Answer:4
Step-by-step explanation:
A zero-coupon bond doesn’t make any payments. Instead, investors purchase the zero-coupon bond for less than its face value, and when the bond matures, they receive the face value.
To figure the price you should pay for a zero-coupon bond, you'll follow these steps:
Divide your required rate of return by 100 to convert it to a decimal.
Add 1 to the required rate of return as a decimal.
Raise the result to the power of the number of years until the bond matures.
Divide the face value of the bond to calculate the price to pay for the zero-coupon bond to achieve your desired rate of return.
First, divide 4 percent by 100 to get 0.04. Second, add 1 to 0.04 to get 1.04. Third, raise 1.04 to the sixth power to get 1.2653. Lastly, divide the face value of $1,000 by 1.2653 to find that the price to pay for the zero-coupon bond is $790,32.
25 POINTS
Examine the following solution to a conversion problem. Do you see a mistake? If so, identify the location of the first mistake and explain why it is incorrect.
Original Problem: Convert 3.25 kg to mg
(1) 3.25 kg
(2) 1 kg = 1000 g
(3) 1000 mg = 1g
= (4) 3.25 mg
A) The conversion is not possible.
B) The first problem occurs in column (1). The problem should begin with mg.
C) The first problem occurs in column (2). 1 kg is not equal to 1000 g, so that should not be used as the conversion factor.
D) The first problem occurs in column (2). The conversion factor is upside down (grams should be on top, and kg should be on bottom).
E) The first problem occurs in column (4). The multiplication and division was performed incorrectly.
F) No mistakes.
Thanks a bunch!
Answer:
[tex]\boxed{\sf Option \ E}[/tex]
Step-by-step explanation:
(1) 3.25 kg
(2) 1 kg = 1000 g
(3) 1000 mg = 1g
= (4) 3.25 mg
The first problem occurred in column (4) where we actually had to multiply it by 1000 but we divided it by 1000 and so our conversion was incorrect.
The correct form of it is:
1) 3.25 kg
2) 1 kg = 1000 g ; 3.25 kg = 3250 g
3) 1 g = 1000 mg ; 3250 * 1000 = 3,250,000 mg
4) Answer = 3,250,000 mg
Answer:
[tex]\boxed{\sf Option \ E}[/tex]
Step-by-step explanation:
1 kg = 1000 g
1000 mg = 1g
3.25 kilograms is to be multiplied by 1000 to get the value in grams. Then the result should be multiplied again by 1000 to get the value in milligrams.
3.25 kg ⇒ 3250 g ⇒ 3250000 mg
The first problem occurs in column (4). The multiplication and division was performed incorrectly.
The length, width and height are consecutive whole numbers. The volume is 120 cubic inches.
Answer:
4, 5 and 6
Step-by-step explanation:
Consecutive means right next to each other.
4 x 5 x 6 = 120 cubic inches.
4 X 5 = 20
20 X 6 = 120
The values of the consecutive numbers will be 4, 5, and 6.
Let the numbers be represented by a, a+1, and a+2.
Therefore, a(a+1)(a+2) = 120
a³ + 3a² + 2a = 120
a = 4
Therefore, a + 1 = 4+1 = 5
a + 2 = 4 + 2 = 6
Therefore, the values will be 4, 5, and 6.
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For the functions f(x)=4x−3 and g(x)=3x2+4x, find (f∘g)(x) and (g∘f)(x).
Answer:
(16x + 21) and (16x - 6)
Step-by-step explanation:
f(g(x)) = f(6 + 4x)
Applying the f(x) function on (6 + 4x) gives
4(6 + 4x) - 3
Which equals 16x + 24 - 3
= 16x + 21
g(f(x)) = g(4x - 3)
Applying the g(x) function on (4x - 3) gives
6 + 4(4x - 3)
Which equals 6 + 16x - 12
= 16x - 6
Answer:
(g∘f)(x)=48x2+48x+10
(g∘f)(x)=12x^2-6
Step-by-step explanation:
To find (f∘g)(x), use the definition of (f∘g)(x),
(f∘g)(x)=f(g(x))
Substituting 3x2−2 for g(x) gives
(f∘g)(x)=f(3x2−2)
Find f(3x2−2), where f(x)=4x+2, and simplify to get
(f∘g)(x)(f∘g)(x)(f∘g)(x)=4(3x2−2)+2=12x2−8+2=12x2−6
To find (g∘f)(x), use the definition of (g∘f)(x),
(g∘f)(x)=g(f(x))
Substituting 4x+2 for f(x) gives
(g∘f)(x)=g(4x+2)
Find g(4x+2), where g(x)=3x2−2, and simplify to get
(g∘f)(x)=3(4x+2)^2−2
(g∘f)(x)=48x2+48x+12−2
(g∘f)(x)=48x2+48x+10
Solve for x 2x^2-5=13 lesser and greater
Answer:
I got x=3,-3
Step-by-step explanation:
Squares are the results of multiplying a value by itself. The value of x in the given equation 2x² - 5 = 13 is -3 and 3.
What is square root?Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.
The value of x for the given equation 2x²-5=13, can be solved as shown below.
2x² - 5 = 13
Add 5 on both the sides of the equation,
2x² - 5 + 5 = 13 + 5
2x² = 18
Divide both the sides of the equation by 2,
2x² / 2 = 18 / 2
x² = 9
Taking the square root on both the sides of the equation,
√x² = √9
x = ±3
x = -3, 3
Hence, the value of x in the given equation 2x² - 5 = 13 is -3 and 3.
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Suppose the price level and value of the U.S. Dollar in year 1 are 1 and $1, respectively. Instructions: Round your answers to 2 decimal places. a. If the price level rises to 1.50 in year 2, what is the new value of the dollar? b. If, instead, the price level falls to 0.40, what is the value of the dollar?
Answer:
$0.80
Step-by-step explanation:
If price level rises to 1.25 from 1 then:
Value of dollar = 1/1.25 = $0.80
A 6-ounce container of Greek yogurt contains 150 calories. Find the unit rate of calories per ounce.
Answer:
25
Step-by-step explanation:
150/6
The Unit rate of calories per ounce will be 25 calories per ounce.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Weight of the Greek yogurt container = 6 ounce
Calories per container = 150 calories
The Unit rate of calories per ounce = 150 / 6 = 25
Therefore, the unit rate of calories per ounce will be 25 calories per ounce.
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Matt won 95 pieces of gum playing hoops at his school's game night. Later, he gave three to each of his friends. He only has 8 remaining. How many friends does he have?
Answer:
11
Step-by-step explanation:
95/8=11.875
so he has around about 11-12 friends
Answer:
the answer is 29. i placed down 3 dots until i hit 95, counted 8 dots, and started group the 3 dots i put together, so i made sure i didnt count the eight ( pieces of gum) and i started counting the groups of three and i got 29. there was 29 groups of three.
Step-by-step explanation:
An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. it is an unbiased estimator. the variance of the estimator is zero. the difference between the estimator and the population parameter stays the same as the sample size grows larger.
Answer:
the difference between the estimator and the population parameter grows smaller as the sample size grows larger.
Step-by-step explanation:
In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.
Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.
An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.
Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]
Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).
A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.
Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.
-3 1/2= 1/2x+1/2x+x A)-1 3/4 B)-5 1/2 C)-1 1/2 10points each
Answer:
-1 3/4 =x
Step-by-step explanation:
-3 1/2= 1/2x+1/2x+x
Combine like terms
-3 1/2 = 2x
Change to an improper fraction
- ( 2*3+1)/2 = 2x
-7/2 = 2x
Multiply each side by 1/2
-7/2 *1/2 = 2x* 1/2
-7/4 = x
Changing to a mixed number
-4/4 -3/4 =x
-1 3/4 =x
Select the correct answer. Brad is planting flowers in a grid-like pattern in his garden. He is trying to determine the possible numbers of rows and columns in which he can plant his flowers. He determines that two possibilities are 8 rows and 25 columns or 10 rows and 20 columns. What is the constant of proportionality in this inverse variation?
Answer:
[tex]C.\ 200[/tex]
Step-by-step explanation:
Given
Let R represents rows and C represents Columns
When R = 8, C = 25
When R = 10, C = 20
Required
Given that there exist an inverse variation, determine the constant of proportionality;
We start by representing the variation;
[tex]R\ \alpha \ \frac{1}{C}[/tex]
Convert proportion to an equation
[tex]R\ = \ \frac{k}{C}[/tex]
Where k is the constant of proportion;
[tex]R * C\ = \ \frac{k}{C} * C[/tex]
Multiply both sides by C
[tex]R * C\ = k[/tex]
Reorder
[tex]k = R * C[/tex]
When R = 8, C = 25;
The equation [tex]k = R * C[/tex] becomes
[tex]k = 8 * 25[/tex]
[tex]k = 200[/tex]
When R = 10, C = 20;
The equation [tex]k = R * C[/tex] becomes
[tex]k = 10 * 20[/tex]
[tex]k = 200[/tex]
Hence, the concept of proportionality is 200
Write an equation for the line that passes through the point (4,5) and is perpendicular to−7x+y=2. Use slope-intercept form.
Answer:
y= -1/7x + 39/7
Step-by-step explanation:
Slope - intercept form is:
y= mx +b, where m represents the slope of the lineGiven the line:
- 7x +y= 2,which can be shown as:
y= 7x+2 if we add 7x to both sides of equationWe need to write an equation for the line that it perpendicular to the given line and passes through the point (4,5)
As we know, perpendicular line has a slope opposite-reciprocal to the given, so the slope is:
m= - 1/7and the form of the line is:
y= -1/7x +bWe can find b, by using the point (4, 5), which means x=4 and y=5:
5= -1/7 * 4 + b ⇒ b= 5+ 4/7= 5 4/7 = 39/7And the equation for this line is:
y= -1/7x + 39/7Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . Use 3.14 for π as necessary. - - - no lengthy explanation needed! all I need is the answer! first answer gets brainliest!
Answer:
810.66 ft²
Step-by-step explanation:
Short answer:
Shaded region:
(12+2*7)*20 - 12*20 + 3.14*((12+2*7)/2)² =14*20 + 530.66 = 810.66 ft²Answer: 810.66 ft²
I agree.
A spinner has 4 equal sectors with tour options Dubai, Seoul, Switzerland, and Paris. What is the probability of landing on Seoul or Paris after spinning spinner
The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
What is Probability ?Probability is the measure of likeliness of an event to happen.
It is given that
Total Outcomes = 4 ( Dubai, Seoul, Switzerland, and Paris)
the probability of landing on Seoul or Paris after spinning spinner = ?
The probability of Landing on Seoul P(S) is 1 /4
The probability of Landing on Paris P(P) is 1 /4
The probability of landing on Seoul or Paris after spinning spinner is
P( S∪P) = P(S) + P(P)
= (1/4) + (1/4)
= 1/2
Therefore , The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
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Algebra 1 worksheet inequalities
Answer:
see explanation
Step-by-step explanation:
(1)
2x - 3 ≤ 3 ( add 3 to both sides )
2x ≤ 6 ( divide both sides by 2 )
x ≤ 3
(2)
2 - 3y > 16 ( subtract 2 from both sides )
- 3y > 16
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.
y < - [tex]\frac{14}{3}[/tex]
Which inequality is equivalent to this one y-8_<-2
Answer:
[tex]\boxed{y\leq 6}[/tex]
Step-by-step explanation:
[tex]y-8 \leq -2[/tex]
Adding 2 to both sides
[tex]y \leq -2+8[/tex]
[tex]y \leq 6[/tex]
The question is with the image.
Answer:
A
Step-by-step explanation:
the graph of x'3 is B
the graph of x'(-1/3) is C
Which is hyperplane is better between B1 and B2? a. B1 is better than B2 b. B2 is better than B1 c. Both B1 and B2 are the same d. Neither B1 nor B2
Answer:
a. B1 is better than B2.
Step-by-step explanation:
Hyperplane is a geometric shape which has subspace whose dimension is one less than ambient space. Hyperplane that maximizes the margin it will have better generalization. Margin is calculated by [tex]\frac{2}{||W||}[/tex]. The correct option is a.
Answer:
A
Step-by-step explanation:
Which of the following equations are identities? Check all that apply.
A. sec x=
CSC X
1
B. CSCX=
sinx
1
C. tanx=
secx
D. tanx=
sin x
COS
Answer:
B. CSCX= sinx / 1
D. tanx= sin x / COS x
Step-by-step explanation:
A. sec x= 1/cos(x)
CSC X / 1 = sin(x)
B. CSCX
sinx / 1 = csc(x)
C. tanx= sin(x) / cos(x)
secx = 1 / cos(x)
D. tanx= sin(x) / cos (x)
sin (x) / cos(x)
The correct option is (D). tanx = sinx/cosx
Option (D). is correct.
What is Trigonometry?The trigonometric function, which comprises the sine, cosine, tangent, cotangent, secant, and cosecant. Can be used for practical applications.
As per the given data:
We are given some trigonometric identities, and we have to find out which of the given identities in the options are correct.
(A). secx = cscx/1
This is incorrect, as secx = 1/cosx
(B). cscx = sinx/1
This is incorrect, as cscx = 1/sinx
(C). tanx= secx
This is incorrect, as tanx = sinx.secx
(D). tanx = sinx/cosx
This is correct as, tanx = sinx/cosx
The correct option is (D). tanx = sinx/cosx
Hence, The correct option is (D). tanx = sinx/cosx
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Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
Use Newton's method with initial approximation x1 = −1 to find x2, the second approximation to the root of the equation x3 + x + 8 = 0. (Round your answer to four decimal places.) x2 =
Answer:
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Step-by-step explanation:
The Newton's method is a numerical method by approximation that help find roots of a equation of the form [tex]f(x) = 0[/tex] with the help of the equation itself and its first derivative. The Newton's formula is:
[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]
Where:
[tex]x_{i}[/tex] - i-th approximation, dimensionless.
[tex]x_{i+1}[/tex] - (i+1)-th approximation, dimensionless.
[tex]f(x_{i})[/tex] - Function evaluated at the i-th approximation, dimensionless.
[tex]f'(x_{i})[/tex] - First derivative of the function evaluated at the i-th approximation, dimensionless.
The function and its first derivative are [tex]f(x) = x^{3}+x+8[/tex] and [tex]f'(x) = 3\cdot x^{2}+1[/tex], respectively. Now, the Newton's formula is expanded:
[tex]x_{i+1} = x_{i}-\frac{x_{i}^{3}+x_{i}+8}{3\cdot x_{i}^{2}+1}[/tex]
If [tex]x_{1} = -1[/tex], the value of [tex]x_{2}[/tex] is:
[tex]x_{2} = -1 - \frac{(-1)^{3}+(-1)+8}{3\cdot (-1)^{2}+1}[/tex]
[tex]x_{2} = -1.5000[/tex]
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Answer:
-2.5000
Step-by-step explanation:
rectangular field has a total perimeter of 128 feet. The width is
A
24 feet less than the length. What are the dimensions of the field?
Answer:
l = 44 ft
w = 20 ft
Step-by-step explanation:
Perimeter is
P = 2 ( l+w)
The width is
w = l -24
We know the perimeter is 128 and substituting into the equation for perimeter
128 = 2 ( l + l-24)
128 = 2 ( 2l -24)
Divide by 2
128/2 = 2/2 ( 2l-24)
64 = 2l - 24
Add 24 t o each sdie
64+24 = 2l
88 = 2l
Divide by 2
44 =l
The length is 44
Now find w
w = l - 24
w = 44-24
w = 20
Answer:
[tex]\boxed{l=44 \: \mathrm{feet}, \: \: w=20 \: \mathrm{feet}}[/tex]
Step-by-step explanation:
The width (w) = l - 24
The length (l) = l
The perimeter (P) = 128
The shape is a rectangle. Use the formula for the perimeter of a rectangle.
P = 2w + 2l
Plug in the values.
128 = 2(l - 24) + 2l
Solve for l.
Expand brackets.
128 = 2l - 48 + 2l
Combine like terms
128 = 4l - 48
Add 48 on both sides.
176 = 4l
Divide both sides by 4.
44 = l
Apply formula again.
P = 2l + 2w
Solve for w.
Subtract 2w and P on both sides.
-2w = 2l - P
Divide both sides by -2.
w = -l + P/2
Plug in the values for l and P, solve for w.
w = -(44) + 128/2
w = -44 + 64
w = 20
The length is 44 feet.
The width is 20 feet.
What is the solution set to log:(4x + 2) + 4 2 5?
(-0.5, 00)
[1.5, 00)
thy5.c)
[5,00)
Answer: (-0.5,00)
number one i think good luck
Step-by-step explanation:
Please help with this question ASAP!
You are studying for the SAT and start the first week spending 2 hours studying. You plan to increase the amount you study by 10% each week. How many hours do you study in the 8th week?
Answer:
8w : 3.8974342 ≈ 3.9 or 4 (hope it help)
Step-by-step explanation:
1w : 2
2w : 2 + 10% = 2.2
3w : 2.2 + 10% = 2.42
4w : 2.42 + 10% = 2.662
5w : 2.662 + 10% = 2.9282
6w : 2.9282 + 10% = 3.22102
7w : 3.22102 + 10% = 3.543122
8w : 3.543122 + 10% = 3.8974342
3.8974342 ≈ 3.9 or 4
A heptagon can be divided into how many triangles by drawing all the diagonals from one vertex
Answer:
5 triangles from the vertex
Answer:
5 triangles from the vertex
Step-by-step explanation:
You are given 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice, meaning you win $7 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.
Answer:
The expected value of the game is $0.33.
Step-by-step explanation:
There are N = 36 outcomes of rolling two 6-sided fair dice.
The sample for the sum of two numbers to be 7 is:
S = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)}
n (S) = 6
It is provided that there is a 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice.
That is, you win $7 if you succeed and you lose $1 if you fail.
Compute the expected value of the game as follows:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
[tex]=[\$(7)\times \frac{6}{36}]+[\$(-1)\times \frac{30}{36}]\\\\=\frac{7}{6}-\frac{5}{6}\\\\=\frac{7-5}{6}\\\\=\frac{1}{3}\\\\=\$0.33[/tex]
Thus, the expected value of the game is $0.33.
The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probability that the sample mean will be larger than 1224
Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
[tex]S \sim N ( 1200,60)[/tex]
the probability that the sample mean will be larger than 1224 will now be:
[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]
[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]
[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082
Rotation
The triangle DEF with vertices D (-4, 4), E (-1, 2), F (-3, 1). Graph the figure and its image after a 90 ° clockwise rotation about its origin.
Answer:
Step-by-step explanation:
The vertices of the already rotated triangle are:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Answer:
D '(4, 4)
E '(1, 3)
F '(2, 1)
Step-by-step explanation:
a box contains 20 blue marbes, 16 green marbles, and 14 red marbles. two marbles are selected at random. let 3 be the event that first marbke selected is green. find p(fe) g
Answer:
Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.
Step-by-step explanation:
In how many ways can the letters of the word CARPET be arranged
Answer: In so many ways ;
acre cape care carp cart cate pace pact pare part pate pear peat pert prat race atrapt rate reap race tape tare tarp tear tepatrapace act ape apt arc are art ate cap car cat cep ear eat era pack par pat pea pec per pet rap rat rec rep ret tap tar teaAnd so on .
720
Explanation:you would be using permutation i believe
because carpet has 6 letters you have six placement options
_x_x_x_x_x_
if you can only use the letters once
you can put all letters in p1
so 6x_x_x_x_x_
but because of that you would only be able to put all but one in p2 and one less than p2 in p3 going all the way to 1 in the last
so 6x5x4x3x2x1
i might be wrong but this has worked for me
Need help with this, I don’t need an explanation, just the answer.
Answer:
-4
Step-by-step explanation:
give me brainliest please
Answer: x= 4.25 y= 12.75
Step-by-step explanation: