\(-4(3x+1)+x-3=15\)

Answer:-9.869

Step-by-step explanation:

The linear equation with integer slope representing the situation is

p = 5441 t

An algebraic description of a set of points in a coordinate system that form a line is a line equation. A line's numerous points on the coordinate axis are represented as a set of parameters x, y in order to create an algebraic equation known as a line equation. Each line's equation can be used to determine whether or not a given point is on the lines.

The equation of Line is, in fact, a one-degree linear equation.

Population in 1990 = 123000

Population in 2007 = 215500

Difference in population = 215500-123000 = 92500

Rate (slope ) of change of the population

= 92500÷17

= 5441.176 ...

≈ 5441

Hence the linear equation with integer slope to represent the population growth is given by p = 5441 t .

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It is true that statistics summarize and organize groups of numbers to make them easier to comprehend.

Statistics involves the collection, analysis, interpretation, presentation, and organization of numerical data. One of the key purposes of statistics is to summarize and organize groups of numbers to make them more meaningful and easier to comprehend. This can be done through various statistical techniques, such as measures of central tendency (e.g., mean, median, mode), measures of variability (e.g., range, standard deviation), graphical representations (e.g., histograms, bar charts), and summary statistics (e.g., percentiles, correlations). By summarizing and organizing data, statistics provide valuable insights and facilitate better understanding, interpretation, and communication of numerical information.

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2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

Given that,

TV viewers frequently doubt the validity of particular advertising. In an attempt to counter their critics, a large advertiser wants to determine the true proportion of consumers who believe what is depicted in ads. About 40% of individuals examined, according to preliminary studies, seem to believe what is depicted in advertisements.

We have to find what is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

We know that,

Let

Population proportion (p)= 0.40

Margin of error = 2% = 0.02

Confidence level = 95% = 0.95

α = 1- 0.95 = 0.05

α/2 = 0.025

Let's find out the Z critical value using excel for the 95% confidence level,

Use the following excel command.

= ABS(NORMSINV(α/2))

= ABS(NORMSINV(0.025))

We will get, Z critical value = 2.17009

Sample size (n) = p(1-p)×(Zα/2)/E

n = 0.40(1-0.40)({2.17009}÷{0.05})²

Sample size (n) = 2327

Therefore, 2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

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Answer:

they can buy 4 sodas

Step-by-step explanation:

Therefore , the solution of the given problem of angle  comes out to be  the sharp angle cos(892°) equals cos(172°) = -cos(8°).

In Euclidean geometry, the wall's top and bottom separate two circle faces, which make up of both a tilt's sides. A junction point can occur when two rays come together. Another result of two things interacting is an angle. They most closely resemble dihedral forms. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

This implies that the given angle can have multiples of 360° subtracted or added without altering the angle's cosine value.

Find an angle between 0° and 360° that has the same cosine value as 892° by doing so first.

For this, we can continually subtract 360 degrees from 892 degrees to obtain an angle between 0 degrees and 360 degrees:

=> 892° - 360° - 360° - 360° = 172°

=> Cos(892°)

therefore has the same number as cos(172°).

Since the final side of 172° and the x-axis in the second quadrant form an acute angle, we know that this angle serves as the reference angle.

We can deduce this reference angle by deducting 172° from 180°:

=> 180° - 172° = 8°

As a result, the sharp angle cos(892°) equals cos(172°) = -cos(8°).

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Answer:

4 hours

Step-by-step explanation:

3.6 / .8

The probability of Mila and Sara presenting first in that specific order can be calculated by dividing the favorable outcomes by the total number of possible outcomes. In this case, the probability is 1/105.

To determine the probability, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since the order matters in this scenario, we will use the concept of permutations. There are 15 students in the class, so the total number of possible outcomes is the number of ways to arrange 15 students, which is denoted by 15!.

For the first presentation, there is only one specific student, Mila, who needs to present first. Therefore, there is 1 way to arrange the first presentation. After Mila presents, there are 14 students left, and Sara needs to present second. So there is 1 way to arrange the second presentation as well. The remaining 13 students can be arranged in 13! ways.

To calculate the probability, we divide the number of favorable outcomes (1 * 1 * 13!) by the total number of possible outcomes (15!). Thus, the probability of Mila and Sara presenting first in that specific order is 1/105.

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To calculate the necessary amount to be deposited now and determine the interest earned in various scenarios, we can utilize the formulas and concepts related to compound interest.

a) To determine the amount that must be deposited now at a 4% interest rate compounded semiannually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the future value, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the given values, we have:

A = $305,000
r = 4% = 0.04
n = 2 (semiannually compounded)
t = 5 years

Solving for P:

$305,000 = P(1 + 0.04/2)^(2*5)

Simplifying the equation, we find that the amount to be deposited now is approximately $259,282.63.

b) To calculate the interest earned, we subtract the principal amount from the future value:

Interest = A - P = $305,000 - $259,282.63 = $45,717.37

Therefore, the interest earned is approximately $45,717.37.

c) If the company can only deposit $200,000 now, we can subtract this amount from the required future value:

Additional amount needed = $305,000 - $200,000 = $105,000

Therefore, an additional amount of $105,000 will be needed in 5 years.

d) To determine the interest rate needed for continuous compounding with a $200,000 deposit, we use the formula:

A = Pe^(rt)

Where e is the base of the natural logarithm.

Plugging in the given values:

$305,000 = $200,000 * e^(r*5)

Simplifying the equation, we find:

e^(5r) = 305,000/200,000

Taking the natural logarithm of both sides and solving for r, we can find the interest rate required for continuous compounding.

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Answer:

15

Step-by-step explanation:

f(X)= f(5)

meaning X= 5

x²-2x

5²-2(5) = 15

Answer:

a reflection over the line y= -x

Answer:

For the first question, the answer is 32 oz.

For the second question, the answer is 16 oz.

Step-by-step explanation:

For the first one, since there are 16 ounces in a pound, we can assume that since she has 3 pounds of fudge, she would have 48 ounces. She then eats one pound of fudge, which means we subtract 16 from 48 getting us to 32 ounces.

For the second question, it states that she gives one half of her fudge to her sister. 2 times 1/2 is 1, and since there are 16 ounces in a pound, she therefore gave 16 ounces of fudge to her sister.

Answer:

1. 32 ounces

2. 16 ounces

Step-by-step explanation:

First, you have to subtract. The equation for the subtraction is 3-1 because the student took 1 pound of fudge away from the 3 pounds she already has. And 3-1 equals 2. Now, you have to convert 2 pounds to ounces. Lastly, multiply 2 by 16 as it says in the picture (it says 16 ounces equals 1 pound). The answer to this equation can be expressed as 32 or 32 ounces.

First, you have to take information from the previous question which is that she has 2 pounds of fudge left. Then, she gives \(\frac{1}{2}\) of the fudge to her sister, so you have to divide 2 by \(\frac{1}{2}\) which is 1. Now, you have to express 1 as ounces as shown in the picture. You just have to multiply 1 by 16 which is 16. Therefore the answer can be expressed as 16 or 16 ounces.

The numeric value of the function when x = 0 is found replacing each instance of x by zero in the definition of the function.

If a graph is given, then the numeric value is given as the value of y when the function crosses the y-axis.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Supposing we have a function definition, then the numeric value at x = 0 is found replacing each instance of x by zero.

On graph, x = 0 is when the graph of the function touches or crosses the y-axis.

The problem is incomplete, hence the general procedure to obtain the numeric value at x = 0 was presented.

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The perimeter of a square is given by

Where "L" is the length of one side, if the perimeter is 32 inches, we can use the equation to solve it

Each side is 8 inches.

Answer:

SAS (Side Angle Side)

Step-by-step explanation:

It is SAS because both triangles are congruent due to 2 congruent sides and one congruent angle, thus being SAS.

Answer:

7.7

Step-by-step explanation:

Answer:

7:7

Step-by-step explanation:

Control variables are the type of variable that does not change during an experiment, and serves as a comparison point for all data points.

Control variables are also called constant variables or control variables.

A control variable in an experiment is a variable that is held constant or controlled by the researcher.

A control variable is a variable or item that the researcher wants to keep constant throughout the study so as not to affect the results.

A typical study design measures the influence of an independent variable on the dependent variable. In order for this to be done properly, it is important to control another external or standardized variable. Experimentation is not as simple as changing factors and recording results. In practice, any study has many different factors that can affect its results. A control variable is a way to keep some of these factors constant so that comparisons are unbiased and transparent.

In many experiments, even slight variations in some factors can lead to inaccurate or skewed results. Voxco's Experimental Research Toolkit aims to give researchers greater control over variables to help them achieve the results they want.

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The possible range of the measurement is 211.43 to 216.57

The range in statistics for a given data set is the difference between the highest and lowest values.

The range could also be defined as the difference between the highest observation and lowest observation.

The obtained result is called the range of observation.

In the given question it is given measurement 214oz ± 1.2%

To find the range first we need to find its minimum and maximum value.

So,

1.2% of 214 = 0.012×214

=2.568

Rounding off to nearest hundredths

=2.57

Then the minimum possible value is

214-2.57=211.43

And the maximum possible value is

214+2.57=216.57

So the range would be between 211.43 to 216.57

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Answer:

-40

Step-by-step explanation:

-7 x 7 + 9 x (-1) / (-1)

-49 + 9 x (-1) / (-1)

-49 - 9 / (-1)

-49 + 9

= -40

The ratio of cell A's length to cell B's length is 20 m.

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Based on the information provided above, we have the following ratio parameters:

Length of cell A : Length of cell B = 8 × 10⁻⁵ : 0.000004

Length of cell A : Length of cell B = 8 × 10⁻⁵ : 4 × 10⁻⁶

Length of cell A : Length of cell B = (8 × 10⁻⁵)/4 × 10⁻⁶

Length of cell A : Length of cell B = 20 m.

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Answer: 13.8

Step-by-step explanation:

Answer:

13.8

Step-by-step explanation:

I make a up a scenario as if it were  a problem, the steps to solving this scenario are below:

Step 1: Set up your problem. 1/2 of 1/3 = 1/2 x 1/3. You will notice that your problem has unlike denominators, meaning the bottom numbers are different from each other. Although this is important when adding or subtracting fractions, it is not a problem when multiplying.

Step 2: Multiply the top numbers, called the numerators. 1 x 1 = 1. This is the numerator for your answer.

Step 3: Multiply the denominators. 2 x 3 = 6. This is the denominator for your answer.

Step 4: Put your answer together: 1/6. Your brother and sister will end up with 1/6 of the pizza each!

Answer:

x4-6x=8x+1 don’t know for sure but hope this helps

Step-by-step explanation:

Answer:

6x-4 = 8x+12

Step-by-step explanation:

4 less than 6 times a number > 6x - 4

Same as eight times the number increased by 12 > = 8x + 12

6x-4 = 8x+12

Answer:

No, the table is not proportional. I know this because when you divide x by y the answer is not the same.

y/x = Unit rate or constant rate

Work : (The numbers that are bold are the quotient of y/x)

85 = 17       79 = 7.9      73 = 3.65    67 = 1.67

5                10               20               40

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4.

A box plot, also known as a box-and-whisker plot, is a graphical representation of numerical data that displays the distribution of a dataset. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers that may be present.

To construct a box plot from the given data (diameters of cans in an assembly line: 5.7, 5.6, 5.1, 5.4, 5.2, 5.6, 5.7, 5.3, 5.8, 5.2), follow these steps:

1. Sort the data in ascending order: 5.1, 5.2, 5.2, 5.3, 5.4, 5.6, 5.6, 5.7, 5.7, 5.8.

2. Find the median (middle value) of the dataset, which is 5.4.

3. Determine the first quartile (Q1), which is the median of the lower half of the data. In this case, it is the median of the numbers below 5.4: 5.2.

4. Find the third quartile (Q3), which is the median of the upper half of the data. In this case, it is the median of the numbers above 5.4: 5.7.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 5.7 - 5.2 = 0.5.

6. Identify any outliers in the dataset. Outliers are values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers.

7. Construct the box plot using a number line. Draw a box from Q1 to Q3, with a line inside representing the median. Add whiskers (lines) extending from the box to the minimum value (5.1) and the maximum value (5.8).

The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4. The whiskers would extend from 5.1 to 5.8. This visual representation provides an overview of the distribution and key statistical measures of the diameters of cans in the assembly line.

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The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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There are 30 members in the football squad.

To determine the number of members in the football squad, we can use combinatorics. Since there are 2 positions (captain and assistant captain) to be filled, and the order in which they are chosen does not matter, we can use the formula for combinations. The number of ways to choose 2 people from a group of n is given by n choose 2, which is equal to n(n-1)/2. Therefore, we can set up the equation:

n(n-1)/2 = 930

Solving for n, we get:

n^2 - n - 1860 = 0

Factoring this quadratic equation, we get:

(n - 30)(n + 62) = 0

Since n must be a positive integer, we have:

n = 30

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Answer:

Step-by-step explanation:

There are  80 black squares in A. The % is 80/100 or 80%

There are 12 1/2 black squares in B. The % is 12 1/2 % black

There are 10 black squares in C   The % is 10% black

This is a really bad question. We are not told which to represent, white or black.

A: 20% white

B: 87 1/2% white

C: 90% white

I'm going to leave the second part because I don't know which way is wanted.