5.
Solve each equation mentally. (from Unit 1, Lessor
a. 5/2 •x =1
b. x• 7/3 =1
c. 1 divided by 11/2= x

The area of the shaded region is 19, which can be calculated by subtracting the unshaded region from the shaded region.

Area of the whole square= side *side

= 5*5

= 25

Area of the rectangle inside the square= lenght*breadth

=3*2

=6                                                                  

Now,

Area of the shaded region= Area of the square - Area of the rectangle

= 25-6

= 19.

The area of a square is the measure of the region enclosed by a square, and it is equal to the length of one side squared. The area of a rectangle is equal to its length multiplied by its width.

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Answer:

-17y-4

Step-by-step explanation:

we can simplify it to -17y-4 by combining like terms.

California has the larger population, and it is approximately 20 times larger than Nebraska's population.

The population of California is 3.8 million, while the population of Nebraska is 1.9 million. To find the difference between the two populations, we can calculate 3.8 million minus 1.9 million, which equals 1.9 million. To find the ratio, we can divide the population of California by the population of Nebraska, which is 3.8 million divided by 1.9 million, which equals 2. Thus, California has a population that is 20 times larger than the population of Nebraska.

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The inner surface area of the vessel, given the diameter of the hemisphere and the total height, is 133π cm².

To find the inner surface area of the vessel, we will consider the hemisphere and the cylinder separately, and then sum their inner surface areas.

Hemisphere:

The diameter of the hemisphere is 14 cm, so its radius (r1) is half of that:

r1 = 14 cm / 2 = 7 cm

Inner surface area (hemisphere) = 2 * π * r1² / 2 = π * r1² = π * (7 cm)² = 49π cm²

The radius of the cylinder is the same as the hemisphere's (r2 = r1 = 7 cm). The height (h) of the cylinder can be found by subtracting the height of the hemisphere from the total height of the vessel:

h = total height - hemisphere height = 13 cm - 7 cm = 6 cm

Inner surface area (cylinder) = 2 x π x r2 x h = 2 x π x (7 cm) x (6 cm) = 84π cm²

Total inner surface area = inner surface area (hemisphere) + inner surface area (cylinder)

Total inner surface area = 49π cm² + 84π cm² = 133π cm²

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The sequence converges to ln 2 / ln 6 as n approaches infinity.

How to find limit?

To determine whether the sequence converges or diverges, we need to take the limit of the sequence as n approaches infinity.

a_n = (ln 2n) / (ln 6n)

We can simplify this expression by applying logarithm rules:

a_n = (ln 2n) / (ln 6n) = (ln 2 + ln n) / (ln 6 + ln n)

Now we can use the fact that for any constant a>1, ln n is dominated by ln a as n approaches infinity, i.e., ln n / ln a approaches infinity as n approaches infinity.

Thus, as n approaches infinity, we have:

a_n = (ln 2 + ln n) / (ln 6 + ln n) ≈ ln 2 / ln 6

Therefore, the sequence converges to ln 2 / ln 6 as n approaches infinity.

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Answer: Table 3

Step-by-step explanation:

exponential relationship means the y value is increasing/decreasing exponentially

In table 1: the value of y is NOT increasing/decreasing exponentially as 2 is being added continuously (linear), so not table 1

In table 2: the value of y is NOT increasing/decreasing exponentially as 4 is being subtracted continuously (linear), so not table 2

In table 3: the value of y IS increasing exponentially as the y variable is multiplied by 2, so table 3

In table 4: the value of y is NOT increasing exponentially as the y variable is only being increased by 5 constantly (linear), so not 4

The object distance is 0, which implies that the object is at the focus of the concave mirror.

For a concave mirror, the magnification is given by the formula:

m = -di/do

where m is the magnification, di is the image distance, and do is the object distance. Since we are given that the magnification is -2.0, we can write:

-2.0 = -di/do

Simplifying this expression, we get:

di = 2do

We can also use the mirror formula for a concave mirror:

1/f = 1/do + 1/di

where f is the focal length of the mirror. Substituting di = 2do and f = -16 cm (since the mirror is concave), we get:

1/-16 = 1/do + 1/(2do)

Multiplying both sides by -16do, we get:

do - 2f = -32

Substituting f = -16 cm, we get:

do - (-32) = -32 + 32

do = 0

This means that the object distance is 0, which implies that the object is at the focus of the concave mirror. This is a valid result, since a concave mirror can form a real, inverted image for an object placed at a distance equal to its focal length. In this case, the magnification would be -1, not -2. So, it is not possible to have a magnification of -2 for an object distance in front of a concave mirror with a focal length of 16 cm.

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The resale value of the laptop after each year is calculated by multiplying the previous value by 0.65 (100% - 35% = 65%). After 4 years the resale value will be $250.

Answer:

48

Step-by-step explanation:

a² - 16                        a = 8

8² - 16

= 64 - 16

= 48

Answer: They are not

Step-by-step explanation:

To be linear it needs to be a diagonal arrow across. Most of these don't follow that rule, therefore it is not linear.

Answer:

B) 2

Step-by-step explanation:

First, we need to find BD:

by the Pythagorean theorem, (sqrt13)^2 + (sqrt23)^2 = BD^2

we can simplify this to 13+23=BD^2, which means BD^2 = 36, and BD is 6.

Therefore to find BC, we can use the Pythagorean theorem again and create the formula:

(4sqrt2)^2 + BC^2 = 6^2

This simplifies to 32 + BC^2 = 36, which means that BC^2 = 4, and BC = 2.

The cylinder has a radius of 2 times the square root of 5 meters, or roughly 4.5 meters rounded to the nearest tenth.

The formula for the volume of a cylinder is:

V = πr²h

where V is the volume, r is the radius, and h is the height.

In this case, we have:

V = 160π m³

h = 8 m

Substituting these values into the formula, we get:

160π = πr²(8)

Simplifying the equation by canceling out π on both sides, we get:

160 = 8r²

Dividing both sides by 8, we get:

20 = r²

Taking the square root of both sides, we get:

r = √20

Simplifying the radical by factoring out 4, we get:

r = 2√5

To express the radius as a decimal rounded to the nearest tenth, we can use a calculator to get:

r ≈ 4.5

Therefore, the radius of the cylinder is 2√5 meters or approximately 4.5 meters to the nearest tenth.

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We would see a logarithmic sequence of values if we plotted the amount of time Edna spends watching TV weekly on a logarithmic scale.

If we plot the amount of time Edna spends watching TV on a logarithmic scale, we would see a continuous sequence of values that increase as her viewing time increases. Specifically, the sequence would be a logarithmic scale of the number of hours she watches TV per week.

On a logarithmic scale, each increment corresponds to a multiplication by a constant value. For example, if we use a logarithmic scale base 10, then each increment of 1 corresponds to a multiplication by 10. So, if we plot Edna's TV watching time on a logarithmic scale, we would see a sequence of values that increase by a factor of 10 as her TV watching time increases by an order of magnitude.

For example, if Edna watches 2 hours of TV per week, the logarithmic value would be log(2) = 0.3. If she watches 7 hours per week, the logarithmic value would be log(7) = 0.85. If she watches 20 hours per week, the logarithmic value would be log(20) = 1.3. As her viewing time increases, the logarithmic values would continue to increase in a continuous sequence.

Therefore, if we plotted the amount of time Edna watches TV each week on a logarithmic scale, we would see a logarithmic sequence of numbers.

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Answer:

5/12

Step-by-step explanation:

Simply times the fractions together to get the area

5/8 x 2/3 = 10/24

Now simplify 10/24 by dividing by the HCF which is 2

So, in simplest form, your final answer is 5/12

i do not know what to say its twenty words to add an answer#

Answer:

(a) Using the given mean and standard deviation, we can standardize the random variable X representing the lifespan of a light bulb as:

Z = (X - μ) / σ = (10,500 - 9,000) / 1,000 = 1.5

Then, we can use a standard normal distribution table or calculator to find the probability that a randomly chosen light bulb lasts more than 10,500 hours:

P(X > 10,500) = P(Z > 1.5) ≈ 0.0668

So the probability is approximately 0.0668, rounded to four decimal places.

(b) The distribution of the mean lifespan of 15 light bulbs can be described as approximately normal with a mean of 9,000 hours, and a standard deviation of 1,000 hours divided by the square root of 15 (since the sample size is 15).

This is because, according to the Central Limit Theorem, the distribution of sample means tends to be approximately normal regardless of the underlying distribution of the population, as long as the sample size is large enough. In this case, a sample size of 15 is large enough to assume a normal distribution.

Answer: q = -3, p = 6

Step-by-step explanation:

Multiply second equation by 3. 6q + 9q = 9. Equation one minus equation two which gives you p = 6. Then plug it in the second equation. 12 + 3q = 3. 3q = -9. q = -3.

The link between the base price and the selling price with the markup is expressed differently in both equations, but they are both true and accurately depict the same scenario using the distributive property.

A basic tenet of mathematics is the distributive property of multiplication over addition, which asserts that the product of a number and a sum is equal to the total of the products of the number and each addend. In other words, if a, b, and c are all real numbers, then a(b + c) = ab + ac. By factoring out common components, this characteristic is employed in algebra to simplify statements and resolve equations.

The link between the base price and the selling price with the markup is expressed differently in both equations, but they are both true and accurately depict the same scenario using the distributive property.

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Repeat this process for a large number of trials (e.g., 1000) and use the proportion of trials where all three-coin flips resulted in tails as an estimate of the probability that three randomly chosen people do not work out for the desired amount.

by the question.

To simulate this situation, you can use a set of three-coin flips, where heads represent the event that a person exercises for 30 minutes a day at least three times a week, and tails represent the event that a person does not exercise for that amount.

To simulate the first person, flip a coin once. If it lands heads, consider the person as exercising enough; otherwise, consider the person as not exercising enough.

Repeat this process for the second and third person as well, each time flipping the coin once to determine if the person exercises enough.

After the three-coin flips, count the number of times the coin landed tails, which represents the number of people who do not exercise for 30 minutes a day at least three times a week.

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The probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative is approximately 0.158

To solve this problem, we need to use the binomial distribution. Let's define the following

n = 100 (sample size)

p = 1 - 0.534 = 0.466 (probability of not identifying as conservative)

x = number of respondents who do not identify as conservative (we want at least 50)

We want to find P(X >= 50), which represents the probability of getting at least 50 respondents who do not identify as conservative in a random sample of 100 Mississippi residents.

We can use the cumulative distribution function (CDF) of the binomial distribution to calculate this probability. The CDF gives us the probability of getting up to a certain number of successes (in this case, respondents who do not identify as conservative).

Using a calculator or statistical software, we find

P(X >= 50) = 1 - P(X < 50) = 1 - binomcdf(100, 0.466, 49) = 0.158

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The given question is incomplete, the complete question is:

Mississippi is the most conservative U.S. state, with 53.4 percent of its residents identifying themselves as conservative. What is the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative?

The solution of the absolute inequality is x < -9 or x > 1

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Absolute inequalities are inequalities  that involve algebraic expressions with absolute value symbols and inequality symbols.

Therefore, let's solve the absolute inequality as follows:

|2x + 8| > 10

2x + 8 > 10 or 2x + 8 < - 10

Let's solve them individually,

2x + 8 > 10

2x > 10 - 8

2x > 2

x > 2 / 2

x > 1

Therefore,

2x + 8 < - 10

2x < - 10 - 8

2x < -18

divide both sides of the inequality by 2

x < -18 / 2

x < - 9

Therefore,

x < -9 or x > 1

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Based on the information provided, it is most likely that the variable Amari used to construct the bar graph is the "Type of orange". This is because a bar graph is a visual representation of categorical data and is used to show the frequency or proportion of each category in a dataset. The other variables mentioned - diameter of the oranges, number of navel oranges, and price per pound of oranges - are all quantitative variables and are better represented using other types of graphs such as histograms, scatterplots, or line graphs.

As per the given commission, the sales price of the property is $405,000.

To do this, we need to break down the commission earned by the agent into two parts: the commission earned on the first $300,000 and the commission earned on the remaining amount. The commission earned on the first $300,000 can be calculated as:

Commission on first $300,000 = 6% of $300,000

Commission on first $300,000 = 0.06 x $300,000

Commission on first $300,000 = $18,000

So, the remaining commission earned by the agent on the amount that exceeds $300,000 is:

Total commission - Commission on first $300,000 = $21,150 - $18,000

Total commission - Commission on first $300,000 = $3,150

Now, we know that the commission earned on the remaining amount is 3% of the sales price that exceeds $300,000. Let's assume the sales price of the property is x. Then we can write the following equation:

3% of (x - $300,000) = $3,150

We can simplify this equation as follows:

0.03(x - $300,000) = $3,150

x - $300,000 = $3,150 / 0.03

x - $300,000 = $105,000

x = $300,000 + $105,000

x = $405,000

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Answer:

Step-by-step explanation:

Given equations,

→ x - y = 5

→ 4x + y = 10

Now we have to,

→ Find the required value of x and y.

Let's solve for the value of x,

→ (x - y) + (4x + y) = (5) + (10)

→ x + 4x - y + y = 5 + 10

→ 5x + 0 = 15

→ 5x = 15

→ x = 15/5

→ [ x = 3 ]

Then the value of y will be,

→ 4x + y = 10

→ 4(3) + y = 10

→ 12 + y = 10

→ y = 10 - 12

→ [ y = -2 ]

Hence, the value of y is -2.

Equation one can be solved by additive property two by subtractive property.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

7=m+1.2

m=7-1.2

6.8

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Answer:

[tex]15x^2+4y-4z^2[/tex]

Step-by-step explanation:

Solve this question patiently.

See explanation in the attached picture.

Mira can afford to pay at most $1,094.03 per month in rent if she wants to limit her rent to 28% of her annual salary of $46,830.

To calculate the monthly maximum rent Mira can afford to pay, we need to follow these steps:

Step 1: Find 28% of Mira's annual salary:

28% of $46,830 = 0.28 x $46,830 = $13,128.40

Step 2: Divide the result from Step 1 by 12 to get the maximum monthly rent:

$13,128.40 ÷ 12 = $1,094.03 (rounded to the nearest cent)

Therefore, Mira can afford to pay at most $1,094.03 per month in rent if she wants to limit her rent to 28% of her annual salary.

Step 1 involves finding 28% of Mira's annual salary, which is done by multiplying her annual salary by 0.28 (which is equivalent to 28/100 or 0.28). This gives us the maximum amount of money Mira can spend on rent in a year while still staying within her 28% limit.

In Step 2, we divide the result from Step 1 by 12 to get the monthly maximum rent Mira can afford to pay. This is because there are 12 months in a year, so we need to divide the yearly rent limit by 12 to get the monthly limit.

In this case, the maximum amount of money Mira can spend on rent in a year is $13,128.40. Dividing this by 12 gives us a monthly maximum rent of $1,094.03 (rounded to the nearest cent). This means that if Mira wants to keep her rent payments at or below 28% of her annual salary of $46,830, she should look for a rental property that costs no more than $1,094.03 per month.

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The probability that the newspapers sample will lead it to predict defeat is 92.36%.

To solve this problem, we need to use the binomial distribution formula.

Let's define the following:

X: number of voters in the sample who do not support the budget (i.e., the sample leads to a prediction of defeat).

n: sample size, which is 377.

p: proportion of voters who support the budget, which is 0.54 (since 54% support it, 46% do not support it).

The probability of the sample leading to a prediction of defeat is:

P(X = k) = (n choose a) * pᵃ * (1-p)ⁿ⁻ᵃ

where (n choose a) = n! / (a! * (n-a)!) is the binomial coefficient.

We want to find P(X >= 189), which means that at least 189 voters in the sample do not support the budget.

P(X >= 189) = 1 - P(X < 189)

To calculate P(X < 189), we can use a normal approximation to the binomial distribution, since n is large and p is not too close to 0 or 1.

The mean of the binomial distribution is mu = n * p = 377 * 0.54 = 203.58

The standard deviation is sigma = √(n * p * (1-p)) = √(377 * 0.54 * 0.46) = 10.20

We can standardize X using the z-score formula:

z = (X - mu) / sigma

P(X < 189) = P(z < (189 - 203.58) / 10.20) = P(z < -1.43)

Using a standard normal table or calculator, we can find that P(z < -1.43) = 0.0764.

Therefore, P(X >= 189) = 1 - P(X < 189) = 1 - 0.0764 = 0.9236.

So the probability that the newspaper's sample will lead it to predict defeat is approximately 0.9236, or 92.36%.

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Answer:

x = y = 20

Step-by-step explanation:

The two triangles shown are similar because one is simply an extension of othe other.

From this, we can use a similar side lengths formula specifically for triangles.

[tex]\frac{y + 5}{y} = \frac{15}{12}\\[/tex]

Notice that this represents the ratio of the whole side to the smaller side and says that this proportion is equal to the proportion for its adjacent side lengths. Cross mutiply the above equation to solve for y.

12(y+5) = 15y

12y + 60 = 15y

y = 20

Now we need to find the value of x. We have a side and hypotenuse's length of this large triangle, so we can use the pythagorean theorem to calculate the unknown side length.

(12 + 3)² + x² = (20 + 5)²

15² + x² = 25²

225 + x² = 625

x² = 400

x = ±20

The negative 20 doesn't make sense for this application so use the positive 20.

Therefore x = 20, y = 20.

Answer:

$3.45

Step-by-step explanation:

the large salad costs 1.40 more

large salad = 4.85

small salad = 4.85 - 1.40

small salad costs $3.45

Answer:

3.45$ is the price of small salad as it costs 1.40$ less than large salad

Step-by-step explanation:

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