How many three-digit numbers can be formed under each condition?
(a) The leading digit cannot be zero.

(b) The leading digit cannot be zero and no repetition of digits is allowed.

(c) The leading digit cannot be zero and the number must be a multiple of 3.

(d) The number is at least 400.

Answer:

.20x = 72, so x = 360

.30(360) = 108

Answer:

The 10th term is -524,288

Step-by-step explanation:

The general format of a geometric sequence is:

\(a_{n} = r*a_{n-1}\)

In which r is the common ratio and \(a_{n+1}\) is the previous term.

We can also use the following equation:

\(a_{n} = a_{1}*r^{n-1}\)

In which \(a_{1}\) is the first term.

The common ratio of a geometric sequence is the division of the term \(a_{n+1}\) by the term \(a_{n}\)

In this question:

\(a_{1} = 2, a_{2} = -8, r = \frac{-8}{2} = -4\)

10th term:

\(a_{10} = 2*(-4)^{10-1} = -524288\)

The 10th term is -524,288

Answer:

g

Step-by-step explanation:

The given expression is arcsin (-√3/2), which represents the angle whose sine is equal to -√3/2. Recall that the range of the arcsin function is from -π/2 to π/2 radians, so we can narrow down the possible solutions to the second and third quadrants.

Since the sine function is negative in the third quadrant, we can start by considering the angle 4π/3, which is in the third quadrant and has a sine of -√3/2:sin(4π/3) = -√3/2

However, we need to check if there are any other angles in the second or third quadrants that satisfy the equation. Recall that sine is periodic with a period of 2π, so we can add or subtract any multiple of 2π to the angle and still obtain the same sine value.

In the second quadrant, we can use the reference angle π/3 to find the corresponding angle with a negative sine:

sin(π - π/3) = sin(2π/3) = √3/2

This angle does not satisfy the equation, so we can eliminate it as a possible solution.In the third quadrant, we can use the reference angle π/3 to find another possible solution:

sin(π + π/3) = sin(4π/3) = -√3/2

This confirms our initial solution of 4π/3, so the answer is (g) 4π/3.

Let me know if this helped by hitting brainliest! If you have a question, please comment and I"ll get back to you ASAP!

Answer:

We know that sin(π/3) = √3/2, so we can write:

arcsin(-√3/2) = -π/3 + 2nπ or π + π/3 + 2nπ

where n is an integer.

Therefore, the values of arcsin(-√3/2) are:

a. π/3 + 2nπ

c. 11π/6 + 2nπ

e. 2π/3 + 2nπ

f. 7π/6 + 2nπ

So, options a, c, e, and f are all correct.

The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

To know more about standard deviation here

https://brainly.com/question/12402189

#SPJ1

The question is incomplete. The complete question will be -

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

1:1 ratio is 1 part or 1 unit of a particular quantity.

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

For similar questions on athletes

https://brainly.com/question/25631156

#SPJ11

The antifreeze used by each brand will be V₁ = 72 gal. and V₂ = 108 gal.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that

ω₁ = 70% ÷ 100% = 0.7; 70% pure antifreeze.

ω₂ = 95% ÷ 100% = 0.95.

ω₃ = 85% ÷ 100% = 0.85.

V₁ = ?; volume of 70% antifreeze.

V₂ = ?; volume of 95% antifreeze.

V₃ = V₁ + V₂.

V₃ = 180 gal.

The quantity will be calculated as:-

V₁ = 180 gal - V₂.

ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.

0.70 · (180 gal - V₂) + 0.95 · V₂ = 0.85 · 180 gal.

126gal - 0.7V₂ + 0.95V₂ = 153 gal.

0.25V₂ = 27 gal.

V₂ = 27 gal ÷ 0.25.

V₂ = 108 gal.

V₁ = 180 gal - 108 gal.

V₁ = 72 gal.

To know more about an expression follow

https://brainly.com/question/13947685

#SPJ1

Answer:

Matrix :

\(\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}\)

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

\(\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}\)

Matrix :

\(\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}\)

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

\(\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}\) - Swap Matrix Rows

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}\) - Cancel leading Co - efficient in second row

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}\) - Cancel leading Co - efficient in third row

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}\) - Swap second and third rows

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}\) - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

\(\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}\)

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Answer:

2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7

To solve for the value of 3/5x, we can start by distributing.

-86 = 4 + 5(3x - 3) → -86 = 4 + 15x - 15

-86 = 15x - 11

-86 = 15x - 11 → -75 = 15x

-75 = 15x → -5 = x

Therefore, x = -5.

To find the value of 3/5x, we can plug in -5 for x.

3/5(-5) = -3

Hence, the value of 3/5x is -3.

Answer:

It will take 28 minutes to complete a 7-kilometer race

Step-by-step explanation:

If you can job 3 kilometers in 12 minutes, that means you can jog 1 kilometer in 4 minutes. so if you multiply 7 times 4, you would get 28. So your answer is 28 minutes.

Systematic sampling involves selecting every nth item from a list, potentially with bias and non-random results, so choose carefully.

The method used to choose the sample in this study is called "systematic sampling". This involves selecting a starting point (in this case using a random number generator) and then selecting every nth item (in this case, every 3rd person) from a list to form the sample. This type of sampling can introduce biases in the sample if the list has some pattern or structure, so it's important to be aware of these potential issues when using this method.

In systematic sampling, the selection of each member of the sample is based on a fixed and systematic rule. The advantage of this method is that it is easy to implement and cost-effective. The disadvantage is that if the list has any pattern or structure, such as alternation or clustering, the sample may not be representative of the population. It's important to carefully consider the list and choose an appropriate starting point and interval to reduce the potential for bias.

It's also worth noting that systematic sampling may not result in a random sample, as the sample members may not be independent of each other. This can have implications for the validity of inferences made from the sample to the population. Therefore, it's important to carefully consider the properties of the population and the goals of the study when choosing a sampling method.

Learn more about systematic sampling here:

https://brainly.com/question/28454088

#SPJ4

The correct option is A, we have a translation of 7 units to the right.-

To find it, we need to analyze two correspondent vertices.

We can see that vertex A is at (1, 5), while the correspondent vertex A' is at (8, 5)

Taking the difference between that, we will get:

A' - A = (8, 5) - (1, 5) = (8 - 1, 5 - 5) = (7, 0)

The first value gives the horizontal translation and the second the vertical one

So,we have a translation of 7 units to the right, the correct option is A.

Learn more about translations at:

https://brainly.com/question/24850937

#SPJ1

A counter-example to the given conclusion is the difference between the numbers 15 and 25, where both are positive, but the difference gives a negative result.

Here we are shown some differences between positive numbers:

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

And the conclusion is:

"The difference of two positive numbers is always positive".

To find a counter-example we just need to find two positive numbers such that the difference between these two positive numbers gives a negative number as a result.

An example of that can be the numbers 15 and 25, if we take the difference we will get:

15 - 25 = -10

Here we can see that the difference between two positive numbers gives a negative number as an outcome, so this is our counter-example.

If you want to learn more about counter-examples:

https://brainly.com/question/1581078

#SPJ1

Answer:

Step-by-step explanation:

\(-5\frac{1}{7} \div 2\frac{2}{5} =-\frac{36}{7}\div \frac{12}{5}\)

                \(=-\frac{36}{7} \times \frac{5}{12}\)

                \(=-\frac{3}{7} \times \frac{5}{1}\)           (÷ top and bottom by 12)

                \(=-\frac{15}{7}\)

                \(=-2\frac{1}{7}\)

Answer:

The percentage is 68.26%

Step-by-step explanation:

Before we use the empirical rule , we need to find the value of the z-score

Mathematically;

z-score = (x - mean)/SD

Thus;

z-score = (7.85 - 7.45)/0.4 = 0.4/0.4 = 1

So the percentage we want to calculate now is the percentage of values within 1 standard deviation of the mean

According to the empirical rule, 68.26% of values are within 1 standard deviation of the mean

Answer:

\(y = 14x + 3400\)

Step-by-step explanation:

Represent

- number of jackets with x

- costs of jackets with y

So, we have:

\((x_1,y_1) = (150,5500)\)

\((x_2,y_2) = (370,8580)\)

Required

Write an equation in form of y = mx + b

First, we need to determine the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{8580 - 5500}{370 - 150}\)

\(m = \frac{3080}{220}\)

\(m = 14\\\)

The equation is calculated using:

\(y-y_1 = m(x - x_1)\)

Where

\(m = 14\\\)

\((x_1,y_1) = (150,5500)\)

So, we have:

\(y - 5500 = 14(x - 150)\)

\(y - 5500 = 14x - 2100\)

Make y the subject

\(y = 14x - 2100 + 5500\)

\(y = 14x + 3400\)

To find the cubed root of the expression (1000p/12a/3)^(1/3), we can simplify the expression first. Let's break it down step by step:

1. Simplify the expression inside the parentheses:

 \(1000p/12a/3 = (1000p/12) / (a/3)\\ = (1000p/12) * (3/a)\\ = 250p/a\)

2. Now, we have\((250p/a)^(1/3)\), which represents the cubed root of 250p/a.

To find the cubed root, we can rewrite it as (250p/a)^(1/3) = (250p)^(1/3) / (a)^(1/3).

Next, we can simplify each term separately:

a) (250p)^(1/3):

  This represents the cubed root of 250p. Since the exponent is 1/3, we can rewrite it as the cube root of 250p. Evaluating the cube root of 250p gives us a numerical value.

b) (a)^(1/3):

  This represents the cubed root of 'a'. Similarly, we can evaluate the cube root of 'a' to obtain a numerical value.

Finally, we divide the numerical value of (250p)^(1/3) by the numerical value of (a)^(1/3).

It's important to note that without specific values for 'p' and 'a', we can't provide an exact numerical result. However, the steps provided above should help you simplify and calculate the cubed root of the given expression.

For more such questions on cubed root

https://brainly.com/question/30395231

#SPJ8

Answer:

Step-by-step explanation:

Answer:

148 and 143

147.667 round all of the cent you get 148 dollars

same as the first then you get 143 dollars

Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 18 I think?

Answer:

18

Step-by-step explanation:

6 (legs) x 3 (ants) = 18 legs

It can also be represented as 6+6+6 (18)

hope this helps :)

Answer:

105 ≤ x ≤ 255

Step-by-step explanation:

Given that :

Let weight range = x

130 ≤ x ≤ 280

Total weigh of gear = 25 pounds

The weight range without gear that is acceptable :

130 - weight of gear ≤ x ≤ 280 - weight of gear

130 - 25 ≤ x ≤ 280 - 25

105 ≤ x ≤ 255

The fountain is depicted by the white circle in the picture. The surrounding walkway is depicted by the grey areas.

From the sketch shown above, the semi-circle inscribed in the rectangle is one half of the fountain. We shall calculate the area of the semi-circle and subtract this from the area of the rectangle.

The area of the rectangle is;

Therefore, the area of the shaded region would be,

Area = 1275 - 127.17

Area = 1147.83

Next step is to calculate the other half of the figure (the right side), as follows;

Observe that the outer semi-circle is the shaded region while the inner one is the white portion.

The area is

The area of the shaded region is;

Area = 353.25 - 127.17

Area = 226.38

Therefore the total area of the walkway surrounding the fountain is;

Area = 1147.83 + 226.38

Area = 1374.21

Area = 1,374 feet squared (rounded to the nearest foot)

It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

Answer:

D

Step-by-step explanation:

h(x)=12-0.5x

x=hour

Answer:

y = 3

Step-by-step explanation:

Here we have:

change in y             y - 5

----------------- = -2 = ----------    or

change in x              4 - 3

 y - 5

---------- = -2, or y - 5 = -2.  Thus, y = 3

      1

Answer:

number of caps is the ratio

blue + white + green = 96

5x + 4x + 7x = 96

16x = 96

x = 6

Blue caps : 5x = 5(6) = 30

white caps : 4x = 4(6) = 24

green caps : 7x = 7(6) = 42

total of : 96 caps

Step-by-step explanation: