Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 21 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Answer:

Step-by-step explanation:

2 hour

Step-by-step explanation:

City A to City B : 1580 miles

Plane speed (C) to City B from A : 400 miles per hour

Plane speed (D) to City A from B : 390 miles per hour

Time taken for plane (C) :

=1580 ÷ 400

=3⁹/²⁰ hours

Time taken for plane (D) :

=1580 ÷ 390

=4²/³⁹ hours

Finding time difference

= 4²/³⁹ - 3⁹/²⁰

=469/780

Finding midpoint

= 469/780 ÷ 2

=469/1560

Total

= 3⁹/²⁰ + 469/1560

= Aprroximately 3¾ hours

1) There are 3.4 * 10^1 in Mexico than in Canada.

2) The number of ounces that were consumed is 20.8 * 10^7 ounces

3) The number of ounces of the students at the community college is 1.25 * 10^1 that of the students in the University.

Scientific notation is a way of writing very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power.

1) Ratio of people in Mexico to those in Canada;

1.3 * 10^8/3.8 * 10^7

= 3.4 * 10^1 : 1

2) Number of Ounces consumed by students = 5.2 * 10^4 * 4 * 10^3

= 20.8 * 10^7 ounces

3) Ratio of the number drank by community college to University

= 4 * 10^3/3.2 * 10^2

1.25 * 10^1

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Using the given percentages, we can see that 126 students preferred cola.

To find this number, we just need to multiply the correspondent percent by the total number of students.

First, write the percent in decimal form, to do so, divide it by 100%.

20% of the students preferr cola, so we need to write:

20%/100% = 0.2

And the total number of students is 630, so the number that preffered cola is:

0.2*630 = 126

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The equation that represents the relationship is y = -14.8x - 35. (option D)

A linear equation is an equation that consists of a single variable that is raised to the power of one. The general form of a linear equation is y = mx + c

Where:

The form of the equation that represents the relationship is:

Millimeters of oil = amount of oil the diya holds - (burn rate x number of hours)

y = 35 - (14.8 x x)

y = 35 - 14.8x

y = -14.8x - 35

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27.30 round to the 2nd decimal place is 27.30.

Now we have to find 7.2% of $27.30.

7.2% of $27.30 is 1.9656.

If you mean that we have to round the answer bt 2 decimal place then the answer is 1.97.

Answer:

okay?

Step-by-step explanation:

is this a true or false

Answer:  the team won 154g / (g + 1) games and lost 154 / (g + 1) games.

Step-by-step explanation: The mathematical equation "W/L = g" is expressed in a concise manner, wherein "W" refers to weight, "L" refers to the length, and "g" represents the gravitational acceleration. This equation can be utilized in various scientific and academic disciplines, particularly in the field of physics, engineering, and mechanics. The relationship between weight, length, and gravitational acceleration can be further explored and examined through research studies and experiments.

The equation in consideration may be rendered less intricate through the process of multiplication of both sides by L.

"The equation W = gL" can be expressed in an academic manner as follows: The equation denoted by W = gL can be deduced as the product of the gravitational acceleration (g) and the length (L) of an object in a given direction. This equation is commonly used in physics to determine the work (W) performed on an object as a result of a force acting on it, in correlation with the displacement it undergoes in the same direction.

It is understood that the summation of the games won and lost by the team is equivalent to the overall number of games that were played.

The equation denoting the sum of W and L yields a value of 154.

The first equation may now be replaced in the second equation, resulting in:

The mathematical equation GL + L = 154 represents an algebraic expression, where 'G' and 'L' are variables that denote unknown numerical values. The equation dictates that the sum of the values assigned to 'GL' and 'L' must equal to 154. Such equations are commonly used to solve numerical problems in mathematics and related disciplines.

One should perform the mathematical operation of factoring out the variable L on the left-hand side.

The equation L(g + 1) = 154 can be expressed with greater academic rigor.

The sides can be divided by (g + 1) to simplify the equation.

The equation L = 154 / (g + 1) represents a mathematical relationship wherein L is determined by dividing 154 by the sum of g and one.

The aforementioned equation can be utilized to derive a solution for W, ascertaining the relationship that W is equivalent to gL.

The presented expression, W = g(154 / (g + 1)), exhibits a mathematical relationship between the variables W and g, whereby W is a function of g. The numerator of the parenthetical expression, 154, is divided by the sum of g and one, then this ratio is multiplied by g to produce the value of W. The formula can be utilized in various disciplines, such as physics, engineering, and mathematics.

The expression can be simplified to yield:

The expression W can be denoted as 154g / (g + 1) in accordance with the commonly recognized conventions of formal academic writing.

Answer:27 paper cups.

Step-by-step explanation:

The volume of each cone-shaped cup can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the cone (half the diameter), and h is the height of the cone.

Substituting the given values, we get:

V = (1/3)π(10/2)^2(12) ≈ 1256.64 cubic centimeters

We can convert the 9 gallons of lemonade to cubic centimeters using the conversion factor given:

1 gallon ≈ 3785 cubic centimeters

Therefore:

9 gallons * 3785 cubic centimeters/gallon ≈ 34,065 cubic centimeters of lemonade

To find out how many paper cups are needed, we can divide the volume of the lemonade by the volume of one cone-shaped cup:

34,065 cubic centimeters / 1256.64 cubic centimeters ≈ 27 cups

Therefore, approximately 27 paper cups are needed to sell all of the lemonade.

A 95% confidence interval for the population mean length of engineering conferences is 3.70, 4.26.

The error bound based on the information will be 0.28.

95% confidence interval for the population mean length of engineering conferences is:

= 3.98 +- (1.969 (0.142)

= 3.98 +- 0.218

= 3.70, 4.26

The error bound based on the information will be:

= (1.96( (0.142)

= 0.28.

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The answer  is , (a) the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).  , (b) we cannot definitively conclude that the results contradict the expectation.

A confidence interval is a range of values that is used to estimate the true value of an unknown parameter, like a population mean or proportion, based on a sample of data. It is a statistical measure of the precision and reliability of an estimate, and it provides a measure of the uncertainty or margin of error associated with the estimate.

a. To construct  95% confidence interval for percentage of yellow peas, we can use  following formula as :

CI = p ± z*(√((p*(1-p))/n))

Where:

p = proportion of yellow peas = 152/(431+152) = 0.2613

z = z-value for a 95% confidence interval = 1.96 (from standard normal distribution table)

n = sample size = 431+152 = 583

Plugging in the values, we get:

CI = 0.2613 ± 1.96*(√((0.2613*(1-0.2613))/583))

CI = 0.2613 ± 0.0365

CI = (0.2248, 0.2978)

Therefore, the 95% confidence interval for the percentage of yellow peas is (22.48%, 29.78%).

b. The expected percentage of the yellow peas is 25%. Since the lower limit of the confidence interval is 22.48%, which is less than 25%, it suggests that the actual percentage of yellow peas may be lower than expected. However, since the confidence interval does include 25%, we cannot definitively conclude that the results contradict the expectation.

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Answer: b

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation: The probability that the company will hire two women for positions is : 1/4 because..

The total number of possible outcomes = 4.

The event in which two women are chosen = 1.

or (1/2)*(1/2) = 1/4

The slope of the line passing through points A and B is 1/3.

The formula for the slope of a line to find the slope passing through points A and B. The formula is:

slope = (change in y) / (change in x)

Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).

Then, substitute the values and calculate the slope:

slope = (y₂ - y₁) / (x₂ - x₁)

slope = (3 - 2) / (3 - 0)

slope = 1 / 3

Therefore, the slope of the line passing through points A and B is 1/3.

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[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_4(y)=2\implies 4^2=y\implies 16=y\hspace{5em} {\Large \begin{array}{llll} \log_4(16)=2 \end{array}}[/tex]

The volume of the right pyramid is 23 1/3 cm³. The correct option is E,

Given that the length of the side of the right pyramid is 3.75 cm, While the height of the pyramid is 5 cm. Therefore, the volume of the given right pyramid is:

Volume = (1/3) × (side length)² × Height

              = (1/3) × (3.75 cm)² × 5 cm
              = 23.33 cm³

              = 23 1/3 cm³

Hence, the volume is 23 1/3 cm³.

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The complete question must be:

What is the volume of the right pyramid with the base lenght of 3.75 cm and height of 5cm?

A. 186 and 2-thirds centimeters cubed

B. 84 centimeters cubed

C. 25 centimeters cubed

D. 23 and 1-third centimeters cubed

E. 18 and 2-thirds centimeters cubed

The set of odd integers between three and five can be found to be D. A null set.

An odd number is defined as an integer that cannot be split exactly by two. For example: 1, 3, 5, 7, and so on.

We are asked about the set of odd integers ranging from 3 to 5. Because the question asks for odd numbers between 3 and 5, 3 and 5 will not be considered in the set.

This indicates that 3 and 5 are out. We are left with only one even number, four.

As a result, the set of odd integers between 3 and 5 is a Null Set (it contains no numbers).

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The full question is:

What is the set of odd integers between three and five?

4

3,4,5

all reall numbers

null set

[tex]\tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \qquad \tan(\alpha - \beta) = \cfrac{\tan(\alpha)- \tan(\beta)}{1+ \tan(\alpha)\tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-1+\tan(x)}{1+\tan(x)}\implies \cfrac{-1+\tan(x)}{1-(-1)\tan(x)} \\\\\\ \cfrac{\tan\left( \frac{3\pi }{4} \right)+\tan(x)}{1-\tan\left( \frac{3\pi }{4} \right)\tan(x)}\implies \tan\left( \cfrac{3\pi }{4} + x\right)[/tex]

Answer: The Length of the radius of the circle is 17 inches.

Round off 87654 to the nearest hundred?

Marching into my territory,eh?

we need to look at the tens and ones digit of the number. The digit in the hundreds place is 6, which tells us that the number is already in the thousands place.

The tens digit is 5, which is greater than or equal to 5. This means we need to round up the hundreds place to the next digit. Therefore, the rounded number to the nearest hundred is 87700.

The binary system is a numerical system that uses only two digits, 0 and 1, to represent numbers.

We have,

It is also known as the base-2 system.

In contrast, the decimal system, which is the most commonly used numerical system, uses ten digits (0 to 9) to represent numbers.

In the binary system, each digit represents a power of 2, starting with 2^0, which equals 1, and then doubling for each successive position (2^1, 2^2, 2^3, and so on).

Therefore, the decimal number 10, for example, is represented in binary as 1010, where the first 1 represents 2^3, the next 0 represents 2^2, the next 1 represents 2^1, and the last 0 represents 2^0.

The binary system is used in digital electronics and computing, where the two states of a switch or transistor can represent 0 or 1.

Thus,

The binary system is a numerical system that uses only two digits, 0 and 1, to represent numbers.

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The complete question:

What is the binary system?

Using the monthly interest rate and the principal given the interest saved is -$16.8 which shows that nothing was saved.

To find the interest saved, let's calculate the interest paid on the credit card.

Monthly interest = 9.85 / 12 = 0.82%

The monthly interest rate on the card is 0.82%

For that particular month, the interest charged will be;

Interest = 2154.35 * 0.0082 = $17.7

However, the interest earned on the savings account will be;

Interest = 2.5 / 12 = 0.21%

We can calculate the interest earned as;

Interest = 0.0021 * 435 = $0.91

The interest saved can be calculated as 0.91 - 17.7 = -16.8

This shows that nothing was saved as the interest earned is lower than the interest charged.

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The composition f∘g is given by (13) / (x - 13).

The domain of the composition is all real numbers except for x = 13, which can be represented in interval notation as (-∞, 13) U (13, ∞).

To find the composition f∘g, we need to substitute g(x) into f(x) in the following way:

f(g(x)) = f(13/x) = (13/x) / ((13/x) - 1)

To simplify this expression, we can multiply both the numerator and denominator by x, which gives us:

f(g(x)) = (13) / (x - 13)

The domain of f(g(x)) is restricted by the domain of g(x), which is all real numbers except for x = 0. Therefore, the domain of f(g(x)) is the set of all real numbers except for x = 13.

Using interval notation, we can write the domain of f(g(x)) as:

(-∞, 13) U (13, ∞)

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The given trinomial is [tex]2a^2+5ab+7b^2[/tex]. The trinomial can be factored as (2a+7b)(a+b).

A trinomial is an algebraic expression consisting of three terms. It can be written in the form ax² + bx + c, where a, b, and c are constants and x is a variable. Trinomials are also used to solve equations, such as quadratic equations.

To factor this trinomial, we will first split the trinomial into two groups. The two groups are (2a, 7b) and (a, b).

Now we will multiply the first terms of both the groups.

We will get 2a × a = 2a².

This is the first term of the trinomial. Now we will multiply the second terms of both the groups.

We will get 7b × b = 7b².

This is the last term of the trinomial. Now we will multiply the first term of the first group and the second term of the second group.

We will get 2a × b = 2ab.

This is the middle term of the trinomial.

Hence, the trinomial can be factored as (2a+7b)(a+b).

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The measure of each angle in the triangle is 60 degrees each

To determine the measure of the angles, we need to note that the sum of the angles in a triangle is equal to 180 degrees.

This is represented as;

<A + <B + <C = 180

From the information given in the diagram, we have;

Then, we have that;

2x - 120 + x - 30 + 1/2x + 15 = 180

add the like terms

2x + x + x/2 = 180 + 120 + 30 - 15

Add or subtract the like terms

3x + x/2 = 315

6x + x/2 = 315

cross multiply the values

7x = 630

Divide both sides by the coefficient

x = 90

Then, the angles are;

2x - 120 = 60 degrees

x/2 + 15 = 60 degrees

x - 30 = 60 degrees

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The value of A when we rewrite 6^x as A^x/4 is 3/2

An algebraic expression can simply be defined as a mathematical expression that consists of terms, factors, constants, coefficients and variables.

They are also known as expressions made up of arithmetic operations, such as;

From the information given, we have that;

The function is given as;

6^x

Here, the coefficient or rather the base is 6

To determine the value of A when ^^x is given as A^x/4

The value of A would be;

6/4 = 3/2

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Answer:

240 cubic inches.

Step-by-step explanation:

To calculate the volume of the sandcastle decoration in the fish tank, we can use the formula:

Volume of the decoration = Total volume of water after adding the decoration - Volume of water before adding the decoration

The volume of water before adding the decoration is the volume of the rectangular prism formed by the fish tank, which is:

Volume of water before = Length x Width x Height

= 16 x 15 x 12

= 2,880 cubic inches

After Kyle added the sandcastle decoration, the water level rose to 13 inches. This means the volume of water in the tank increased by the volume of the decoration. The new volume of water in the tank is:

Volume of water after = Length x Width x Height

= 16 x 15 x 13

= 3,120 cubic inches

Therefore, the volume of the sandcastle decoration is:Volume of decoration = Volume of water after - Volume of water before

= 3,120 - 2,880

= 240 cubic inches

Therefore, the volume of the sandcastle decoration in the fish tank is 240 cubic inches.

Answer:

Step-by-step explanation:

i sorry dont know

For the experiment by Cliff, the bar graph will most likely have the same height for the number of times each letter appears.

For the experiment by Devon, the bar graph will most likely have the same height for the number of times the letter A, E, and U appears and the same height for the number of times O and I appear. However, the height of the bar graphs for O and I will most likely be half that of A, E, and U.

For the experiment by Cliff, the probability of the letters appearing is given below:

The letters have equal chances of being picked, hence, their probabilities are equal.

Probability = 1/5

For the experiment by Cliff, the probability of the letters appearing is given below:

The letters A, E, and U have equal chances of being picked, hence, their probabilities are equal.

P(A) = 1/4

P(E) = 1/4

P(U) = 1/4

The letters O and I have equal chances of being picked, hence, their probabilities are equal.

P(O) = 1/8

P(I) = 1/8

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1)  the number pattern is obscure2) The number pattern seems to be alternating 3)  The number pattern seems to be increasing

1) The pattern of the numbers is obscure. The connections between the numbers are not immediately apparent.

2) The number pattern seems to be alternating between subtracting 1 and adding 2 to the previous number. The missing numbers are 27 and 28.

3) The number pattern seems to be increasing by 3, then decreasing by 4, then increasing by 2, and so on. The missing numbers are 19 and 16.

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The prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.

Using prime factorisation:

a). 17850 = 2 × 3 × 5² × 7 × 17

b). Greatest common factor of 735 and 1715 is;

735 = 3 × 5 × 7²

1715 = 5 × 7³

GCF = 5 × 7²

GCF = 244

c). Lowest common multiple of 180 and 450 is;

180 = 2² × 3² × 5

450 = 2 × 3² × 5²

LCM = 2 × 3² × 5³

LCM = 900

Therefore, the prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.

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