Answer:
The height of the building is of 48.24 feet.
Step-by-step explanation:
Height after t seconds:
The height after t seconds of the coin is given by:
[tex]S(t) = -16t^2 + 2t + h[/tex]
In which h is the height of the building.
If the coin hit the ground in exactly 1.8 seconds, how high is the building?
This means that when [tex]t = 1.8, S(t) = 0[/tex]. We use this to find h.
[tex]S(t) = -16t^2 + 2t + h[/tex]
[tex]h = 16t^2 - 2t[/tex]
[tex]h = 16(1.8)^2 - 2(1.8)[/tex]
[tex]h = 48.24[/tex]
The height of the building is of 48.24 feet.
look at attachment below
The prices of a term of notebooks are between $2 and $5. If
you plan to spend $10 on notebooks, calculate the least
number of notebooks you can buy in this situation.
notebooks
Answer: Number “2”
Step-by-step explanation: I took the ck-12 Applications with Inequalities
What are the solutions to this equation?
-7 + (x2 – 19) = 20
-10
5.6
There are no solutions.
10
-5.6
For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?
Answer:
m = +/- 12
Step-by-step explanation:
A quadratic function has only one x-intercept when the discriminant is equal to 0. The discriminant is b^2 - 4(a)(c).
When we plug in what we know, we have:
m^2 - 4(18)(2) = 0.
Then using algebraic properties, solve for m.
m^2 - 144 = 0
m^2 = 144
m = +/- 12
When you plug in positive or negative 12, and then factor you will see that it comes out to a difference of squares, proving that there is only one x-intercept.
Answer: C
Step-by-step explanation:
EDGE 2023
If you deposit ₱10,000 into an account that earns 5% annual interest compounded semiannually, how long will it take until there is ₱12,000 in the bank account
Answer:
t = 3.69 ≈ 3. 7 years
Step-by-step explanation:
Given :
P = 10,000
r = 5%= 0.05
A = 12,000
n = 2 ( because it is compounded semi - annually )
[tex]A = P (1 + \frac{r}{n})^{nt}\\[/tex]
[tex]12000 = 10000(1 + \frac{0.05}{2})^{2 t}\\\\1.2 = ( 1 + \frac{0.05}{2})^{2t}\\\\1.2 = (1.025)^{2t}\\\\log \ 1.2 = 2t \ log \ 1.025\\\\2t = \frac{log 1.2 }{log 1.025} \\\\2t = \frac{0.1823}{0.0247}\\\\2t = 7.3805\\\\t = 3.69[/tex]
What is the median of the following set of numbers?
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD.
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD. ????????????????
Median of the given data is 8.5.
What is median?In statistics, the median is the middle value of the given list of data in order. Data or observations can be sorted in ascending or descending order.
Given data,
1 , 5, 12, 1, 121, 1, 121, 13
Arranging in ascending order
1, 1, 1, 5, 12, 13, 121, 121
Number of elements N = 8
When number of elements is odd
Median = (N/2 th term + (N/2)+1 th term)/2
Median = (8/2 th term + (8/2)+1 th term)/2
Median = (4th term + 5th term)/2
Median = (5+12)/2
Median = 17/2
Median = 8.5
Hence, 8.5 is the median of the given data.
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PLEASE HELPPPPP ASAP
A function is shown in the table.
x g(x)
−3 17
−1 −3
0 −4
2 13
Which of the following is a true statement for this function?
The function is increasing from x = −3 to x = −1.
The function is increasing from x = −1 to x = 0.
The function is decreasing from x = 0 to x = 2.
The function is decreasing from x = −3 to x = −1.
Answer:
it's the last one, the function is decreasing from x=-3 to x=-1
Find the value for the side marked below.
Round your answer to the nearest tenth.
13
23°
у
у
[?]
Enter
Answer:
y = 30.96
Step-by-step explanation:
take 23 degree as reference angle
using tan rule
tan 23 = opposite / adjacent
0.42 = 13/y
y = 13/0.42
y = 30.96
Graph the Image of square KLMN after a translation 3 units left .
Answer:
N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)
Step-by-step explanation:
To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.
The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the square be represented as KLMN
Now , the coordinates of the square KLMN is
K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )
Now , let the translated square be represented as K'L'M'N'
When translating the square to three units to the left , the x coordinate of the square gets reduced by 3
So , the new coordinate of the square will be ( x - 3 , y )
Substituting the values in the equation , we get
K' = K ( -5 - 3 , 3 )
L' = L ( 1 - 3 , 3 )
M' = M ( 1 - 3 , 9 )
N' = N ( -5 - 3 , 9 )
So , on simplifying the equation , we get
The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )
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4. Solve the following system of equations for x.
2x + 3y = -14
y = 6x + 22
A. X = -2
B. X = 2
C. X = -4
D. X = 4
We are given the system of equations -:
[tex] \large{ \begin{cases} 2x + 3y = - 14 \\ y = 6x + 22 \end{cases}}[/tex]
Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.
[tex] \large{2x + 3(6x + 22) = - 14}[/tex]
Expand 3 in the expression so we can combine like terms and isolate x-variable.
[tex] \large{2x + 18x + 66 = - 14}[/tex]
Then combine like terms.
[tex] \large{20x + 66 = - 14}[/tex]
Get rid of 66 from the left side by subtracting both sides by itself.
[tex] \large{20x + 66 - 66 = - 14 - 66} \\ \large{20x = - 80}[/tex]
To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.
[tex] \large{ \frac{20x}{20} = \frac{ - 80}{20} }[/tex]
Simplify to the simplest form.
[tex] \large{x = - 4}[/tex]
Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.
Answer
x = -4I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!
Answer:
A. x = -2
C. x = -4
Step-by-step explanation:
y = 6x + 22
2x + 3•(6x+22) = -14
20x = - 80
x = -4
y = 6x+22
y = 6(-4)+22 = -2
Find the following list of data calculate a demean be the maid and see mode or mothers for the following numbers listed in the picture above above
Answer:
Mean = 4.8875
Median = 4.6
Mode = 4.5 and 7.7
Step-by-step explanation:
Mean is the sum of total of data divided by the sample size
Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5
Sum total = 39.1
Sample size = 8
Mean = 39.1/8
Mean = 4.8875
To get the median we need to first rearrange
1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7
Median = 4.5 + 4.7/2
Median = 4.6
Hence the median is 4.6
Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7
A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of n = 120 college students is selected and each student is given all three phones to use for one week. At the end of the week, the students must identify which of the three designs they prefer. The distribution of preference is as follows:
Design 1 Design 2 Design 3
54 38 28
Required:
Do the results indicate any significant preferences among the three designs?
Answer:
There is significant preference among the 3 designs
Step-by-step explanation:
Given :
Design 1 Design 2 Design 3
54 38 28
H0 : no significant preference among the 3 designs
H1 : The preference among the designs are different
To test, we use the Chisquare test for independence ;
χ² = (observed - Expected)² / Expected
The sample size, n = 120
Expected = 120 / number of designs = 120 / 3 = 40
(54-40)^2/ 40 + (38 - 40)² / 40 + (28 - 40)² / 40
= 4.9 + 0.1 + 3.6
= 8.6
The Chisquare critical value at 95% = 5.99
Since ;
|χ² critical| < χ² statistic ; we reject the null and conclude that there is significant preference among the 3 designs
If the diameter of the Ferris wheel is 70 feet across, find the total distance traveled in one revolution.
Answer: Assuming pi is rounded off to 3.14, it is 219.8 feet; if not it is 70π feet
Circumference=one revoloution
Circumference=Diameter times pi
C=Dπ
C=3.14*70
=219.8
219.8 feet
Consider rolling two fair dice and observing the number of spots on the resulting upward face of each one. Letting A be the event that at least one of the dice results in 6 spots on its upward face, and E be the event that exactly one of the dice results in 6 spots on its upward face, give the value of P(E|A). (Note: This value can be easily obtained by looking at p. 2.3 of the class notes and using a reduced sample space. In fact, such an approach makes the solution so trivial, that for this problem, you don’t have to give any justification for your answer.)
Answer:
[tex]P(E|A)= \frac{10}{11}[/tex]
Step-by-step explanation:
Given
Two rolls of die
[tex]E \to[/tex] one of the outcomes is 6
[tex]A \to[/tex] atleast one is 6
Required
P(E|A)
First, list out the outcome of each
[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]
So:
[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]
Where:
[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]n(E\ n\ A) = 10[/tex]
[tex]n(A) = 11[/tex]
So:
[tex]P(E|A)= \frac{10}{11}[/tex]
Listed below are the top 10 salaries (in millions of dollars) of television personalities in a recent year.
38 36 35 27 15 13 12 10 9.6 8.4
Use the sample data to construct a 95% confidence interval for the population mean and correctly interpret your answer.
Answer:
The correct answer is "(11.69, 29.11)".
Step-by-step explanation:
Given:
[tex]38 \ 36\ 35\ 27\ 15\ 13\ 12\ 10\ 9.6\ 8.4[/tex]
[tex]n=10[/tex]
As per the question,
Mean,
[tex]\bar x=20.40[/tex]
Standard deviation,
[tex]s=12.17[/tex]
or,
[tex]df=10-1[/tex]
[tex]=9[/tex]
For 95% confidence interval,
[tex]t^*=2.262[/tex]
hence,
The 95% confidence interval will be:
= [tex]\bar x \pm \ t^*\times \frac{s}{\sqrt{10} }[/tex]
By substituting the values, we get
= [tex]20.40 \pm 2.262\times \frac{12.17}{\sqrt{10} }[/tex]
= [tex](11.69, 29.11)[/tex]
What is the graph of 4x + 2 < 10
It is A (45). Hope this helps!
PLEASE HELP! I'm lost. :(
In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean
µ = 520 and population standard deviation = 115.
What math SAT score is 1.5 standard deviations above the mean? Round answer to a whole number.
Answer:
A math SAT score of 693 is 1.5 standard deviations above the mean
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean µ = 520 and population standard deviation = 115.
This means that [tex]\mu = 520, \sigma = 115[/tex]
What math SAT score is 1.5 standard deviations above the mean?
This is X when [tex]Z = 1.5[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.5 = \frac{X - 520}{115}[/tex]
[tex]X - 520 = 1.5*115[/tex]
[tex]X = 693[/tex]
A math SAT score of 693 is 1.5 standard deviations above the mean
find the 11th term of the series
8,14,20,26.......
Answer:
a11 = 8+(11-1)6
a11 = 8+54
a11=68
hopefully this is correct
Step-by-step explanation:
what is the slope of this graph?? :,)
Answer:
1/2
Step-by-step explanation:
This line is going up towards the right- that makes it positive. It is increasing. So it can't be negative or going "down"
The question wants to see if you know the direction of the line.
2) find an equation of the line theough the given
points. Give the final answer in slope-intercept form.
(2,-2) (-1,4)
Answer:
y = -2x + 2
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (2, -1)
Points on the y-axis (y1, y2) = (-2, 4)
To find the equation of line in slope intercept form;
First of all, we would determine the slope of the line.
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]
[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]
[tex] Slope, m = \frac {6}{-3} [/tex]
Slope, m = -2
Next, we would use the following formula to find the equation of the line;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - (-2) = -2(x - 2)
y + 2 = -2x + 4
y = -2x + 4 - 2
y = -2x + 2 = mx + c
FIND THE ∛ OF 188
(USE √
9514 1404 393
Answer:
∛188 ≈ 5.72865
Step-by-step explanation:
Any scientific or graphing calculator or spreadsheet can tell you the cube root of 188.
∛188 ≈ 5.72865431598...
__
You know that 5³ = 125 and 6³ = 216, so the root will lie between 5 and 6, closer to 6. As a first approximation, you can figure it is about ...
x = ∛188 ≈ 5 + (188-5³)/(6³ -5³) = 5 + 63/89 ≈ 5.71
You can figure this much using a 4-function calculator.
A closer approximation (x') can be had using the iteration formula ...
x' = (2x³ +188)/(3x²)
For x = 5.71, the value of x' is ...
x' ≈ (2×5.71³ +188)/(3×5.71²) ≈ 560.3388/97.8123 ≈ 5.7287
This value is correct when the root is rounded to 4 decimal places. Another execution of the iteration formula using this value will give the root accurate to 9 decimal places.
Find the sine and the cosine of 30^degrees
Answer:
Step-by-step explanation:
sine 30° = opposite / hypotenuse = 4/8 = 1/2
cosine 30° = adjacent / hypotenuse = 4sqrt(3) / 8 = sqrt(3) / 2
Standard form equation
Answer:
5x+4y=24
Step-by-step explanation:
So Ax+By=C is the standard form equation of a line.
y=mx+b (in which m is the slope and b is the y-intercept) is the equation that most people start off with.
Since the line intersects the y-axis at (0,6), the y-intercept is 6.
So, we can substitute 6 with b, which is y=mx+6.
Now, we can find the slope (m) by either inserting a known point (x,y) or using rise/run. Either way, you get the slope as -5/4 because we go five units DOWN and four units RIGHT from (0,6), one known point, to (4,1), another known point.
The y=mx+b equation becomes: y=(-5/4)x+6.
Now, we subtract (-5/4)x on both sides to get (5/4)x+y=6
Multiply 4 on both sides because standard form requires no fractions or decimals.
The final answer is 5x+4y=24.
That's your answer, fully simplified!
Need help ASAP!! Giving brainliest!
A group of people were asked if they had run a red light in the last year. 315 responded "yes", and 190 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
0.624
Step-by-step explanation:
Number who have run a red light = 315
Number who haven't run a red light = 190
From the data :
The total number of people sampled = total possible outcome = (315 + 190) = 505
Selecting a person at random, probability that the selected person has run a red light :
P = required outcome / Total possible outcomes
Required outcome = Number who have run a red light = 315
P(having run a red light) = 315 / 505 = 0.624
How many different license plates are possible if digits and letter can be repeated if the configuration is 3 letters, 2 digits, 2 letters?
Answer:
1,188,137,600 possible combinations
Step-by-step explanation:
The first three and last two digits can be any letter while the middle two digits can be any number.
26*26*26*10*10*26*26=1,188,137,600
7a - 2b = 5a + b
a = 2b
a = 3b
a = a equals StartFraction 3 Over 2 EndFraction b.b
a = a equals StartFraction 2 Over 3 EndFraction b.b
Answer:
iii) a=3b/2
Step-by-step explanation:
7a-2b= 5a+b
7a-5a=2b+b
2a=3b
a=3b/2
I hope this helps!
Tìm căn bậc hai của số phức z=1+i√3
Write z in polar form:
z = 1 + √3 i = 2 exp(i π/3)
Taking the square root gives two possible complex numbers,
√z = √2 exp(i (π/3 + 2kπ)/2)
with k = 0 and k = 1, so that
√z = √2 exp(i π/6) = √(3/2) + √(1/2) i
and
√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i
What should the m<3 be for —- ?
9514 1404 393
Answer:
m∠3 = 63°
Step-by-step explanation:
Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. The obtuse and acute angles are supplementary.
Angle 1 is an obtuse angle; angle 3 is an acute angle.
angle 3 = 180° - angle 1 = 180° -117° = 63°
The measure of angle 3 is 63°.
_____
Additional comment
There are a number of applicable theorems describing the different angle relationships. Taken together, they are summarized by the first statement above. For example, we could declare angles 1 and 4 to be "corresponding" (hence, congruent), and angles 4 and 3 to be a "linear pair", hence supplementary. The net result is that angle 1 is supplementary to angle 3, as we said above.
We could also get there via relations between alternate exterior angles, alternate interior angles, consecutive exterior or interior angles, and other ways. While that terminology is useful to understand in some problems, it is largely irrelevant here.
