Answer:
89
Step-by-step explanation:
Given that
2 O, 2 T and 1 M
Now based on this, the following ways are there
1
Three ways i.e. {M,T,O}
2
XX or XY
XX in 2C1 = two ways i.e. {OO or TT}
XY in 3C2 × 2! = six ways
3
XXY or XYZ
XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve ways
XYZ in 3C3 × 3! = six ways
4
XXYY or XXYZ
XXYY = 4! ÷ (2! × 2!) = six ways
XXYZ in 2C1 × 4! ÷ 2! = twenty four ways
5
= 5! ÷ (2! ×2!)
= 120 ÷ 4
= 30
Therefore, the total is
= 3 + (2 +6)+ (12 +6) + (6 +24) + 30
= 89
There are 30 different letter permutations.
The word is given as:
MOTTO
From the given word, we have the following parameters:
[tex]n = 5[/tex] --- the number of characters in the word[tex]T = 2[/tex] --- the number of times letter T appears[tex]O = 2[/tex] --- the number of times letter O appearsThe number of different (d) letter permutation is then calculated as:
[tex]d = \frac{n!}{T!O!}[/tex]
This gives
[tex]d = \frac{5!}{2!2!}[/tex]
Evaluate each factorial
[tex]d = \frac{120}{2 \times 2}[/tex]
Evaluate the product of 2 and 2
[tex]d = \frac{120}{4}[/tex]
Divide 120 by 4
[tex]d = 30[/tex]
Hence, there are 30 different letter permutations.
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tristan wants to build a square garden in his backyard. if the garden is going to be 64 ft squared how many feet of material will he need for the perimeter of the garden?
Answer:
32 ft
Step-by-step explanation:
First Tristan must determine the length of one side of his square garden. Sine A = x^2, where x is the length of one side, and since 64 ft^2 = x^2, we can find the length x by taking the square root of both sides: 8 ft = x.
Now the length of the material enclosing the garden is the perimeter, P.
For a square, P = 4x.
Therefore, in this case, P = 4(8 ft) = 32 ft
graph x= -2y by plotting the intercepts.
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
slope:-1/2
y-intercept:(0, 0)
Answer:
slope: [tex]-\frac{1}{2}[/tex]
y intercept: [tex]0,0[/tex]
Step-by-step explanation:
Here is a graph.
Hope this Helps!
Which of the following lines is parallel to x = 8?
a. 3y = 16
b. x = 7
c. х = y
d y = 8
Answer:
d. y = 8
Step-by-step explanation:
The given line is of the form ...
y = constant
A parallel line must be of the same form. The matching answer is ...
y = 8
Find the least whole number that can replace ? To make the statement true
? ÷9>700
Answer:
6301.
Step-by-step explanation:
First we find the integer such that ? / 9 = 700.
? = 700 * 9 = 6300.
Therefore the least whole number for ? / 9 > 700 should be 6301.
Four out of 12 goldfish in an aquarium ate their food. What ratio represents the
goldfish that ate their food to those that did not?
Answer:
4-8
Step-by-step explanation:
Answer:
1:3
Step-by-step explanation:
I changed 4/12 to a fraction then simplified it
4/12=1/3
one gold fish ate their food for every 3 they fed
The average hourly wage of computer programmers with 2 years of experience has been $21.80.Because of high demand for computer programmers,it is believed there has been a significant increase in the average wage of computer programmers.To test whether or not there has been an increase,the correct hypotheses to be tested area. H0: μ < 21.80 Ha: μ >= 21.80b. H0: μ = 21.80 Ha: μ ≠ 21.80c. H0: μ > 21.80 Ha: μ =< 21.80d. H0: μ <= 21.80 Ha: μ > 21.80
Answer:
d. H0: μ <= 21.80 Ha: μ > 21.80
Step-by-step explanation:
We set the null hypothesis as what is already given . We are already informed that the average wage is equal to μ <= 21.80 against the claim that is required. It is required to test whether the average wage of the computer programmers is greater than μ > 21.80
So option d is the best answer.
Hypotheses testing is done using an observation and a claim. The observation is set as a null hypothesis and claim is set as an alternative hypothesis. The null and alternative hypotheses must be chosen wisely to get the correct results.
The critical region is dependent on the claim set.
The domain for variable x is the set of all integers. Select the statement that is true.
A. ∃x (3x=1)
B. ∃x (x2<1)
C. ∀x (x2=1)
D. ∃x (x2<0)
Answer:
B. ∃x (x2<1)
Step-by-step explanation:
When we take X = 0 and Placing it in each option as follow
A.
∃x (3x=1)
∃x (3(0)=1)
∃x (0=1)
Which is not true
B.
∃x (x2<1)
∃x ((0)2<1)
∃x (0<1)
Which is true
C.
∀x (x2=1)
∀x ((0)2=1)
∀x (0=1)
Which is not true
D.
∃x (x2<0)
∃x ((0)2<0)
∃x (0<0)
Which is not true.
three subtracted from twice a number ?
The product of two whole numbers is 504 and their sum is 45. What are the two numbers?
Answer:
21, 24
Step-by-step explanation:
1. Given:
[tex]xy=504[/tex][tex]x+y=45[/tex] [tex]y=45-x[/tex]2. Solution:
[tex]x(45-x)=504[/tex][tex]45x-x^2=504[/tex] [tex]x^2-45x+504=0[/tex] [tex]x^2-24x-21x+504=0[/tex] [tex]x(x-24)-21(x-24)=0[/tex] [tex](x-24)(x-21)=0[/tex] [tex]x_1=24[/tex] ⇒ [tex]y_1=21[/tex] [tex]x_2=21[/tex] ⇒ [tex]y_2=24[/tex]Open the line reflection application. The right line is a reflection across the y-axis of the left line. Click the reflect over y-axis button. Are these lines the same? What does this mean about how a line changes when you reflect it?
Answer:
The lines are the same, they are just in a different position.
Step-by-step explanation:
A reflection is a type of rigid transformation. Rigid transformations do not change the size nor the length of the pre-image.
In other words, the pre-image and the image in a rigid transformation are congruent.
Hope this helps.
Based on the fact that the right line is a reflection across the y-axis, the lines are the same, they are just in a different position.
What is a Reflection?This refers to the rigid transformation type that is used to represent an image and does not change its size or length of it.
With this understanding, we can see that the pre-image and the image in a rigid transformation are congruent which makes the lines to be the same, even if they are in a different position.
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Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point (6, -7) are Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
Answer: [tex](6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)[/tex] are the required points.
or (18.124,0) and ( -6.124,0) are the required points.
Step-by-step explanation:
Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .
Then by distance formula , we have
[tex]\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}][/tex]
Taking square on both the sides , we get
[tex](x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0[/tex]
Using quadratic formula : [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}[/tex]
so, [tex](6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)[/tex] are the required points.
since [tex]\sqrt{3}=1.732[/tex]
so, [tex](6+7(1.732),0)\text{ and }(6-7(1.732),0)[/tex] are the required points.
i.e. (18.124,0) and ( -6.124,0) are the required points.
Help immediate... What are the like terms and to simplify fully. -7y^2-6-2-6x+x
Answer:
the fully simplified expression is: [tex]-7y^2+7x-8[/tex]
Step-by-step explanation:
The like terms are:
-6 and -2, which combined give -8
and 6 x and x, which combine give 7 x
So the simplified form of this is:
[tex]-7y^2+7x-8[/tex]
If a student gets an A on a final exam, then the student will pass the course.
The student gets an A on the final exam.
Answer: PERIOD
Step-by-step explanation:
Get good grades on your assignments and the student will pass the course with an A.
Match the following items by evaluating the expression for x = -6. x^-2 x^-1 x^0 x^1 x^2
Answer:
see below
Step-by-step explanation:
x = -6 ⇒
x^-2 = (-6)^-2 = 1/36x^-1 = (-6)^-1 = -1/6x^0 = (-6)^0 = 1x^1 = (-6)^1 = -6x^2 = (-6)^2 = 36Answer:
x = - 6
Step-by-step explanation:
x = -6x⁻² x⁻¹ x⁰ x¹ x²
x² = 0, x = 0
x¹ = 0, x = 0
the following points are undefined
x = 0
combine undefined points with solutions:
x = - 6
What is the equivalent algebraic expression of " 5 less than four times a
number x " ?
if jeff had 10 cookies and sam ate 10 how many are left?
Answer:
0
Step-by-step explanation:
10-10=0
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.2 million cells per microliter and a standard deviation of 0.5 million cells per microliter. What is the minimum red blood cell count that can be in the top 24% of counts? What is the maximum red blood cell count that can be in the bottom 15% of counts? can somebody help me?
Answer:
5.55 million cells per microliter
4.68 million cells per microliter
Step-by-step explanation:
First, use a chart or calculator to find the z-score for reach percentage.
P(Z > z) = 0.24
P(Z < z) = 1 − 0.24 = 0.76
z = 0.706
Next, use definition of z-score to find the value.
z = (x − μ) / σ
0.706 = (x − 5.2) / 0.5
x = 5.55
Repeat for the other percentage.
P(Z < z) = 0.15
z = -1.036
z = (x − μ) / σ
-1.036 = (x − 5.2) / 0.5
x = 4.68
what is the sum of 2,888 and 74
Answer:
2962
Step-by-step explanation:
2 8 8 8
+ 7 4
----------------
2 9 6 2
2962
Step-by-step explanation:2888 +
74
---------
2962
8 + 4 = 12
8 + 1 + 7 = 16
8 + 1 = 9
WILL GOVE BRAINIEST !!!! HELP
Answer:
1. 15
2.-54
3.-19
4.1.5
5.-5
6.63
7.1
8.-26
9.-4
10.7
11. 0
12. -4
Step-by-step explanation:
all you do is plug in the number within the parentheses to the equation as the variable x and solve from there.
I NEED HELP ASAP please
Answer:
A
Step-by-step explanation:
How to find measurement of degree?
Answer:
It's 30 degrees. YSX and QSL are verticals so they are equal. Then QSL AND MLP are corresponding so they are too equal. So then yeah.
Answer:
30°
Step-by-step explanation:
It’s important to note the angle relationships.
We have two parallel lines intersecting one line. This means that each of the angles formed by one line will be equal to the angles formed by the other.
Using this info, we can tell that XYZ and MLP are alternate exterior angles, since they are formed by two parallel lines.
Alternate exterior angles are equal: since we know XYZ is 30°, MLP must be 30°.
Hope this helped!
evaluate the expression when p= 12 and m =15;p-m
Help pls what is the answer to this 3(n+1)=5.4 Solve for n.
Answer:
N = 0.8
Step-by-step explanation:
3(n + 1) = 5.4
3n + 3 = 5.4
- 3 = -3
3n = 2.4
3n/3 = 2.4/3
N = 0.8
A company recently replaced its 9-oz cup of yogurt with a 7-oz cup and reduced the suggested retail price from 87 cents to 75 cents. Was the price per ounce reduced by the same percent as the size of the cup? If not, find the price difference per ounce in terms of a percent.
Answer:
Question 1
Was the price per ounce reduced by the same percent as the size of the cup? No it's not the same
Question 2
If not, find the price difference per ounce in terms of a percent.
13.8%
Step-by-step explanation:
The first yoghurt cup size = 9 oz
The second and recent yoghurt cup size = 7 oz
The difference in ounces = 9 oz - 7 oz
= 2 oz
Converting this difference to percentage
= 2 oz/ 9 oz × 100%
= 22.222222222%
The percent reduction in cup size is approximately
22.2%.
The first retail price per ounce = 87 cents
The second and recent retail price per ounce =75 cents
The difference in prices = 87 cents - 75 cents
= 12 cents
Converting this difference to percentage
= 12 cents / 87 cents × 100%
= 13.793103448%
The percent reduction in yoghurt price per ounce is approximately
13.8%.
Question 1
Was the price per ounce reduced by the same percent as the size of the cup?
From the above calculation,
Percent reduction in price per ounce =
13.8%
Percent reduction in the size of the cup = 22.2%
13.8% ≠ 22.2%
Therefore, it is not the same
Question 2
If not, find the price difference per ounce in terms of a percent.
Therefore, the price difference per ounce in terms of percent is
13.793103448%.
Approximately ≈ 13.8%
Jennifer is currently standing at 25 feet above sea level. Jim is swimming at 9 feet below sea level. How far apart are Jim and Jennifer? A. -34 b. -16 c. 16 d. 34
Answer:
D. 34 ft
Step-by-step explanation:
25+9=34
Jim is 34ft below Jenifer
When Barbara started her trip, the odometer read 13,487.8. When she ended the trip, it read
14,108.6. Barbara's car gets 22 miles per gallon. Her tank was full at the beginning of the
trip. When she filled the tank, it cost her $88.04. How many gallons did Barb use, and what
price did she pay per gallon of gas on this fill-up?
HELP ASAP PLEASE
Answer:
28.2 gal
$3.12/gal
Step-by-step explanation:
Length of trip:
14,108.6 mi - 13,487.8 mi = 620.8 mi
(620.8 mi)/(22 mpg) = 28.218 gal
She used 28.2 gallons.
price per gallon = $88.04/(28.218 gal) = $3.12/gal
Suppose you have a credit card debt of $4,000. Last month the bank charged you $40 interest on the debt. The solution to the equation 40= 4000/12r represents the annual interest rate (r) on the credit card. Find the annual interest rate on the credit card.
Answer:
12%
Step-by-step explanation:
As per the given formula:
40= 4000/12rr = 40*12/4000r = 0.12 0.12*100% = 12%Interest rate is 12%
There are 40 nickels in a roll. If you have 150 rolls of nickels, how many nickels do you have?
You would have 6,000 nickels. Multiply 40 by 150
There are 6000 Nickels in 150 rolls of Nickle.
To find out the total number of nickels you have, you need to multiply the number of nickels in a single roll by the number of rolls.
Given that there are 40 nickels in a roll and you have 150 rolls..
So, the total number of nickels can be calculated as:
= 40 nickels/roll x 150 rolls
= 6000 nickels.
Therefore, you have 6000 nickels.
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Draw a figure to represent the following information: T
is between S and U, ST = 7x, SU = 45, and TU = 5x –
3.
Answer:
ST = 28 unit
TU = 17 units
Step-by-step explanation:
Given:
ST = 7x
SU = 45
TU = 5x – 3
Find:
Each value
Computation:
SU = ST + TU
45 = 7x + 5x - 3
48 = 12x
x = 4
So,
ST = 7x
ST = 7(4)
ST = 28 unit
TU = 5x – 3
TU = 5(4) – 3
TU = 17 units
If LM=8 and MN=5 , what is LN
Answer:
23
Step-by-step explanation:
Answer:
The answer is 23
Step-by-step explanation:
Hope this answer is helpful...
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