Answer:
20
Step-by-step explanation:
Let father's age be x
let son's age be y
x + y = 60 - (eq 1)
Six years ago,
(x - 6) = 5(y - 6) -(eq 2)
From (1)
x = 60-y
Therefore, 60-y - 6= 5y - 30
y = 14
in six years, y = 20
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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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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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
Given that yx is a diameter of V, find mZVX if mYVZ=(15r -1)", mWVX =(8x- 2).mUVW =(7x +15).
and mYVU = 3x + 5).
A 32
B 45°
C 70
D. 134
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)
a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Solution :
a). P(X = x)
= [tex]$p(1-p)^x$[/tex] for x = 0, 1, 2, ....
P(x ≤ 3) = 0.837
b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]
= 1.7397
Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]
= 4.7663726
Standard deviation = 2.1832
Therefore, mean + standard deviation
= 1.7397 + 2.1832
= 3.9229
[tex]$P(x > 3.9229) = 0.1626$[/tex]
So the required P = 2 x 0.1626
= 0.325
What are the solutions to this equation?
-7 + (x2 – 19) = 20
-10
5.6
There are no solutions.
10
-5.6
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
Which angle is coterminal to a 185° angle?
Answer:
the answer is -175. I hope that helped
Express the following repeating decimal as a fraction in simplest form.
Answer:
[tex]0.\overline{369} = \frac{41}{111}[/tex]
Step-by-step explanation:
x = 0.369369369...
10x = 3.69369369...
100x = 36.9369369...
1000x = 369.369369...
1000x - x = 369
999x = 369
[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]
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
|-5| >3 true or false plssssss answer it’s important
Answer:
TRUE
Step-by-step explanation:
Those lines around the -5 mean the absolute value of the number, basically the value of the number without any negative signs. SO the absolute value of -5 is just 5.
5 IS GREATER than 3, so this is true
ur welcome :)
Two triangles have the same area. One triangle has a base of 4 cm and a height of 7 cm. If the height of the other triangle is 14 cm, then what is its base length?
3 cm
2 cm
4 cm
5 cm
Answer:
x = 2
Step-by-step explanation:
→ Work out the area of the first triangle
0.5 × 4 × 7 = 14
→ Set up an equation for the second base
0.5 × x × 14 = 14
→ Simplify
7x = 14
→ Divide both sides by 7
x = 2
Answer:
option B = 2cm
Step-by-step explanation:
[tex]Area \ of \ first \ triangle = \frac{1}{2} \times base_1 \times height_1 \ [ \where base_1 = 4\cm \ height_1 \ = 7cm \ ][/tex]
[tex]=\frac{1}{2} \times 4 \times 7 \\\\= 14 \ cm^2[/tex]
Given area of second triangle is same as first.
[tex]Area \ of \ second \ triangle = \frac{1}{2} \times base_2 \times height_2 \ [ \ where \ height _ 2 = 14cm \ ][/tex]
[tex]14 = \frac{1}{2} \times base_2 \times 14\\\\14 = 7 \times base_2\\\\base_2 = 2 \ cm[/tex]
Which of the following best describes the use of the formula S = (n - 2)180°,
where n is the number of sides?
A. It is used to find the number of interior angles in a regular polygon.
B. It is used to find the sum of the interior angles in a regular
polygon.
O c. It is used to find the sum of the exterior angles in a regular
polygon
O D. It is used to find the number of exterior angles in a regular
polygon
SUBMIT
Which is correct?????????????
Answer:
It discusses the role of the God in influencing our decisions
Answer:
I believe it is choice D
Step-by-step explanation:
in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️
The dean of the UTC Engineering School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Engineering School graduates are selected at random, and data on GPA and starting salary ( in $thousands) for each graduate were used to fit the model The dependent variable is____________________________.
Answer:
grade-point average (GPA).
Step-by-step explanation:
The Independent variable may be explained as the variable which is used to manipulate the variable to be predicted. The Independent variable also called the predictor variable takes up several input values in other to observe how the predicted variable changes due to this independent variable. In the scenario described above, the independent variable is the Grade - point average, as it is used to make prediction or manipulate the value of the starting salary earned by a graduate. The starting salary earned is the predicted variable or dependent variable in this scenario.
Use the formula v = IR for current flowing through a resistor, where V is the voltage in volts, I is current in amps, and R is resistance in ohms. Find the current through a resistor with resistance 15 ohms if the voltage across it is 3 volts.
Answer:
0.2 amps
Step-by-step explanation:
Given data
The formula V=IR is the formula for ohms law
Which state that the voltage is directly proportional to the current and the resistance in an electric circuit
Now
R= 15 ohms
V= 3volts
V= IR
3= I*15
I= 3/15
I= 0.2 amps
Hence he current flowing is 0.2 amps
What is the equation of the following line? Be sure to scroll down first to see
(-1/2, 3) (0,0)
A. y = 1/2 X
B. y = -1/2 X
C. y = 3 X
D. y= 2X
E. y= 6
F. y= -6

a p e x :(
Answer: (f)
Step-by-step explanation:
Given
Line that passes through [tex](-\frac{1}{2},3)[/tex] and [tex](0,0)[/tex]
Using two point form, equation of a line is given by
[tex]\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert the values
[tex]\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x[/tex]
Thus, option (f) is correct
Find the inverse of \(\Large h(x) = \frac {3}{2}x + 1 \)
Answer:
[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]
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!
5/8 + 3/4 / -2/3- 5/6.
Answer:
-5/16 or -0.3125
Step-by-step explanation:
Answer:
-11/12
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
Factor each trinomial completely.
A. 2x^2 + 17x + 21
B. 3x^2 - 17x + 10
Answer:
A) (2x+3)(x+7) B) (3x-2)(x-5)
Step-by-step explanation:
A) 2x^2+17x+21=(2x+3)(x+7)
B) 3x^2-17x+10=(3x-2)(x-5)
For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.
Answer:
a) A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
b) attached below ( Matrix dose not exist )
c) attached below ( Matrix does not exist )
Step-by-step explanation:
a) Matrix
A = [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2
From the matrix ; Column 1 and Column 2 Belong to COL(A)
while : (1,1)^T = ( 1,0 )^T + ( 0,1 )^T i.e. (1,1)^T ∈ Row( A )
and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T i.e. (1, 2)^T ∈ Row( A )
Hence ; all requirements are fulfilled in Matrix A
b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
Matrix is Non-existent because condition is not met
attached below
c) Rank | A |
dimension of column space= 4 , dimension of Row space = 3
Given that ; column space ≠ Row space
Hence Matrix does not exist
Verify that a÷(b+c)=(a÷b)+(a ÷c), a=10 , b=5 , 6=2
Answer:
a÷(b+c)≠(a÷b)+(a ÷c)
Step-by-step explanation:
To verify that a÷(b+c)=(a÷b)+(a ÷c)
Using the values ;
a=10 , b=5 , 6=2
plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;
That is, right hand side = left hand side
a÷(b+c) = 10 ÷ (5+ 2)
a÷(b+c) = 10 / 7
Also;
(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7
Given the result, it can be seen that ;
RHS ≠ LHS
10/7 ≠ 7
Find X in the triangle. Round answer to the nearest TENTH of a degree (GIVING BRAINLEST TO BEST ANSWER :D )
Answer:
x = 59,53445508
Tan(x) = 34/20
Step-by-step explanation:
Answer:
30÷20 degree x=n
Step-by-step explanation:
Mark me as brainliest
A box of golf balls contains 10 balls. Each golf ball has a diameter of 3.6 centimeters. What is the total
volume of golf balls in 3 boxes?
about 1465.74 cm
c. about 1221.45 cm
b. about 732.87 cm
d. about 81.43 cm
Answer:
C
Step-by-step explanation:
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
Elysia has 2 apples she gives 1 to her friend so how many does she have?
Answer:
One Apple.
Step-by-step explanation:
This is a basic subtraction and addition problem. She began with one apple and gave one to her friend. How many apples is Elysia holding now? 2-1= 1
One apple.
Elysia will have one apple, as one apple is being subtracted because she gave it to her friend.
What is subtraction?In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.
Given that, Elysia has 2 apples she gives 1 to her friend,
To find the number of apples Elysia left with, we will subtract the number of apples she gave to her friend to the number of apples she had,
Number of apples Elysia left with = 2-1 = 1
Hence, Elysia will have one apple.
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subtract
a2-b2 from a2 +b2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
plus a square and minus a square gets cancel
b^2 + b^2
since they are like terms they can be added
2b^2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
= b^2 + b^2
like terms can be added
+2b^2
prove that 1 + sin a + cos 2A upon 1 + Sin A minus Cos 2A = 2 cot a prudent
Answer:
LHS×0=RHS×0
0=0
hence,proved
Which function is a translation of the parent absolute value function?
f(x) = 2x1
f(x) = |x+6| f(x)=|x| f(x)=-4|x|
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Step-by-step explanation; did it on the website euphoria
The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the transformation of the function be a translation , where
The parent function is f ( x ) = | x |
And , the translated function is f ( x ) = | x + 6 |
So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
And , the function is translated 6 units to the left
Hence , the translated function is f ( x ) = | x + 6 |
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