Is value of the 2 in the tenths place the same value of the 2 in the ones place?

There are 21 different city combinations possible for Peter's summer traveling.

To determine the number of different city combinations possible for Peter's summer traveling, we need to calculate the number of combinations of choosing 5 cities out of the 7 available cities.

Since the order in which he visits the cities does not matter, we are dealing with combinations rather than permutations.

The formula to calculate the number of combinations is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k) or (nCk).

In this case, we have 7 cities to choose from, and Peter will visit 5 cities. Thus, we can calculate the number of city combinations as follows:

C(7, 5) = 7! / (5! * (7-5)!)

= 7! / (5! * 2!)

= (7 * 6 * 5!) / (5! * 2)

= (7 * 6) / 2

= 42 / 2

= 21

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The range of the starting salaries is 53,000

Given,

The box and whisker plot below shows the starting salaries

The number of graduates in a small college = 120

We have to find the range of the starting salaries;

Range of a data;

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.

Here,

Lowest value = 19,000

Highest value = 72,000

Then,

Range of the set = 72,000 - 19,000 = 53,000

That is,

The range of the given data set is 53,000

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The value of c such that the function f is a probability density function is 2

The density function is given as:

f(x) = cxe^(−x^2) if x ≥ 0

f(x) = 0 if x < 0.

We start by integrating the function f(x)

∫f(x) = 1

This gives

∫ cxe^(−x^2) = 1

Next, we integrate the function using a graphing calculator.

From the graphing calculator, we have:

c/2 * (0 + 1) = 1

Evaluate the sum

c/2 * 1 = 1

Evaluate the product

c/2 = 1

Multiply both sides of the equation by 2

c = 2

Hence, the value of c such that the function f is a probability density function is 2

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Answer:

f(-2) = -1

Step-by-step explanation:

f(p) = p^2 + 3p + 1

Let p = -2

f(-2) = (-2)^2 + 3*-2 + 1

      = 4 -6 +1

     -1

1. About 144 scoops of ice cream were served last Thursday.

2.Doris has 5 quarters, 10 dimes, and 5 nickels, and 4 pennies.

1. There are 16 ounces in a pound, so 18 pounds of ice cream weigh:

18 pounds * 16 ounces/pound = 288 ounces

Since one scoop of ice cream weighs 2 ounces, the number of scoops served is:

288 ounces / 2 ounces/scoop = 144 scoops

Therefore, about 144 scoops of ice cream were served last Thursday.

2. Let's use "q", "d", "n", and "p" to represent the number of quarters, dimes, nickels, and pennies that Doris has, respectively.

From the problem statement, we know that:

n = q (the number of nickels equals the number of quarters)

d = 2q (the number of dimes is twice the number of quarters)

n = 5 (she has 5 nickels)

We can use this information to write an equation for the total value of Doris's coins:

0.25q + 0.10d + 0.05n + 0.01p = 2.54

Substituting the values for n and d in terms of q, we get:

0.25q + 0.10(2q) + 0.05(5) + 0.01p = 2.54

Simplifying and solving for q, we get:

0.45q + 0.05 + 0.01p = 2.54

0.45q + 0.01p = 2.49

45q + p = 249

Since Doris has a total of 24 coins, we can write another equation:

q + d + n + p = 24

Substituting the values for n and d in terms of q, we get:

q + 2q + q + p = 24

4q + p = 24

We now have two equations with two unknowns:

45q + p = 249

4q + p = 24

Subtracting the second equation from the first, we get:

41q = 225

Solving for q, we get:

q = 225/41 ≈ 5.49

Since q must be a whole number, the closest integer value is 5. Substituting this value back into the equations for n and d, we get:

n = q = 5

d = 2q = 10

Finally, we can use the equation for the total number of coins to find the value of p:

q + d + n + p = 24

5 + 10 + 5 + p = 24

p = 4

Therefore, Doris has 5 quarters, 10 dimes, and 5 nickels, and 4 pennies.

Quarters are a type of coin used in the United States currency system. A quarter is worth 25 cents or 1/4 of a dollar. It has a diameter of 0.955 inches (24.26 mm) and a thickness of 0.069 inches (1.75 mm). The front side of the coin features a portrait of George Washington, the first president of the United States, and the back side features an eagle. Quarters are commonly used in daily transactions to make small purchases or provide change.

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The expression we have is

To simplify the expression, the first step is to separate the fourth root:

On the right-hand side, in the numerator, we can no simplify further, but in the denominator, we can use the following law of exponents:

Thus:

Since 2/4 is equal to 1/2:

Next, we use the same law of exponents:

With n/m as 1/2:

Finally, we simplify the expression to:

Answer:

Answer:

y = 4

Step-by-step explanation:

distribute

10 + 2y = 18

minus 10 from both sides

2y = 8

divide by 2

y = 4

Answer: y=4

Step-by-step explanation:

2(5+y)=18

youre going to start by distributing the 2 to (5+y)

10+2y=18

then subract 10 from 18

2y=8

and then divide 2 on both sides

y=4

The evaluation of the expression using the order of operations, indicates the operations that come first as follows;

(5 + 5)² + 15 - 10 Parenthesis

40 ÷ 8 · 4  + 2; Division

4 - 2 + 3 · 5; Multiplication

(3² + 8) ÷ 7 - 5; Parenthesis

The order of operations is a rule that serves as a guide for the correct sequence of performing operations in an equation or expression.  

The evaluation expressions can be presented as follows;

First operation;

(5 + 5)² + 15 - 10

The order of operations, PEMDAS, indicates that we get;

1) Parenthesis first

2) Exponents

3) Multiplication and division

4) Addition and subtraction

Based on the above PEMDAS order of operation, the step that should be completed first is the operation within the parenthesis, which is the addition operation (5 + 5)

The correct option is; Parenthesis

Second expression;

40 ÷ 8 · 4 + 2

The operations in the expression are; division, multiplication, and addition

The order of operations indicates that division, which comes first, from the left, should be performed first. The correct option is therefore;

40 ÷ 8 · 4 + 2; division

Third expression;

4 - 2 + 3 · 5

The subtraction is the first operation from the left, but the order of operations, PEMDAS, indicates that the multiplication, 3 · 5 should be performed first, therefore;

Fourth expression;

(3³ + 8) ÷ 7 - 5

The parenthesis which comes first in the order of operations and first among the operations from left to right comes first

Therefore, the parenthesis comes first;

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There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer: x<69

Step-by-step explanation:

For this problem, we solve is just as we would if it was an equal sign.

x+9<78       [subtract 9 on both sides]

x<69

The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.

Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\)  2. 2\(x^{0}\)\(y^{-2}\)

Expression for x =2 and y=5

-4x-2 + 3y0

= -4(2)-2 + 3(5)0

= 16+3

=19

Now

2x0y-2

= 2(2)0x(5)-2

= 2 x (1/25)

= 2 x 0.04

= 0.08

Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

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Answer:

Please check the explanation.    

Step-by-step explanation:

Given the expression

\(\:x^3+25\:\)

Please note that the given expression could not factor further.

But, wait!

Let me take a sample expression and factor that sample expression so that you could get an idea of how to factorize the expression

Given the sample expression

\(x^2-5x+6\)

Breaking the expression into groups

\(\:x^2-5x+6=\left(x^2-2x\right)+\left(-3x+6\right)\)

Factor out x from x²-2x: x(x-2)

Factor out -3 from -3x+6: -3(x-2)

                   \(=x\left(x-2\right)-3\left(x-2\right)\)

Factor out the common term (x-2)

                   \(=\left(x-2\right)\left(x-3\right)\)

Thus, factorizing the expression such as:

\(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)      

Answer:

G and J

Step-by-step explanation:

Answer:

z > -9

Step-by-step explanation:

Combine like factors.

18 - 5z + 6z > 3 + 6

18 - 5z + 6z > 9

18 + z > 9

Solve for z.

18 + z > 9

(18 + z) - 18 > 9 - 18

z > -9

The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

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Step-by-step explanation:

higher

Answer:

a. p`± z₀.₀₂₅\(\sqrt{ \frac{p`q`}{n}\)  

b.0.6 ±  1.96 \(\sqrt \frac{0.6* 0.4}{1000}\)  

c. { -1.96 ≤  p`± z₀.₀₂₅\(\sqrt{ \frac{p`q`}{n}\)     ≥ 1.96} = 0.95  

Step-by-step explanation:

Here the total number of trials is n= 1000

The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4

The degree of confidence is 95 %  therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)

a.  The formula used will be

p`± z₀.₀₂₅\(\sqrt{ \frac{p`q`}{n}\)       ( z with the base alpha by 2 (α/2 = 0.025))

b. Putting the values

0.6 ±  1.96 \(\sqrt \frac{0.6* 0.4}{1000}\)  

c. Confidence Interval in Interval Notation.

{ -1.96 ≤  p`± z₀.₀₂₅\(\sqrt{ \frac{p`q`}{n}\)     ≥ 1.96} = 0.95  

{ -z( base alpha by 2) ≤  p`± z₀.₀₂₅\(\sqrt{ \frac{p`q`}{n}\)     ≥ z( base alpha by 2)  } = 1- α

Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A' = (-3, 3 + 3) = (-3, 6)

B' = (0, 7 + 3) = (0, 10)

C' = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).

So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).

Answer:

b is the answer am not sure you know

Answer:

a) 3/10

b)3/10

Step-by-step explanation:

let the sample of people be 10

so,

a) total outcome=10

favourable outcome=3

P(seeing a UFO)= 3/10

b) total outcome=10

favourable outcome=2 or 3

P(seeing a UFO)= 2/10+3/10-(2/10

5/10-2/10

=3/10

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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Answer:

8:7

Step-by-step explanation:

Answer: 1980 calories

Step-by-step explanation:

290grams of carbs=1160g

60 grams of fat=540

70 grams of protein=280 calories

290 x 4=1160

60 x 9=540

70 x 4=280

1160+540+280=1980 calories

carbs provide 4 calories per gram

fat provides 9 calories per gram

protein provides 4 calories per gram

Answer:

\(58 m^{2}\)

Step-by-step explanation:

Seperate it into two pieces;

Piece 1, base of 2, height of 9

Piece 2, base of 8, height of 5.

Area of Piece 1:

A = bh

A = 2 (9) = 18

Area of Piece 2:

A = bh

A = 8 (5) = 40

Add the areas of both pieces:

18 + 40 = 58 m2

Answer:

\(\dfrac{1}{216}\) = 0.005 (nearest thousandth)

Step-by-step explanation:

geometric series formula:  \(a_n=ar^{n-1}\)

where a is the first term and r is the common ratio

Given:

\(r=\dfrac{a_2}{a_1}=\dfrac{36}{216}=\dfrac16\)

\(\implies a_n=216 \cdot \dfrac16^{n-1}\)

\(\implies a_7=216 \cdot \dfrac16^{7-1}=\dfrac{1}{216}=0.005\)