The number of different sodas that can be made is given by "n!" or factorial form.
If the soda tastes different depending on the order in which the flavors are chosen, we can calculate the number of different sodas that can be made without repetition using the concept of permutations.
Let's assume we have "n" different flavors of soda available. To calculate the number of different sodas we can make, we need to find the number of permutations of "n" flavors taken "r" at a time, where "r" is the number of flavors we want to choose for each soda.
The formula to calculate permutations is given by:
P(n, r) = n! / (n - r)!
Here, "n!" represents the factorial of "n," which is the product of all positive integers less than or equal to "n."
In this case, if repetition is not allowed, each soda can have only one flavor. Therefore, we have "r = 1" for each soda.
Applying the formula, we have:
P(n, 1) = n! / (n - 1)!
= n! / (n - 1)
= n
Hence, the number of different sodas that can be made without repetition is "n."
Therefore, the number of different sodas that can be made is given by "n!" or factorial form.
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coordinate plane with segment AB located at A 0 comma 2 and B 2 comma 3 segment AB is dilated from the origin to create segment A prime B prime at A′ (0, 8) and B′ (8, 12). What scale factor was segment AB dilated by? one half 2 3 4
The required scale factor for the dilation of segment AB to create segment A'B' is 2.
If the length of the original segment AB is 5 units and the length of the dilated segment A'B' is 10 units, the scale factor can be calculated as follows:
Scale factor = Length of A'B' / Length of AB
Scale factor = 10 / 5
Scale factor = 2
Therefore, the correct scale factor for the dilation of segment AB to create segment A'B' is 2.
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Sheila was setting up a room with tables for an event. The room had
12 plastic tables and 3 composite tables. Each table can seat 8
people.
What is the probability that the first person to enter the room will be
randomly seated at a plastic table?
The probability that the first person will be seated at a plastic table is 0.8
The probability that the first person will be seated at a plastic table?From the question, we have the following parameters that can be used in our computation:
Plastic tables = 12
Composite tables = 3
Using the above as a guide, we have the following:
Total tables = 12 + 3
Evaluate the sum
Total tables = 15
So, we have the probability to be
P = Plastic tables/Total tables
Substitute the known values in the above equation, so, we have the following representation
P = 12/15
Evaluate
P = 0.8
Hence, the probability that the first person will be seated at a plastic table is 0.8
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When we write four thousand two hundred that is what form?
The equivalent value of the expression is A = four thousand two hundred and A = 4,200
Given data ,
Let the expression be represented as A
Now , the value of A is
A = four thousand two hundred
On simplifying the equation , we get
A = 4,200
And , when we write "four thousand two hundred," it is written in word form
Hence , the equation is A = 4,200
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I need help with number three.
Answer:
1761 ft²
Step-by-step explanation:
The shape of the attic is a triangular prism.
It has 5 faces: The bases are 2 faces that are congruent triangles. The other 3 faces are rectangles, 2 of which are congruent.
surface area = area of the bases + area of 3 rectangles
surface area = 2 × area of triangle + 2 × area of rectangle + area of other rectangle
surface area = 2 × (1/2)bh + 2 × length × width + LENGTH × WIDTH
surface area = 2 × (1/2)(15 ft)(15 ft) + 2(15 ft)(30 ft) + (21.2 ft)(30 ft)
surface area = 225 ft² + 900 ft² + 636 ft²
surface area = 1761 ft²
The principal would like to assemble a committee of 7 students from the 15-member student council. How many different committees can be chosen?
Answer:
6,435
Step-by-step explanation:
The number of different committees that can be chosen can be calculated using the combination formula, also known as "n choose k," which calculates the number of ways to choose k items from a set of n items without regard to the order.
In this case, the principal wants to assemble a committee of 7 students from a student council of 15 members. Therefore, the number of different committees that can be chosen is given by the formula:
C(15, 7) = 15! / (7! * (15-7)!)
Calculating this expression gives:
C(15, 7) = 15! / (7! * 8!)
Simplifying further:
C(15, 7) = (15 * 14 * 13 * 12 * 11 * 10 * 9) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
C(15, 7) = 6435
Therefore, there are 6,435 different committees that can be chosen from the 15-member student council.
Find the measures of the acute angles.
29.67°
37°
168°
12°
The triangle below is isosceles. Find the length of side x to the nearest tenth.
The length of side x to the nearest tenth is equal to 2.4 units.
What is an isosceles triangle?In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.
This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.
Therefore, we would apply Pythagorean theorem in order to find the length of side x as follows;
x² + x² = (√11)²
2x² = 11
x² = 11/2
x² = 5.5
x = 2.4 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which number is equivalent to 7/11
?
The equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55
There are infinitely many numbers equivalent to 7/11
since 7/11 is a fraction that can be simplified in different ways.
We can multiply the numerator and denominator with the same number to get the equivalent fractions
7/11×2/2 = 14/22
7/11×3/3= 21/33
7/11×4/4 =28/44
7/11×5/5 =35/55
Hence, the equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55
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Gillians net worth is 90,500 based on the information in the table what is the amount of money gillans owens student loans
The amount of money Gillians owes for student loans is $12,250
How to determine this
When Gillians net worth = $90,500
House(Current value) = $87,900
Checking account = $950
Credit- card = -$2,650
Automobile(current value) = $10,300
Student loans = ?
Investment = $5,000
Personal loans = 1,200
Savings account = $2,450
To calculate the money Gillians Owen owes student loans
Let x represent the student loans
$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450
$90,500 = $102,750 + x
Collect like terms
x = $90,500 - $102,750
x = 12,250
Therefore, the money Gillians owes student loans is $12,250
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PLEASE HELP MEEE RIGHT NOWWWW
Tell whether volume applies to the situation ( please tell a , b , c , d , and e)
A. Wrapping paper used to wrap a gift
B. Milk poured into a glass
C. Air needed to blow up a ball
D. Fabric for making a quilt
E. How much will fit in a suitcase
Last one
Describe another situation in which volume would apply.
THANKS
WILL GIVE BRAINLIEST PLEASE HELP
Find the variance and standard deviation of each of the following scores.
x
1-3
4-6
7-9
10-12
13-15
16-18
19-21
f
1
9
25
35
17
10
3
The variance and standard deviation of the frequency distribution data are;
The variance, s² = 14
The standard deviation, s ≈ 3.742
What is a frequency distribution?A frequency distribution displays the number of data within a specified interval.
The steps to find the variance and the standard deviation of the grouped data are as follows;
The midpoints of the class intervals are found as follows;
Class interval [tex]{}[/tex] Midpoint
1 - 3 [tex]{}[/tex] 2
4 - 6 [tex]{}[/tex] 5
7 - 9 [tex]{}[/tex] 8
10 - 12 11
13 - 15 [tex]{}[/tex] 14
19 - 21 [tex]{}[/tex] 20
The mean is then found as follows;
(2×1 + 5×9 + 8×25 + 11×35 + 14×17 + 17×10 + 20×3)/(1+9+25+35+17+10+3)
The variance can then be found as follows;
s² = (2-11)²×1 + (5-11)²×9 + (8-11)²×25 + (11-11)²×35 + (14-11)²×17 + (17-11)²×10 + (20-11)²×3)/(1+9+25+35+17+10+3 - 1) = 14The standard deviation is therefore; s = √(14) ≈ 3.742Learn more on the standard deviation of a dataset here: https://brainly.com/question/11340286
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Consider the equation -3 x e^5w = -88
Solve the equation for (W) Express the solution as a logarithm in base-e.
___
Approximate the value of (W). Round your answer to the nearest thousandth.
___
The solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.
Exponential functions are always increasing or decreasing, depending on the sign of the base "a".
The graph of an exponential function has a characteristic shape that depends on the base "a". When "a" is greater than 1, the graph is an increasing curve that becomes steeper as x increases; when "a" is between 0 and 1, the graph is a decreasing curve that approaches the x-axis as x increases.
Starting with the equation:
[tex]-3xe^{(5w)} = -88[/tex]
We can first isolate the exponential term by dividing both sides by -3x:
[tex]e^{(5w)} = \dfrac{88 }{ (3x)}[/tex]
Then, taking the natural logarithm of both sides, we get:
[tex]5w = ln(\dfrac{88} { 3x})[/tex]
Finally, dividing both sides by 5, we obtain the solution for w:
[tex]w = (\dfrac{1}{5}) ln(\dfrac{88} { 3x})[/tex]
Therefore, the solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.
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Dakota measured a neighborhood park and made a scale drawing. The scale of the drawing was 1 inch : 5 yards. A soccer field in the park is 12 inches wide in the drawing. How wide is the actual field?
The actual width of the soccer field is 60 yards.
Given, the scale of the drawing is 1 inch : 5 yards.
The width of the soccer field in the drawing is 12 inches.
So, the actual width of the soccer field can be found by multiplying the width in the drawing by the scale factor:
Actual width = Width in drawing x Scale factor
The scale factor is 5 yards per inch, so we can write:
Actual width = 12 inches x 5 yards per inch
Actual width = 60 yards
Therefore, the actual width of the soccer field is 60 yards.
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4) Students in Ms. Udon
science class planted 13
conifers in different places
around the school yard. They
measured the heights (in inches)
of the conifers one month after
planting them. How many
conifers are greater than 6 1/4
inches tall but less than 8 1/2
inches tall?
Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.
This shows, with dots, the number of times that each of the measures appears in a data set.
For finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4
= 6.25 inches.
The tallest conifer measures 9.5 inches.
The difference is:
9.5 - 6.25 = 3.25 inches.
Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.
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Write two numbers that multiply to the value on top and add to the value on bottom. 24 + - 25
The two numbers that multiply to the number 24 and add up to the number -25 as required to be determined are; -24 and -1.
What are the two numbers as described?It follows from the task content that the two numbers which multiply to give 24 and add up to give -25 are to be determined.
By observation, the two numbers in discuss are; -24 and -1. This follows from the fact that: -24 × -1 = 24 and also, -24 + -1 = -25.
Consequently the two numbers as required to be determined are; -24 and -1.
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Suppose that the common shares of Oceanic Luxury Vessels , Inc. , is trading for $ 38 a share and that 5 million shares are outstanding . The company also has 75,000 bonds outstanding , which are selling at 102 percent of par . If Oceanic Luxury Vessels , Inc. , was considering an active change to its capital structure so that the firm would have a D/E ratio of 1.6 , which type of security ( stocks or bonds ) would it need to sell to accomplish this , and how much would it have to sell ? A. Debt ; $ 349.9 million B. Stock : $ 445.2 million C. Debt ; $ 248.5 million D. Stock ; $ 289.4 million
Answer:
To have a D/E ratio of 1.6, Oceanic Luxury Vessels, Inc. would need to sell debt securities.
First, we need to calculate the market value of the company's equity.
Market value of equity = Number of shares outstanding × Market price per share
Market value of equity = 5,000,000 × $38
Market value of equity = $190,000,000
Next, we can calculate the current debt-to-equity (D/E) ratio of the company:
Current D/E ratio = Total debt / Total equity
Total debt = Number of bonds outstanding × Bond price per bond × Par value
Total debt = 75,000 × 1.02 × $1,000
Total debt = $76,500,000
Current D/E ratio = $76,500,000 / $190,000,000
Current D/E ratio = 0.403
To achieve a D/E ratio of 1.6, the company would need to increase its total debt by a factor of 1.6/0.403 = 3.97.
New total debt = 3.97 × $76,500,000
New total debt = $304,305,000
To calculate the amount of debt securities the company would need to sell, we can subtract the current total debt from the new total debt:
Amount of debt to be sold = $304,305,000 - $76,500,000
Amount of debt to be sold = $227,805,000
Therefore, the company would need to sell debt securities worth $227.8 million to achieve a D/E ratio of 1.6.
The correct answer is C. Debt; $248.5 million.
Sean says the value of a to the -3rd power is always less than 1 if a is positive.
Christine says the value of a to the -3rd power is always less than 1 when a is negative
Which one is correct, and for the one that is incorrect enter the number that proves in to be incorrect (if none say none).
Sean's statement is correct. Christine's statement is incorrect when a is negative.
The value of a to the -3rd power is always less than 1 if a is positive.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.
The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.
Therefore, Christine's statement is incorrect when a is negative.
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19
A
Straight line A passes through the points (-1, 2) and (1,6)
Straight line B has equation y-x
Work out the coordinates of the point where line A crosses line B
You may use the grid to help you.
40
10
+
7
-2
14
T
6
5-
4-
3
2
O
-1-
-2-
-3
-5-
-6-
Answer (
2
3
5
6
[4 marks]
What is the range of the set of coordinates shown below?
(-10, 2), (-5, 3), (-7,4), (0, 0), (-10, 3), (3, 8)
Answer:
{0,2,3,4,8}
Step-by-step explanation:
$11,335
is invested, part at 9%
and the rest at 6%
. If the interest earned from the amount invested at 9%
exceeds the interest earned from the amount invested at 6%
by $865.35
, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:
9% : $10,3036% : $1032Step-by-step explanation:
You want the amounts invested at 9% and 6% if they total $11,335 and the interest from the 9% investment exceeds the interest from the 6% investment by $865.35.
SetupIf we let x represent the amount invested at 9%, the amount invested at 6% is (11335-x). The relation between the values of interest earned is ...
(x)·9% -(11335-x)·6% = 865.35
Solution0.15x -680.10 = 865.35 . . . . . simplify
0.15x = 1545.45 . . . . . . . . add 680.10
x = 10303 . . . . . . . . . . . divide by 0.15
11335 -x = 1032
$10,303 was invested at 9%; $1,032 at 6%.
__
Additional comment
It is convenient to use a single variable, and to let it represent the amount invested at the higher rate. If you use a system of 2 equations, you can effectively do this by substituting for the variable representing the amount invested at the lower rate. Using this approach keeps all of the numbers positive, tending to reduce errors.
Answer:
Amount invested at 9% = $6832.15; Amount invested at 6% = $4502.85
Step-by-step explanation:
We'll need a system of equations to find the amounts invested at both 9% and 6% and we'll need to convert the percentages to decimals (i.e., 0.09 and 0.06):
Let x represent interest earned from the 9% investmentLet y represent interest earned from the 6% investmentLet 0.09x represent the amount invested at 9%Let 0.06y represent the amount invested at 6%First equation in system:
We know that the interest earned from the 9% investment is $865.35 greater than the interest earned from the 6% investment.
Thus, one equation we can use is x = y + 865.35
Second equation in system:
We also know that the amount invested at 9% plus the amount invested at 6% equals $11335.00
Thus, our second equation is 0.09x + 0.06y = 11335
Step 1: We can use substitution to solve. We must plug in x from the first equation for x in the second equation to solve for y:
0.09(y + 865.35) + 0.06y = 11335
0.09y + 77.8815 + 0.06y = 11335
0.15y + 77.88 = 11335
0.15y = 11257.12
y = 75047.46667
y = 75047.47
Step 2: Now we can plug in 75047.47 for y into any of the two equations in our system to solve for y. Because the first equation is simpler, let's use this one:
x = 75047.47 + 865.35
x = 75912.82
Step 3: We can now find the amount invested by multiplying x by 0.09 and y by 0.06:
0.09x = 0.09(75912.82) = 6832.1538 = $6832.15
0.06y = 0.06(75047.47) = 4502.8482 = $4502.85
Optional Step 4: We can check that our numbers are correct by substituting 75912.82 for x and 75047.47 for y in the two equations in our system:
Checking solutions for first equation:
75912.82 = 75047.47 + 865.35
75912.82 = 75912.82
Checking solutions for second equation:
0.09(75912.82) + 0.06(75047.47) = 11335
6832.1538 + 4502.8482 = 11335
6832.15 + 4502.85 = 11335
11335 = 11335
William throws a football in the air from a height of 4 feet with an initial upward velocity of 96 feet per second.
Write a rule in the form of h=at^2+bt+c that models the height h of the football after t seconds.
Answer:
Step-by-step explanation:
its 123 jd
THE ONE-EYED JACK MINE INVESTIGATION
The abandoned One-Eyed Jack Mine is about 31 miles off the main road adjacent to the Salmon River Wilderness area. There is only a rutted dirt track left where the access road used to run. It is so steep that when we hiked up it we had to pause every fifty feet or so to catch our breath. It seemed impossible but 3- 5 miles further we found remnants of the old wagons, the mineshaft, and the mill. The gold ore found in this mine was embedded in quartz and prospectors used the mill to grind up the quartz and rinse it with acid in huge shallow vats that were agitated so that the gold would sink to the bottom and the quartz could be washed away.
One arrangement of equipment we noticed included a circular vat about 18 feet in diameter which must have been connected by a huge belt to a smaller circular drive wheel 10 feet in diameter. The distance between the wheel and the vat was 8 feet. The equipment had been partially pre-fabricated then carried up the hill piece by piece to be re-assembled on the spot. Just the belt to connect the vat to the drive wheel would have been a major burden. We wondered how many times they had to carry new ones up to replace it. Calculate the length of belt needed to go around the drive wheel and the vat.
Answer:
The length of the belt needed to go around the drive wheel and the vat is approximately 79.6 feet. This is calculated by using the circumference formula C = 2πr where r is the radius of the wheel (5 feet) and the radius of the vat (9 feet). The total circumference is then 2 x 3.14 x (5 + 9) = 79.6 feet.
Answer:
79.6 feet.
Step-by-step exp
2 x 3.14 x (5 + 9) = 79.6 feet.
What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The end behavior of a polynomial with positive leading coefficient is either "up-up" or "down-down" depending on the degree of the polynomial the end behavior of a polynomial with negative leading coefficient is either "up-down" or "down-up" depending on the degree of the polynomial.
Actually, the end behavior of a polynomial refers to the behavior of the function as the input variable (usually x) approaches positive or negative infinity.
The end behavior of a polynomial is determined by the degree and leading coefficient of the polynomial.
If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
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Write the number 6,600,000 in scientific notation.
Answer:
6.6 x 10^6
Step-by-step explanation:
A cylinder has the height of 12 inches and radius of 7 inches what is the volume
Answer:
588π
Step-by-step explanation:
Volume of cylinder = π r ² h
= π (7)² (12)
= 588π
8) John wishes to make a line
plot of the heights in inches for a soccer team. The heights are
listed below. How many dots
would be above the greatest
height recorded?
Answer options
1
2
3
4
There are three dots in the greatest height recorded.
We have,
From the table,
We see that,
The greatest height is 75 inches.
The lowest height is 62 inches.
Now,
If we make a line plot with dots above the height as:
* *
* * * * *
* * * * *
62 66 68 72 75
Thus,
There are three dots in the greatest height recorded.
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The ratio 5x +2 : y - 2 is equal to 6:5. Express y in terms of x .
Answer:
y = [tex]\frac{25x+22}{6}[/tex]
Step-by-step explanation:
express the ratios in fractional form
[tex]\frac{5x+2}{y-2}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides
6y - 12 = 25x + 10 ( add 12 to both sides )
6y = 25x + 22 ( divide both sides by 6 )
y = [tex]\frac{25x+22}{6}[/tex]
Carl has a ribbon that is 4/5 of a meter long. He wraps 2/5 of a meter of a meter of the ribbon around a package. He uses another 1/4 of a meter of the ribbon to tie a bow on a gift box. What is the length of the ribbon carl has left
A. 13/20 of a meter
B. 2/5 of a meter
C. 3/20 of a meter
D. 4/5 of a meter
Answer:
C. 3/20 of a meter
Step-by-step explanation:
Step 1: To find out how much ribbon Carl has left, we need to subtract the length of ribbon used from the total length of the ribbon.
Step 2: To add the lengths of the ribbon used, we need to find a common denominator for the fractions used. The least common multiple of 5 and 4 is 20, so we can convert both fractions to twentieths.
Step 3: 2/5 of a meter is equivalent to 8/20 of a meter, and 1/4 of a meter is equivalent to 5/20 of a meter.
Step 4: To add the lengths of ribbon used, we add the two fractions: 8/20 + 5/20 = 13/20.
Step 5: To find the length of ribbon Carl has left, we subtract the fraction of the ribbon used from the total length of the ribbon: 4/5 - 13/20 = 16/20 - 13/20 = 3/20.
Step 6: Therefore, Carl has 3/20 of a meter of ribbon left.
Which graph represents the PARENT function of y = x^2- 5?
Answer:
Graph A--------------------
The function y = x² - 5 is the translation of the parent function y = x² down by 5 units.
Since the parent function is y = x², it is a parabola that has its vertex at the origin and opens up as its coefficient is positive.
Looking at the answer choices, we see option A is the correct one.
Other options are incorrect:
Option B is reflection of parent function in the x-axis, Option C is translated down, Option D is translated to the right.