We conclude that the parent function f(x) = √x has been shifted 1 unit to the left and 5 units downwards.
How was the parent function transformed?
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive, the translation is upwards.If N is negative, the translation is downwards.For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x) + N
If N is positive, the translation is to the left.If N is negative, the translation is to the right.Here we have f(x) = √x, and g(x) = √(x + 1) - 5
Then:
g(x) = f(x + 1) - 5
From this, we conclude that the parent function f(x) = √x has been shifted 1 unit to the left and 5 units downwards.
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If angle 1 is 70°, what is the measure of angle 3?
7
4
2
.
3
Answer:2
Step-by-step explanation:
PLEASE ANSWER ASAP!!
What is the solution to the system of equations below?
y =2/5x - 3 and x = –10
1. (-10, -7)
2. (-10, -1)
3. (-7, -10)
4. (-1, -10)
What is the rule for a geometric sequence whose first term is 6 and the common ratio is 2?
Answer:
6/2
Step-by-step explanation:
Answer:
An = 6*2^(n-1)
Step-by-step explanation:
Simplify (3-4i) (-6-6i)
Answer: -42+6i
Step-by-step explanation:
1. Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd.
−18−18i+24i−24
2. Collect like terms.
(−18−24)+(−18i+24i)
3. Simplify.
−42+6i
What is the output of the function f(p) = 3p – 2 when the input is 2? A. 0 B. 2 C. 4 D. 6 E. 8
Step-by-step explanation:
Step 1: Find f(2)
[tex]f(p) = 3p - 2[/tex]
[tex]f(2) = 3(2) - 2[/tex]
[tex]f(2) = 6 - 2[/tex]
[tex]f(2) = 4[/tex]
Answer: Option C, 4
Answer:
C. 4
Step-by-step explanation:
f(p) = 3p - 2
Is a function with:
Input: p
Output: 3p - 2
p = 2
f(2) = 3(2) - 2 = 6 - 2 = 4
A Pew Research Center poll asked independent random samples of working women and men how much they value job security. Of the 798 women, 702 said job security was very or extremely important, compared with 802 of the 940 men surveyed. Construct and interpret a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important
Final answer:
To construct a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important, calculate the sample proportions for women and men, calculate the standard error, calculate the margin of error, and calculate the lower and upper bounds of the confidence interval.
Explanation:
To construct a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important, we can use the formula for calculating the confidence interval for a difference in proportions.
Calculate the sample proportions for women and men who consider job security very or extremely important. For women, this would be 702/798 = 0.8797, and for men, this would be 802/940 = 0.8532.Calculate the standard error using the formula: sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)), where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes. In this case, the standard error would be sqrt((0.8797 * (1 - 0.8797) / 798) + (0.8532 * (1 - 0.8532) / 940)).Calculate the margin of error using the formula: z * standard error, where z is the z-score for the desired confidence level. For a 95% confidence level, the z-score is 1.96. In this case, the margin of error would be 1.96 * standard error.Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the difference in sample proportions. In this case, the lower bound would be (0.8797 - 0.8532) - margin of error, and the upper bound would be (0.8797 - 0.8532) + margin of error.The resulting 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important would be interpreted as follows: We are 95% confident that the true difference in proportions lies between the lower and upper bounds calculated above. This means that there is a high likelihood that women place a higher value on job security compared to men, but there is still some uncertainty due to sampling variability.
We are 95% confident that the difference in the proportion of working women and men who consider job security very or extremely important is between -0.0043 and 0.0595. This indicates there is no statistically significant difference between the proportions at the 95% confidence level.
To construct a 95% confidence interval for the difference in the proportion of working women and men who consider job security very or extremely important, we will follow these steps:
1. Determine the sample proportions:
For women:
[tex]\[ \hat{p}_1 = \frac{702}{798} = 0.8797 \][/tex]
For men:
[tex]\[ \hat{p}_2 = \frac{802}{940} = 0.8521 \][/tex]
2. Calculate the difference in sample proportions:
[tex]\[ \hat{p}_1 - \hat{p}_2 = 0.8797 - 0.8521 = 0.0276 \][/tex]
3. Calculate the standard error (SE) for the difference in proportions:
[tex]\[ SE = \sqrt{\frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2}} \][/tex]
Plugging in the values:
[tex]\[ SE = \sqrt{\frac{0.8797 (1 - 0.8797)}{798} + \frac{0.8521 (1 - 0.8521)}{940}} \][/tex]
[tex]\[ SE = \sqrt{\frac{0.1059}{798} + \frac{0.1260}{940}} \][/tex]
[tex]\[ SE = \sqrt{0.0001327 + 0.0001340} \][/tex]
[tex]\[ SE = \sqrt{0.0002667} = 0.0163 \][/tex]
4. Determine the critical value (z*) for a 95% confidence interval:
The critical value for a 95% confidence interval (using a standard normal distribution) is approximately 1.96.
5. Calculate the margin of error (ME):
[tex]\[ ME = z^* \cdot SE = 1.96 \cdot 0.0163 = 0.0319 \][/tex]
6. Construct the confidence interval:
[tex]\[ \text{Lower limit} = (\hat{p}_1 - \hat{p}_2) - ME = 0.0276 - 0.0319 = -0.0043 \][/tex]
[tex]\[ \text{Upper limit} = (\hat{p}_1 - \hat{p}_2) + ME = 0.0276 + 0.0319 = 0.0595 \][/tex]
So, the 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important is:
[tex]\[ -0.0043 \text{ to } 0.0595 \][/tex]
Interpretation:
We are 95% confident that the true difference in the proportion of all working women and men who consider job security very or extremely important is between -0.0043 and 0.0595. This interval includes 0, which suggests that there is no statistically significant difference between the proportions of women and men who value job security at the 95% confidence level.
It wants to know what the area of the trapezoid is. Someone please help.
Answer:
is it 54?
Explanation:
there are about 54 squares which could also be called units
Determine a series of transformations that would map polygon ABCDE onto polygon
A'B'C'D'E'?
1-10-9-8-7 -6 -5 -4 -3 -2 -1,
1
2
3
4
5
6
7
8
9 10 11 12
B'
followed by a
1. T1: Translate ABCDE.
2. R1: Rotate the translated polygon.
3. S1: Scale the rotated polygon.
4. F1: Reflect the scaled polygon if needed.
To determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E', you can break down the process into individual steps. Here, I'll describe each transformation step:
1. Translation:
Translate polygon ABCDE to align its center of mass with the center of mass of polygon A'B'C'D'E'. This ensures that the polygons are roughly in the same position. Let's denote this transformation as "T1."
2. Rotation:
Rotate the translated polygon so that one of its sides aligns with a side of polygon A'B'C'D'E'. You can use the center of mass as the pivot point for rotation. Denote this transformation as "R1."
3. Scaling:
Scale the rotated polygon proportionally to match the size of polygon A'B'C'D'E'. This will make sure that the two polygons have the same size. Denote this transformation as "S1."
4. Reflection:
Reflect the scaled polygon if needed to match the orientation of polygon A'B'C'D'E'. This step may not always be necessary, depending on the orientation of the two polygons. Denote this transformation as "F1" (for reflection).
So, the series of transformations can be written as follows:
1. T1: Translate ABCDE.
2. R1: Rotate the translated polygon.
3. S1: Scale the rotated polygon.
4. F1: Reflect the scaled polygon if needed.
These transformations will map polygon ABCDE onto polygon A'B'C'D'E' while preserving their size and shape.
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Claudia buys 12 postcards, 12 stamps, and 1 pen . The postcards cost twice as much as the stamps. The pen costs $1.50. The total cost is $ 14.10. How much does each postcard cost? Show your work.
Answer:
Each postcard cost $0.7.
Step-by-step explanation:
In this problem we have two variables, the price of the postcard and the price of the stamp, since the price for the pain is known. We also have the total cost of the purchase that is $14.1. So we can create an equation as shown:
12*postcards + 12*stamps + pen = 14.1
This represents the total amount spent by Claudia, but we know that each pen costs $1.5, therefore:
12*postcards + 12*stamps + 1.5 = 14.1
12*postcards + 12*stamps = 14.1 - 1.5
12*postcards + 12*stamps = 12.6
We also know that the postcards cost twice as much as the stamps, so we have:
postcards = 2*stamps
Using this info we can solve for stams as shown below:
12*(2*stamps) + 12*stamps = 12.6
24*stamps + 12*stamps = 12.6
36*stamps = 12.6
stamps = 12.6/36
stamps = 0.35
postcards = 2*stamps = 2*0.35 = 0.7
Each postcard cost $0.7.
Answer:
the cost of a post card is $0.7
Step-by-step explanation:
Given
Number of postcard = 12
Number of stamp = 12
Number of pen = 1
Cost of a pen = $1.5
Required
Cost of each postcard..
Let P represent postcards, S represent stamps,Sp represented Pen.
Since there's a total of 12 postcard and 12 staffs, we have:
12P + 12S + 1.50 = $14.10
From the question, we have that the postcards cost twice as much as the stamps.
So, P = 2S.
Substitute 2S for P
12 * 2S+ 12S + 1.5 = 14.10
24S + 12S + 1.5. = 14.10
36S + 1.5 = 14.10
Collect like terms
36S = 14.10 - 1.5
36S = 12.6
Divide through by 36
S = 0.35
Recall that P = 2S.
So, p = 2 * 0.35
P = 0.7
Hence, the cost of a post card is $0.7
A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars
he checks, 4 have defects. If 10,500 cars will be checked this month, predict the total number of cars that will have
defects.
Answer:
i predict the 150 will have defects
Step-by-step explanation:
you do 280 divided by 4 which gives you 70
then 10,500 divided by 70 which gives you
There is a probability that 150 total autos will have defects if 10,500 vehicles are inspected this month.
What is Possibility?A chance that something might exist, happen, or be true: the state or fact of being possible.
Given, A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars he checks, 4 have defects.
Out of 280 cars defected = 4
out of 10500 cars defected = (4* 10500) / 280
out of 10500 cars defected = 150
therefore, If 10,500 cars will be checked this month there is a possibility of getting a total number of cars that will have defects of 150.
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Question 3:
Point Q is
units from Point R.
Point R is
units from Point T.
Point T is
units from Point S.
Question 4:
What is the area of polygon QRSU?
square units.
Answer:
Point Q is 6 units from Point R.
Point R is 7 units from Point T.
Point T is 3 units from Point S.
The area of polygon QRSU is 42 square units.
Please mark my answer brainliest so I can move up to the next rank.
Step-by-step explanation:
Find the area of the figure.
What is the inverse function of dx) = 2x - 4?
Answer:
y = x/2 + 2
Step-by-step explanation:
y = 2x - 4
swap y and x
x = 2y - 4
x + 4 = 2y
x/2 + 2 = y
Answer:
d(x) = 1/2x + 2 or d(x) = (x + 4)/2
Step-by-step explanation:
y = 2x - 4
y + 4 = 2x
(y + 4)/2 = x
y = (x + 4)/2 or y = 1/2x + 2
(5a2 + 4ab – 3b2) – (–5ab + 4b2 + 3a2) = a2 + ab + ( b2)
Answer:
2a^2+ 9ab+ (-7b^2)
Step by Step Explanation
Hope this helps!! Have a great day!! : )
The simplified expression of [tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2)[/tex] is [tex]2a^2+ 9ab - 7b^2[/tex].
The expression is given as:
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2)[/tex]
Remove brackets
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2) = 5a^2 + 4ab - 3b^2 +5ab - 4b^2 - 3a^2[/tex]
Collect like terms
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2) = 5a^2 - 3a^2+ 4ab +5ab - 3b^2 - 4b^2[/tex]
Evaluate like terms
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2) = 2a^2+ 9ab - 7b^2[/tex]
The equation cannot be further simplified.
Hence, the simplified expression is [tex]2a^2+ 9ab - 7b^2[/tex]
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26 Can anyone help!!!
Ok, first let's find how much a nickle is worth, a nickle is worth $0.05.
0.05 x 27 = $1.35
0.05 x 32 = $1.60
0.05 x 39 = $1.95
0.05 x 47 ≠ $2.45 (It's equal to $2.35)
I hope this helps!
It is okay to download information without asking a lab instructor as long as it is for your online class.
Please select the best answer from the choices provided
OT
OF
Answer:
false
Step-by-step explanation:
on eng 2020
The correct option is " Option 2" i.e., False.
It is given that somebody is trying to download an information without asking a lab instructor.
We have to tell that whether it is a right thing or not ?
What do you mean by moral values ?
Moral values are defined as the guidelines that assist a person in deciding between right and wrong.
It is not a right thing to use any private thing without the permission of the owner.
Hence it is also not okay to download information without asking a lab instructor even if you are using it for your online classes.
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Angle 3 and Angle 6 are examples of which type of angle pair?
Answer:
They look like they are 90° angles
Step-by-step explanation:
(What are the options?)
Hermina cut a 10" by 20" piece of cardboard down the diagonal. What is the length c of the cut, in inches?
The length of the diagonal of the rectangular cardboard Hermina cut
is 10√5''.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, Hermina cut a 10" by 20" piece of cardboard down the diagonal.
So, The diagonal can be thought of as the hypotenuse of a right-angle triangle with a base 20'' and a height of 10''.
Therefore,
Hypotenuse² = Base² + Height².
Hypotenuse² = 20² + 10².
Hypotenuse² = 400 + 100.
Hypotenuse² = 500.
Hypotenuse = √(500).
Hypotenuse = 10√5''.
So, The length of the diagonal is 10√5''.
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The length of the cut (c) is 5 times the square root of 20 inches, which is approximately 22.36 inches when rounded to two decimal places.
When Hermina cuts a 10" by 20" piece of cardboard down the diagonal, she essentially creates two right triangles. The diagonal of a rectangle splits it into two congruent right triangles. This diagonal acts as the hypotenuse of each right triangle.
In a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse (c) if we know the lengths of the other two sides (a and b).
The Pythagorean theorem states: c^2 = a^2 + b^2, where c is the length of the hypotenuse.
In this case, one side (a) is 10 inches long, and the other side (b) is 20 inches long. Plugging these values into the formula:
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
Now, to find c, we take the square root of both sides to isolate c:
c = √500
To simplify the square root:
c = √(25 * 20)
c = 5√20
In summary, Hermina's diagonal cut creates two right triangles, and the length of the cut (c) can be found using the Pythagorean theorem. The calculated length is approximately 22.36 inches.
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A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the
reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the
positive y axis and its vertex at the origin.
Answer:
y = [tex]\frac{x^2}{20}[/tex]
The focus of the solar oven's reflector is (0,a)
Step-by-step explanation:
The missing figure( i.e diagram) from the question is attached below:
Now ; given that :
The focus of the sun's rays is at a point L = 5 inches away from the vertex of the reflector. Also the distance of the parabolic curve be a= L = 5
So the equation for a cross section of the oven's reflector with its focus on the
positive y axis and its vertex at the origin is expressed as:
x² = 4 L y
x² = 4 (5) y
x² = 20 y
y = [tex]\frac{x^2}{20}[/tex]
The focus of the solar oven's reflector is (0,a)
There are 72 boys and 90 girls on the math team,
For the next math competition, Mr. Johnson would like to arrange all of the students who
rows with only girls or only boys in each row.
What is the greatest number of students that can be in each row
Answer:
The students can be arranged in rows of 18 that is 4 rows of boys and 5 rows of girls
Step-by-step explanation:
Helena borrowed $189 from her parents to
buy an electric bass. She paid back $56
last week and $64 this week. How much
does Helena still owe her parents?
A $133
C $69
B $120
D $29
What is the answer or this Equation. ‑1/2+(3/4•4/9) =
Answer:
4/25 would be the answer as;
-1/2 + 1/3 = -0.16666666666
Step-by-step explanation:
‑1/2+(3/4•4/9) =
-1/2 + (1/3) = -4/25
-0.16
However true answer is 16666666666/100000000000. = 0.1666666666
The rule is when fractions reoccur, we show closest and -4/25 is closer than -1/6
What is the difference between the absolute value of –8 and the absolute value of 6? 2 8 14 16
Answer:
the answer should be 2
Step-by-step explanation:
the absolute value of something cannot be negative, the eight automatically becomes +8 and the difference between 8 and 6 is 2 (8-6=2)
A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 489.84 yd. What is the surface area of the sphere? Use 3.14 for pi.
BRAINLIEST FOR FIRST CORRECT ANSWER!
NEED HELP ASAP!!!!
Answer:
The surface area of the sphere is about [tex]97,264.64 yd^{2}[/tex]
Step-by-step explanation:
Answer:
76,415.04
Step-by-step explanation:
A car travels 25 ⅕ miles in ⅔ of an hour. What is the average speed, in miles per hour?
Answer:
37 4/5 miles per hour
Step-by-step explanation:
Take the miles and divide by the time
25 1/5 ÷ 2/3
Change the mixed number to an improper fraction
(5*25 +1)/5 ÷ 2/3
126/5 ÷ 2/3
Copy dot flip
126/5 *3/2
378/10
Changing to mixed number
10 goes into 378 37 times with 8 left over
37 8/10 which simplifies to 37 4/5
37 4/5 miles per hour
Use the graph to estimate the solution of the system.
X+2y=5, -x+3y=6
Which integers is the x-value between? What is the x-value to the nearest tenth?
Which integers is the y-value between?
What is the y-value to the nearest tenth?
Answer:.
Step-by-step explanation: Answer:
1. 0 and 1
2. about 0.6
3. 2 and 3
4. about 2.2
For the graph the solution of the system, X+2y=5, -x+3y=6
1. The integer values of x in between -6 and 5 are (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4)
2. The x-value to the nearest tenth is 1
3. The integer values of y in between 0 and 3 are (1, 2)
4. The y-value to the nearest tenth is 2
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given that,
system of lines , X+2y=5, -x+3y=6
by plotting graph of it,
we get following conclusions,
Point of intersection is (0.6, 2.2)
1. both the lines are intersecting x axis at (-6, 0) & (5, 0)
So, integers will be (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4)
2. The coordinate of x is, 0.6
The x-value to the nearest tenth is 1
3. both the lines are intersecting y axis at (0, 2) & (0, 2.5)
So, integers will be ( 0, 1, 2)
4. The coordinate of y is, 2.2
The y-value to the nearest tenth is 2
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Please help me out with this math question... if two people answer, I will brainlist. 5 stars and thanks for every answer and comment. I would really appreciate an answer. :-)
Answer:
20 (Assuming even distribution of letters)
Step-by-step explanation:
There are 26 letters in the alphabet.
Vowels consist of 5 of these letters.
The percentage of total letters that are vowels is:
[tex]\frac{5}{26} *100= 19.231[/tex] (3dp)
As we have total 105 letters, and we know the percentage of vowels to letters - we can work out how many of these letters we expect to be vowels by finding a percentage of the total number.
19% of 105 is:
[tex]105*0.19=19.95[/tex]
Which is approximately equal to 20
If you charge $2,000 on a credit card today, how much will the
balance be in seven years (assuming no additional fees) if the
credit card has 14.99% APR that is compounded monthly?
A = P(1 + )
Answer:
$5,674.30
Step-by-step explanation:
Use the Compound Amount formula:
A = P(1 + r/n)^(n*t), where r = APR as a decimal fraction = 0.1499
and n = 12 (compounded monthly).
Then A = $2,000(1 + 0.1499/12) )^(7*12)
= $2,000(1 + 0.0125)^84
= $2,000(1.0125)^84 = $2,000(2.837) = $5,674.30
what ordered pair represents the y-intercept of the graph of the equation y=-4x-7
Answer:
(0,-7)
Step-by-step explanation:
y-intercepts are when x=0
Sara spent $5 from her savings
to buy a book. Then she spent
half of her remaining savings
when she paid $9 for a shirt.
How much money did Sarah have
in savings before she bought
the book and the shirt?
Answer:
sorry for this just wait im about to slove it
Step-by-step explanation:
found it.it was 23
Answer: 23$
Step-by-step explanation:
If half of Sara's remaining savings was 9$, her remaining savings after buying the book would be 18$. 18$+5$=23$. Good luck and have a nice day!