1) How many terms does the expression r- 9 + 5.5 have? Explain.​

Answer:

Step-by-step explanation:

Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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Step-by-step explanation:

OPTION A

(-40) + (-30) + 28

Answer:

B.

Step-by-step explanation:

First in order to solve this problem we need to simplify the answer choices.

A. 6×8 + 6×6 = 48+ 36

B. 12×4 + 12×1=48+12

C. 4×44 + 4×3=176+12

D. 8×6 + 8×4 = 48+32

As you can see there is one expression that is equivalent to 48+12. Answer choice B is correct.

The expression that is equivalent to 48 + 12 is 12(4 + 1), Option B is correct.

An expression is combination of variables, numbers and operators.

To find the expression that is equivalent to 48 + 12, we need to simplify each of the given expressions and find the one that is equal to 60.

Because the value of 48+12 is 60

A. 6(8 + 6) = 6(14) = 84

B. 12(4 + 1) = 12(5) = 60

C. 4(44 + 3) = 4(47) = 188

D. 8(6 + 4) = 8(10) = 80

Out of the given expressions, only expression B simplifies to 60, which is equivalent to 48 + 12.

Therefore, the expression that is equivalent to 48 + 12 is 12(4 + 1), Option B is correct.

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The probability of picking an ace of hearts from a standard deck of playing cards is 1/52.

Consider a standard deck of cards.

We know that a standard deck of cards contains 52 cards.

So, total number of cards in the standard deck of cards = 52 cards

Now, we have to assume that there are no jokers in the set of cards.

We have to find the probability of picking an ace of hearts from a standard deck of playing cards.

For that we need to first find the number of cards which are ace of hearts.

Number of cards which are ace of hearts = 1

Probability of picking an ace of hearts from a standard deck of playing cards is,

P = Number of ace of hearts / Total number of cards

  = 1/52

Hence the probability is 1/52.

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Ms. Zentz would buy 17 protractors if she buys one quarter of the 65 items.

If you buy 65 items and one quarter of them are protractors, then the number of protractors you buy can be calculated as:

Number of protractors = 65 x 1/4

Number of protractors = 16.25

Since you cannot buy a fractional part of a protractor, you would need to round the answer to the nearest whole number. In this case, you would round up to 17 protractors.

Therefore, Ms. Zentz would buy 17 protractors if she buys one quarter of the 65 items.

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Answer:

\((-2,6)\)

Step-by-step explanation:

Given

\(Elena = (10,-4)\)

\(Midpoint = (4,1)\)

Required

Determine the coordinates of Naya's

Midpoint is calculated as:

\(M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)\)

In this case:

\((x_1,y_1) = (10,-4)\)

\((x,y) = (4,1)\)

So, we have:

\((4,1) = \frac{1}{2}(10+x_2,-4+y_2)\)

Multiply through by 2

\(2 * (4,1) = \frac{1}{2}(10+x_2,-4+y_2) * 2\)

\((8,2) = (10+x_2,-4+y_2)\)

By comparison:

\(8 = 10 + x_2\)

\(2 = -4 + y_2\)

So:

\(8 = 10 + x_2\)

\(x_2 = 8 - 10\)

\(x_2 = -2\)

\(2 = -4 + y_2\)

\(y_2 =2+4\)

\(y_2 =6\)

So, the coordinate is: \((-2,6)\)

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Answer:

8.3 lbs

Step-by-step explanation:

By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Answer:

Step-by-step explanation:

800 - 200 = 600 = range

Inter Quartile Range is hard to measure.

566 2/3 = mean = close enough to 567

The term 625 does not exist

Answer:

Step-by-step explanation:

A range

Answer:

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.

Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.

We can use this information to set up the following equation:

0.08 = (1/2)^n

where n is the number of half-lives that have elapsed. We want to solve for n.

Taking the logarithm of both sides, we get:

log(0.08) = n*log(1/2)

Solving for n, we get:

n = log(0.08) / log(1/2) = 3.42

So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:

Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)

Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.

Answer:

The value of the test statistic is 2.47.

Step-by-step explanation:

The test statistic is:

\(t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the expected mean, \(\sigma\) is the standard deviation and n is the size of the sample.

For a proportion p, we have that:

\(s = \frac{\sigma}{\sqrt{n}} = \sqrt{\frac{p(1-p)}{n}}\)

A political study took a sample of 900 voters in the town and found that 42% of the residents favored annexation.

This means that \(X = 0.42, n = 900\)

Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 38%

This means that the expected is \(\mu = p = 0.38\)

So

\(s = \frac{\sigma}{\sqrt{n}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.38*0.62}{900}} = 0.0162\)

Find the value of the test statistic

\(t = \frac{X - \mu}{s}\)

\(t = \frac{0.42 - 0.38}{0.0162}\)

\(t = 2.47\)

The value of the test statistic is 2.47.

The probability of spinning an even number, flipping tails, then spinning an odd number is:

1/9   (as fraction) or 11.11% (as percent)

To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:

We have only one even number in the spinner, and that is 2. Thus,

P(even number) = 1/3

For a coin, the probability of head or tail is 1/2. Thus,

P(tail) = 1/2

We have two odd number in the spinner, and that is 1 and 3. Thus,

P(odd number) = 2/3

Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:

P(even, tail, odd) = 1/3 * 1/2 * 2/3

                            = 2/18

                            = 1/9   (as fraction)

In percent:

P(even, tail, odd) =  1/9 * 100

                            = 11.11%

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Answer:

d, 6 units

Step-by-step explanation:

its 6 units im pretty sure. hope this helped

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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Answer:

40%

Step-by-step explanation:

Answer:

32%

Step-by-step explanation:

8 of 25=32%

Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

-12v+6y+18

you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18

i hope this helps :)

Step-by-step explanation:

a. It would provide a quantitative data

b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.

c. 44% of the respondents strongly agree

d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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The most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year. Option B

Based on the given equation y = 195(1.10)^x, where x represents the number of years since 2005 and y represents the number of Salad Supreme restaurants, we can draw the following conclusions:

A. Salad Supreme had 110 restaurants in 2005: This conclusion is not supported by the given equation.

B. Salad Supreme is increasing the number of restaurants by 10% each year: This conclusion is supported by the equation.

C. Salad Supreme is increasing the number of restaurants by 195 each year: This conclusion is not supported by the equation.

D. Salad Supreme is increasing the number of restaurants by 110% each year: This conclusion is not supported by the equation. The growth factor of 1.10 (or 10%) indicates a 10% increase each year, not 110%.

Therefore, the most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year.

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According to the information, we can infer that the area of this polygon is 34 units².

To find the area of the figure we must graph it and divide it into different segments. Then we find the area of all the segments and add them to get the total area.

Rectangle 1

6 * 3 = 18

Rectangle 2

2*4=8

Triangle 1

2 * 4 / 2 = 4

Triangle 2

2 * 4 / 2 = 4

Total Area

18 + 8 + 4 + 4 = 34

Based on the above, we can infer that the total area of the polygon is 34 ² units.

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Answer:

(a)

\(\bar x_1 =41.33\)     \(\sigma_1 = 7.48\)

\(\bar x_2 =22.3\)       \(\sigma_2 = 4.53\)

(b)

\(d = 19.03\)

(c)

\(CI = 16.33\) to \(21.73\)

Step-by-step explanation:

Given

\(n_1 = 10\\ n_2 = 12\)

And the accompanying data for private (1) and public (2) colleges

Solving (a): The sample mean and sample standard deviations

Private College

Calculating sample mean

This is calculated as:

\(\bar x_i = \frac{\sum x_i}{n_i}\)

\(\bar x_1 =\frac{52.8+30.6+43.2 +45.8 +33.3+33.3 +50.5 +44.0 +42.0 +37.8}{10}\)

\(\bar x_1 =\frac{413.3}{10}\)

\(\bar x_1 =41.33\)

Calculating sample standard deviation

This is calculated as:

\(\sigma_i = \sqrt\frac{\sum(x_i - \bar x_i)}{n_i-1}\)

\(\sigma_1 = \sqrt\frac{(52.8-41.33)^2+(30.6-41.33)^2+.........+(37.8-41.33)^2}{10-1}\)

\(\sigma_1 = \sqrt\frac{503.261}{9}\)

\(\sigma_1 = \sqrt{55.9178888889\)

\(\sigma_1 = 7.4778264816\)

\(\sigma_1 = 7.48\) -- approximated

Public College

Calculating sample mean

\(\bar x_2 =\frac{20.3 +22.8 +28.2 +18.5 +15.6 +25.6+ 24.1 +14.4 +28.5 +21.8 +22.0 +25.8}{12}\)

\(\bar x_2 =\frac{267.6}{12}\)

\(\bar x_2 =22.3\)

Calculating sample standard deviation

\(\sigma_2 = \sqrt\frac{(20.3 -22.3)^2+(22.8 -22.3)^2+(28.2 -22.3)^2+(18.5 -22.3)^2+(15.6 -22.3)^2+................+(25.8-22.3)^2}{12-1}\)\(\sigma_2 = \sqrt\frac{225.96}{11}\)

\(\sigma_2 = \sqrt{20.5418181818\)

\(\sigma_2 = 4.532308262\)

\(\sigma_2 = 4.53\) -- approximated

Solving (b): Point estimate of the difference between the two population means

This is calculated as:

\(d = \bar x_1 - \bar x_2\)

\(d = 41.33 - 22.3\)

\(d = 19.03\)

Solving (c): 95% confidence interval

First, calculate the degrees of freedom:

\(df = \frac{(\sigma_1^2/n_1 + \sigma_2^2/n_2)^2}{\frac{(\sigma_1^2/n_1)^2}{n_1 - 1} + \frac{(\sigma_2^2/n_2)^2}{n_2 - 1}}\)

\(df = \frac{(7.48^2/10 + 4.53^2/12)^2}{\frac{(7.48^2/10)^2}{10 - 1} + \frac{(4.53^2/12)^2}{12 - 1}}\)

\(df = \frac{53.3647}{31.3045/9 + 2.9244/11}\)

\(df = \frac{53.3647}{3.7441}\)

\(df = 14.2530\)

\(df = 14\)

Calculate the critical value (t)

At 95% confidence interval and df = 14;

\(df = 14\)

The confidence interval is then calculated as:

\(CI = (\bar x_1 - \bar x_2) \± \sqrt{\sigma_1^2/n_1 + \sigma_2^2/n_2}\)

\(CI = (41.33 - 22.3) \± \sqrt{7.48^2/10 + 4.53^2/12}\)

\(CI = 19.03 \± \sqrt{7.305115\)

\(CI = 19.03 \± 2.70\)

Split

\(CI = 19.03 - 2.70\) to \(19.03 + 2.70\)

\(CI = 16.33\) to \(21.73\)

This implies that:

Private colleges have population mean annual cost of $16.33 to $21.73 more expensive than public colleges

P(t) = 3610 * e^(-0.00347t) function can be used to estimate the population of the town at any time in the future, based on the quarterly rate of decay.

What is exponential decay?

Exponential decay is a mathematical process in which a quantity decreases over time in a manner proportional to its current value. This means that the rate of decay is proportional to the amount of the substance remaining, and as the amount of the substance decreases, the rate of decay also decreases.

To find the quarterly rate of exponential decay, we need to first convert the annual rate of 1.4% to a quarterly rate. We can do this using the formula:

Quarterly rate = (1 + annual rate)^ (1/4) - 1

Where the annual rate is expressed as a decimal.

So, for an annual rate of 1.4%, we have:

Quarterly rate = (1 + 0.014)^ (1/4) - 1

Quarterly rate = 0.00347

This means that the population of the town is decreasing by 0.347% per quarter. To write the exponential decay function for this population, we can use the formula P(t) = P(0) * e^(-rt)

Where P(0) is the initial population, r is the quarterly rate of decay, t is the time elapsed in quarters, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

P(t) = 3610 * e^(-0.00347t)

This function can be used to estimate the population of the town at any time in the future, based on the quarterly rate of decay.

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Answer:

6x+3

Step-by-step explanation:

I hope this is what you where looking for

Answer:

nine

Step-by-step explanation:

Answer:

16.8

Step-by-step explanation:

4.8 + 5.4 + 6.6 = 16.8

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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