15, then f-¹(15) = (f(13))-¹ = 13. Given that f is a one-to-one function and f(13) = 15, we need to find the inverse of f evaluated at 15, denoted as f-¹(15).
Since f is one-to-one, it means that each element of the range has a unique corresponding element in the domain. This property allows us to define the inverse function f-¹(x) as the function that maps each element y in the range of f back to the unique element x in the domain such that f(x) = y.
To find f-¹(15), we first observe that f(13) = 15. Thus, we can write f-¹(15) = (f(13))-¹. Since f is one-to-one, we know that f(13) is unique, and therefore its inverse also must be unique. Hence, we can conclude that f-¹(15) = 13.
In summary, if f is one-to-one and f(13) = 15, then f-¹(15) = (f(13))-¹ = 13.
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Match each expression with an equivalent radical form. One of the radical form
options will not have a match.
3 7/2
7 1/2
3 2/7
7 2/3
1. √7
2. √37
3. √3²
4. 3/72
Answer:
3^(7/2) = 2.; 7^(1/2) = 1,; 3^(2/7) = 3.; 7^(2/3) = 4.
Step-by-step explanation:
To convert the expressions to their radical form, we remember this formula:
\(b^\frac{exponent}{index}=\sqrt[index]{b^e^x^p^o^n^e^n^t}\)
Thus, for 3^(7/2), 7 is the exponent and 2 is the index, which gives us
\(\sqrt[]{3^7}\).
For 7^(1/2), 1 is the exponent and 2 is the index, which gives us
\(\sqrt{7}\).
For 3^(2/7), 2 is the exponent and 7 is the index, which gives us
\(\sqrt[7]{3^2}\).
For 7^(2/3), 2 is the exponent and 3 is the index, which gives us
\(\sqrt[3]{7^2}\)
Write a sine function that has a midline of y = 3, an amplitude of 5 and a period of 7pi/2
A sine function which has a midline of y = 3, an amplitude of 5 and a period of 7pi/2 is f(x) = 5 sin(4/7 x) + 3.
We know that, general form of a sine function is represented as,
f(x) = A sin(ω x) + C
Here, A is the amplitude, ω is the frequency and C is the midline.
It is given in the question that,
Amplitude, A = 5
Midline, C = 3
We have to find the frequency.
For a periodic function, f(x) = f(x + T) where T is the period.
Here, we have, T = 7π/2
We also have,
sin (0) = sin (2π)
So,
sin(0) = sin(ω × 0) = sin(ω (0 + 7π/2)
Now, since sin (0) = sin (2π),
sin(ω (0 + 7π/2) = sin(2π)
7π/2 ω = 2π
ω = 4/7
Hence the sine function is f(x) = 5 sin(4/7 x) + 3
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What is the relationship between the volume of a rectangular prism and the volume of a pyramid with the same height and base?
The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.
How to find the volume of a rectangular prism and pyramid?
The formula for the volume of a rectangular prism is:
Volume = Length * Width * Height
The formula for the volume of a pyramid is:
Volume = (Base Area * Height) / 3
The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.
This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.
Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.
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Which expression is equivalent to the given expression? (+2+6)-(- 2+3) x +9 O A I O B. - } +3 O C. x+3 OD. - *+9
Answer:
The equivalent expression is;
\(\frac{5}{7}x+3\)Explanation:
We want to simplify the expression;
\((\frac{1}{7}x+6)-(-\frac{4}{7}x+3)\)we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.
\(\begin{gathered} \frac{1}{7}x+6-(-\frac{4}{7}x)-(+3) \\ \frac{1}{7}x+6+\frac{4}{7}x-3 \\ \text{collecting the like terms we have;} \\ \frac{1}{7}x+\frac{4}{7}x+6-3 \\ \frac{5}{7}x+3 \end{gathered}\)Therefore, the equivalent expression is;
\(\frac{5}{7}x+3\)What is the cube root of 3 and 512
Answer:
1.4422
Step-by-step explanation:
Depends what they are asking for in some cases they will want you to simplify it to 1.4 or
\(\sqrt[n]{x}\) It might also look like this with a 3 on top and bottom
sry if this is confusing
If you have any questions just ask : )
Please help !!! I neeed this ASAP please
I can do a and b for you but im unsure about c and d. I'm sorry :((
a. x = 2
It is the only point that hits the x axis, thus making it a zero of f(x).
b. substitute 2 for x in the original equation and it should equal 0.
f(x)= x^3 - 2x - 4
f(x)= 2^3 - 2(2) -4
f(x)= 8 - 4 - 4
f(x)= 0
One of the most common types of volcanoes is called a cylinder cone volcano. These types of volcanoes are the smallest type of volcano, ranging between 300 feet and 1200 feet tall, and are in the shape of a cone.
Find the volume of a cinder cone volcano with a height of 350 feet and a diameter of 1100 feet. Use 3.14 for and round your answer to the nearest cubic foot.
The volume of a cinder cone volcano will be 110872040 cubic feet.
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
The volume of the cone (V) = 1/3 πhr²
Given,
Radius of cone (r) = 1100/2 = 550 feet
Height of cone (h) = 350 feet
The volume of a cinder cone volcano = 1/3 πhr²
Substitute the values of h and r,
The volume of a cinder cone volcano = 1/3 × 3.14× (550)² × (350)
The volume of a cinder cone volcano = 110872040 cubic feet.
Thus, the volume of a cinder cone volcano will be 110872040 cubic feet.
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