Answer:
Step-by-step explanation:
Permutation has to do with arrangement.
To form different word by rearranging the word KINDNESS, this can be done in the following way;
The total letters present in kindness = 8 letters
Repeated letters are 2N's and 2S's
The arrangement is done in [tex]\frac{8!}{2!2!}[/tex] ways
[tex]= \frac{8!}{2!2!} \\= \frac{8*7*6*5*4*3*2!}{2!*2}\\ = 8*7*3*5*4*3\\= 10,080 \ different\ words[/tex]
For MATHEMATICIAN;
The total letters present in kindness = 13 letters
Repeated letters are 2M's, 2T'S 2I'sand 3A's
The number of words formed =
[tex]\frac{13!}{2!2!2!3!} \\= \frac{13*12*11*10*9*8*7*6*5*4*3!}{6*3!}\\= 13*2*11*10*9*8*7*6*5*4\\= 172,972,800\ different\ words[/tex]
urgenttttt What is the value of x? A right triangle has a vertical hypotenuse labeled 6. A 30 degree angle is marked at the top of the triangle. A second right triangle has a leg that is the same as the side opposite the 30 degree angle of the first triangle. On the second right triangle, the hypotenuse is labeled x and an angle is labeled 45 degrees. Enter your answer, as an exact value, in the box. x =
Answer:
x=30degrees
Step-by-step explanation:
the diagram, if drawn comes as a square. when divided to two triangles, both of them have one right angle each. if the hypotenuse is thirty d on one side, the opposite angle has to be 60d . since the total of all angles is 180d and one side is 90d and the other 60d, the other angle must me 30d
The length of Hypotenuse is 3√2 unit.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
Angle= 45 degrees
Hypotenuse = x
Using Trigonometry in Triangle 1
sin 30 = P/ 6
1/2 = P/6
P= 3 unit
Now, In triangle 2
cos 45 = 3/H
1/√2 = 3 / H
H= 3√2 unit
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Plz help! Marshall's town voted on a new speed limit. 25% of the 64 votes were in favor of the new speed limit. How many votes were in favor?
Answer:
16
Step-by-step explanation:
25% of 64 were votes in favor.
25% × 64
1/4 × 64 = 64/4 = 16
16 votes were in favor.
HELPP VERY URGENT !!!!!!!
Answer:
B
Step-by-step explanation:
Choose the best estimate for the division problem below.
64.309/7.19
A. 12
B. 14
C. 9
Answer:
The estimated answer would be 9
Step-by-step explanation:
The answer I received in the calculator was 8.94422. Since the tenths, place value(9) is closer to 9.0 than 8.0, we round up. I hope this helps you.
A solid shape is made from centimetre cubes.
Here are the plan, side elevation and
Centimetre cubes are added to
front elevation of the shape.
make this cuboid.
Plan Side elevation Front elevation
40
4 cm
3 cm
How many cubes are added?
Write your final answer as,... cubes are added.
Answer:
30 cubes are added
Step-by-step explanation:
The image of the solid shape is attached.
From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.
The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.
30 cubes are added
The number of cubes that are added is 30.
What is Cube?
A cube's form is occasionally referred to as "cubic." Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The cube has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.
From the Plan, Side elevation, and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.
The number of blocks needed to make the cuboid
= 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added
= 48 cubes - 18 cubes
= 30 cubes.
30 cubes are added.
Hence, The number of cubes that are added is 30.
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Dan Stocked up on batteries.
He Brought 10 packages of AA and AAA batteries for a total of 72 batteries.
The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write a system of equations that can be solved to find how many packages of each type of battery Dan bought. Remember to define your variables.
1. C+D=10
2.6c+8D=72
Answer: C
Step-by-step explanation:
i just took a test
Answer:Answer:
x + y = 10
6x + 8y = 72
Step-by-step explanation:
Number of packages = 10
Total batteries = 72
For AA:
batteries per package = 6
Let number of packages = x
For AAA:
batteries per package = 8
Let number of packages = y
Number of AA packages + number of AAA packages = 10
Sum of AA + sum of AAA equals 72 batteries
x + y = 10
6x + 8y = 72
Step-by-step explanation:
What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?
Answer:
4=x
Step-by-step explanation:
1.5(x + 4) – 3 = 4.5(x – 2) distribute
1.5x+6-3 = 4.5x-9 subtract 1.5x from each side
3=3x-9 add 9 to both sides
12=3x divide by on both sides
4=x simplify
Answer:
x=4
Step-by-step explanation
Am I right or wrong (don't answer the last one!)
Answer:
1) Distributive Property of Multiplication (The terms are distributed)
2) Addition property of equality (Adding 14 to both sides)
3) Simplifying (We simplified the expression)
4) Division property of equality (Dividing both sides by 6)
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
- 14 + 6m = 10
Distributive Property of Multiplication
2 is distributed to -7 and 3m
- 14 + 14 + 6m = 10 + 14
Addition Property of Equality
Adding 14 to both sides.
6m = 24
Simplifying
Simplifying the equation.
[tex]\displaystyle \frac{6m}{6} =\frac{24}{6}[/tex]
Division Property of Equality
Dividing both sides by 6.
NEED MATH HELP NOW. Please solve for x-intercept.
Answer:
(1, 0) and (3, 0)
Step-by-step explanation:
y=2x²-8x+6
x- intercept when y=0
2x²-8x+6=0x²-4x+4=1(x-2)²=1x-2=1 ⇒ x= 3x-2= -1 ⇒ x= 1Answer:
(1, 0) / (3, 0)
Step-by-step explanation:
4.6363 as fraction using long division
Answer:
459/99
Step-by-step explanation:
0.6363... is equal to 63/99.
We want to add 4.
4 = 396/99
396/99 + 63/99 = 459/99
We can double check with a calc.
Before using the Gizmo, consider an arithmetic sequence with a first term (a1) of 4 and a common difference (d) of 3.
Challenge: What are the first five terms of the sequence (from lowest to highest)?
Answer:
4, 7, 10, 13 and 16Step-by-step explanation:
The nth term of an arithmetic sequence is expressed as [tex]Tn = a+(n-1)d[/tex].
a is the first term of the sequence
d is the common difference
n is the number of terms
Given the first term a = 4 and common difference d = 3, we can calculate the first five terms of the sequence using the formula.
If n = 2
[tex]T_2 = 4+(2-1)*3\\T_2 = 4+(1)*3\\T_2 = 4+3\\T_2 = 7\\\\when \ n = 3;\\T_3 = 4+(3-1)*3\\T_3 = 4+(2)*3\\T_3 = 4+6\\T_3 = 10\\\\when\ n = 4\\T_4 = 4+(4-1)*3\\T_4 = 4+(3)*3\\T_4 = 4+9\\T_4 = 13\\\\when\ n = 5\\T_5 = 4+(5-1)*3\\T_5 = 4+(4)*3\\T_5 = 4+12\\T_5 = 16\\[/tex]
The first five terms of the sequence from lowest to highest are 4, 7, 10, 13 and 16
Which of the following is equal to 5 1/3
Answer:
C
Step-by-step explanation:
Using the rule of radicals/ exponents
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]5^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{5}[/tex] → C
ABCD is a square. The length of each side of the square ABCD is units, and the length of its diagonal is about units.
Answer:
The answer is below
Step-by-step explanation:
From the diagram attached, to find the length of side AB, we need to use Pythagoras theorem on the right triangles. We can see that AB is the base of the two right triangle.
For the first right triangle with hypotenuse of 13 and height of 12, let x be the base, therefore using hypotenuse:
13² = 12² + x²
169 = 144 + x²
x² = 169 - 144
x² = 25
x = √25 = 5
For the second right triangle with hypotenuse of 15 and height of 12, let y be the base, therefore using hypotenuse:
15² = 12² + y²
225 = 144 + y²
y² = 225 - 144
y² = 81
y = √81 = 9
The length of AB = x + y = 9 + 5 = 14 unit
Since for a square all the sides are equal, therefore the length of each side of the square ABCD is 14 units.
In triangle ADC, the hypotenuse = AC, AD = DC = 14 unit. Using Pythagoras:
AC² = AD² + DC²
AC² = 14² + 14²
AC² = 196 + 196 = 392
AC = √392 = 19.8
The length of its diagonal is about 19.8 units
The average (arithmetic mean) of a - 5 and a is x, and the average of a and a + 9 is y. What is the average of x and y?
a + 1
B) a +2
C) 2a + 1
D) 2a + 2
Answer:
The answer is "Option A"
Step-by-step explanation:
Given:
[tex]\to \frac{(a-5)+a}{2}=x.....(a)\\\\\to \frac{a+(a+9)}{2}=y.....(b)\\\\[/tex]
solve the above equation:
[tex]\to \bold{\frac{(a-5)+a}{2}=x}\\\\\to \frac{a-5+a}{2}=x\\\\\to \frac{2a-5}{2}=x\\\\\to \bold{\frac{a+(a+9)}{2}=y}\\\\\to \frac{a+a+9}{2}=y\\\\\to \frac{2a+9}{2}=y\\\\[/tex]
add both value (x and y):
[tex]\to \bold{x+y}\\\\\to \frac{2a-5}{2}+\frac{2a+9}{2}\\\\\to \frac{2a-5+2a+9}{2}\\\\\to \frac{4a+4}{2}\\\\\to \frac{2(2a+2)}{2}\\\\\to (2a+2)\\[/tex]
average of x and y:
[tex]\to \frac{x+y}{2}\\\\\therefore \bold{x+y= 2a+2}\\\\\to \frac{2(a+1)}{2}\\\\\to \boxed{(a+1)}\\[/tex]
3 3Cylinder A 3 3 4 4Cylinder B 2 2 What is the ratio of the volume of Cylinder A to the volume of Cylinder B? Choose 1 answer: Choose 1 answer: (Choice A, Checked) A 11 27 27 11 start fraction, 11, divided by, 27, end fraction (Choice B) B 16 27 27 16 start fraction, 16, divided by, 27, end fraction (Choice C) C 1 11 (Choice D) D 27 16 16 27
Answer:
(D) [tex]\dfrac{27}{16}[/tex]
Step-by-step explanation:
Volume of a Cylinder =[tex]\pi r^2h[/tex]
Cylinder A
Height = 3 Units
Radius = 3 Units
[tex]Volume =\pi \times 3^2 \times 3 =27\pi$ cubic units[/tex]
Cylinder B
Height = 4 Units
Radius = 2 Units
[tex]Volume =\pi \times 2^2 \times 4 =16\pi$ cubic units[/tex]
[tex]\dfrac{\text{Volume of Cylinder A}}{\text{Volume of cylinder B}}=\dfrac{27\pi}{16\pi}\\\\=\dfrac{27}{16}[/tex]
The correct option is D
For any number y, ⌂y=2y3 . What is the value of ⌂2 + ⌂5 ? NEED HELP ASAP
Answer:
276
Step-by-step explanation:
∆y = 2y3
∆2 = 2(2)3 = 16
∆5 = 2(5)3 = 250
∆2 + ∆5 = 250 + 16 = 276
evaluate 21.5 multiplied by 2.51 to 2 decimal place
Answer:
53.96
Step-by-step explanation:
21.5 times 2.51 is 53.965
53.965 to 2 decimal points is 53.96
Mabel is comparing the prices of two car rental companies. Company A charges $35 per day and an additional $15 as service charges. Company B charges $42 per day and an additional $10 as service charges. Part A: Write an equation to represent each company's total charges for renting a car for a certain number of days. For both equations (one for Company A and one for Company B), define the variable used. (4 points) Part B: Which company would charge less for renting a car for 6 days? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company A instead of Company B to rent a car for 10 days?
Answer:
Part A:
Equation for Company A:
x = Number of days renting a car
35x + 15
Equation for Company B:
x = Number of days renting a car
42x + 10
Part B:
Company A will charge $ 37 less than Company B
Part C:
Company A will charge $ 65 less than Company B
Step-by-step explanation:
Part A:
Equation for Company A:
x = Number of days renting a car
35x + 15
Equation for Company B:
x = Number of days renting a car
42x + 10
Part B:
Renting a car for 6 days
Company A:
35 * 6 + 15 = 210 + 15 = $ 225
Company B:
42 * 6 + 10 = 252 + 10 = $ 262
Company A will charge $ 37 less than Company B
Part C:
Renting a car for 10 days
Company A:
35 * 10 + 15 = 350 + 15 = $ 365
Company B:
42 * 10 + 10 = 420 + 10 = $ 430
Company A will charge $ 65 less than Company B
Find the area of a circle with radius, r = 7.29m. Give your answer rounded to 2 DP
Answer:
Area of a circle is πr²
where r is the radius
r = 7.29m
Area = π × 7.29²
= 166.957
= 166.96m² to 2 decimal places
Hope this helps you
Please help! math is hardddd :(
Answer:
12 in²
Step-by-step explanation:
The area of a triangle is base × height × 1/2.
b × h × 1/2
6 × 4 × 1/2
24 × 1/2
= 12
The area is 12 in².
Answer:
12 in^2Solution,
Base(b)=6 inches
Height(h)=4 inches
Area of triangle=?
Now,
[tex]area \: of \: triangle \\ = \frac{bh}{2} \\ = \frac{6 \times 4}{2} \\ = \frac{24}{2} \\ = 12 \: {inches}^{2} [/tex]
hope this helps ..
Good luck on your assignment...
Jim rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 76 cents for each mile driven. Jim had to pay $236.11 when he returned the truck. For how many miles did he drive the truck?
Answer:
287 miles
Step-by-step explanation:
The base fee was $17.99 and an additional 76 cents ($0.76) for every mile.
We can represent the amount he will pay for rent with the equation below:
C = 17.99 + 0.76m
where m = number of miles driven
Jim paid $236.11, therefore:
236.11 = 17.99 + 0.76m
0.76m = 236.11 - 17.99
0.76m =218.12
m = 218.12 / 0.76 = 287 miles
Jim drove 287 miles.
Prove that interior angles 1 and 3 are congruent when the lines are parallel with a transversal. PLEASE ANSWER ASAP, DUE IN HALF A HOUR
Answer:
They are congruent because angle 1 &3 are alternate interior angles.
Step-by-step explanation:
someone please help, I will give BRAINLIEST!! please explain your answer
Answer: 8.94 is the length of GI
Step-by-step explanation: The two triangles are similar, so the ratios of the sides to each other will be the same.
the unknown length of GI in triangle FIG corresponds to the known length 20 of IH in Triangle GIH, and the known length 4 of side FI in triangle FIG corresponds to GI in Triangle GIH. So the ratio looks like 4:x as x:20
4/x = x/20 multiply both sides by x and 20 to "cancel" the denominators.
20x(4/x) = 20x(x/20)
80 = x² Calculate the square roots
√x² = x . √80 = 8.94
...................
Answer:
x = a(c + b)
Step-by-step explanation:
Step 1: Add b to both sides
x/a = c + b
Step 2: Multiply both sides by a
x = a(c + b)
HELP PLEASE!!! How do I solve this?
Answer:
32
Step-by-step explanation:
tanx=opp/adj.=40/64=5/8=0.625
find tan^-1= 32 degrees
Answer:
A. 32°
Step-by-step explanation:
[tex] \tan \: x \degree = \frac{40}{64} \\ \\ \tan \: x \degree = \frac{5}{8} \\ \\ \tan \: x \degree =0.625 \\ x \degree = {\tan}^{ - 1}( 0.625) \\ \\ x \degree =32.005383208 \degree \\ \\ \huge \red { \boxed{ x =32 \degree}}[/tex]
help please i need help
Answer:
A=6
B=41
c=42
Step-by-step explanation:
What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12? (–6, 0), (2,0) (–2, –16), (0, –12) (–6, 0), (–2, –16), (2, 0) (0, –12), (–6, 0), (2, 0)
Answer:
(-6, 0) and (2, 0)
Step-by-step explanation:
To find the x-intercepts, we can factor the expression:
f(x) = x² + 4x - 12
2 factors of -12 that add up to 4 are 6 and -2
(x + 6)(x - 2)
Set each factor equal to 0 and solve for x:
x + 6 = 0
x = -6
x - 2 = 0
x = 2
So, the x intercepts are (-6, 0) and (2, 0)
Answer:
It's the first option, (-6, 0) (2, 0)
Step-by-step explanation:
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PLEASE ANSWER QUICK. WILL BRAINLIEST
Table I shows the number of hours per week a basketball player practices free throws and the percentage of free throws the player makes. Table II shows the number of hours the player practices per week and the number of points the player scores in the game. 2 tables. A 2-column table with 5 rows titled Practice hours versus free throws made. Column 1 is labeled Practice hours (p) with entries 8, 6, 9, 7, 4. Column 2 is labeled Percentage of free throws made (f) with entries 70, 55, 75, 67, 50. A 2-column table with 5 rows titled Practice hours versus Points Scored. Column 1 is labeled practice hours (p) with entries 6, 5, 10, 3, 2. Column 2 is labeled Number of Points Scored (s) with entries 22, 18, 45, 10, 7. Yasmin made the graphs below to represent the data in the tables. Practice Hours vs. Free Throws Made A graph has practice time (hours) on the x-axis and free throws made (percentage) on the y-axis. Points are grouped together in a line with positive slope. Practice Hours vs. Points Scored A graph has practice time (hours) on the x-axis and points scored on the y-axis. Points are grouped together in a line with positive slope. What comparison can be made between the two sets of data in the table? They both have strong positive correlation. They both have weak positive correlation. They both have strong negative correlation. They both have weak negative correlation.
Answer:
a. They both have strong positive correlation.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Just took the test and did calculations. 100% correct
Answer this question
Answer:
c) 120
Step-by-step explanation:
f(x) = 7x^4 + 3x^2 - 4
f(-2) = 7(-2)^4 + 3(-2)^2 - 4 = 7(16) + 3(4) - 4 = 112 + 12 - 4 = 120
Answer:
120Step-by-step explanation:
Given,
x = -2
Now, let's solve
[tex] {7x}^{4} + 3 {x}^{2} - 4[/tex]
Plug the value of x
[tex] = 7 \times {( - 2)}^{4} + 3 \times {( - 2)}^{2} - 4[/tex]
A negative base raised to an even power equals a positive
[tex] = 7 \times {2}^{4} + 3 \times {2}^{2} - 4[/tex]
Evaluate the power
[tex] = 7 \times 16 + 3 \times 4 - 4[/tex]
Multiply the numbers
[tex] = 112 + 12 - 4[/tex]
Add the numbers
[tex] = 124 - 4[/tex]
Subtract the numbers
[tex] = 120[/tex]
Hope this helps ...
Best regards!!
A necklace contains twenty-four spherical beads of silver, each having a radius of 0.5cm. The beads are to be coated, and the cost of coating is $10 per cm2. What is the approximate total cost, to the nearest cent, for coating the beads?
Answer:
$153
Step-by-step explanation:
To find the total cost, we have to calculate the area of one bead, then all of them:
Area of one bead = pi x r^2 = 3.14 x 0.5^2 = 3.14 x 0.25 = 0.765cm^2
Area of 20 beads = 0.765 x 20 = 15.3cm^2
Now, we are able to calculate the ultimate cost of coating:
If the cost is $10 per cm^2, then we have to find how much it costs to coat 15.3 cm^2.
15.3 x 10 = $153.
Hope this helps