The governor of state A earns ​$54,900 more than the governor of state B. If the total of their salaries is ​$310,850​, find the salaries of each.

Answer:

(y+10 ) years

Step-by-step explanation:

If Yiadom is y  years now.

Then after 10 years, his anew age will be = (y+10) yrs

Answer:

245 1/3

Step-by-step explanation:

The solution to the expression is 3 + 6x

From the question, we have the following parameters that can be used in our computation:

x + 3 + 5x

Collect the like terms in the above expression

So, we have the following representation

3 + 5x + x

Evaluate the like terms

This gives

3 + 6x

Hence, the solution is 3 + 6x

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The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

Step-by-step explanation:

You want to know the intervals on which f(x) = sin(x)/(2+cos(x)²) is increasing and decreasing, and the relative extremes.

The quotient rule can be used to find the derivative of f(x). Where the derivative is positive, the function is increasing.

  f'(x) = ((2+cos(x)²)cos(x) +sin(x)(2cos(x)sin(x)))/(2+cos(x)²)²

  f'(x) = (cos(x)(2 +cos(x)² +2sin(x)²)/(2+cos(x)²)²

  f'(x) = cos(x)(3+sin(x)²)/(2+cos(x)²)²

We observe that the factors (3+sin(x)²) and (2+cos(x)²) are both positive for all x. This means the sign of the derivative will match the sign of cos(x).

The function is increasing where cos(x) > 0, on the intervals ...

  (0, π/2) ∪ (3π/2, 2π)

The function is decreasing where cos(x) < 0, on the interval ...

  (π/2, 3π/2)

The first derivative test tells us the function will have a relative maximum where the function goes from increasing to decreasing, at x = π/2. The function value at that point is ...

  f(π/2) = sin(π/2)/(2 +cos(π/2)²) = 1/2

The relative maximum is at (π/2, 1/2).

The first derivative test tells us the function will have a relative minimum where the function goes from decreasing to increasing, at x = 3π/2. The function value at that point is ...

  f(3π/2) = sin(3π/2)/(2 +cos(3π/2)²) = -1/2

The relative minimum is at (3π/2, -1/2).

Answer:

x = 8 or x = -2

Step-by-step explanation:

x^2 - 6x + 9 = 25

x^2 - 6x - 16 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

with a = 1

b = -6

c = -16

substitute in the formula

x = [-(-6) +/- √(-6^2 - 4(1)(-16))]/2(1)

x = [6 +/- √(36 + 64)]/2

x = [6 +/- √10]/2

x = [6 +/- 10]/2

x1 = [6 + 10]/2 = 16/2 = 8

x2 = [6 - 10]/2 = -4/2 = -2

Answer:

x = 8,-2

Step-by-step explanation:

First, complete the square on LHS (Left-Handed Side).

\(\displaystyle \large{x^2-6x+9=(x-3)^2}\)

Make sure to recall the perfect square formula. Rewrite another equation with (x-3)² instead.

\(\displaystyle \large{(x-3)^2 = 25}\)

Square both sides of equation.

\(\displaystyle \large{\sqrt{(x-3)^2}=\sqrt{25}}\)

Because x² = (-x)² which means that it’s possible for x to be negative. Thus, write plus-minus beside √25 and cancel square of LHS.

\(\displaystyle \large{x-3=\pm \sqrt{25}}\\ \displaystyle \large{x-3=\pm 5}\\ \displaystyle \large{x=\pm 5+3}\)

Therefore, x = 5+3 or x = -5+3

Thus, x = 8,-2

The method above is called completing the square method.

Answer:

The area is 15 feet

Step-by-step explanation:

So you are going to need two different equations-

l = w(3)

2l + 2w = 40

Insert the first equation into the second-

2(3w) + 2w = 40

Simplify this equation-

6w + 2w = 40

8w = 40

Divide both sides by 5

w = 5

Solve first equation

l = 5(3)

l = 15

Then find the area-

5 x 15 = 75

Answer:

$13.92

Step-by-step explanation:

$212.90-198.98

Answer:

0.5 (any number between 0 and 1)

Step-by-step explanation:

34 * 0.5 = 17

34 > 17 > 0

5 1/5 - 3 7/10 simplified and subtracted equals 3/2.

what is improper fraction?

An improper fraction is a fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number). For example, 7/4 is an improper fraction because the numerator (7) is greater than the denominator (4).

To make 5 1/5 - 3 7/10 a simpler problem, we need to convert the mixed numbers into improper fractions, which will make it easier to subtract them.

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator of the fraction and then add the numerator.

So, we have:

5 1/5 = (5 x 5 + 1)/5 = 26/5

3 7/10 = (3 x 10 + 7)/10 = 37/10

Now, we can subtract the two improper fractions:

26/5 - 37/10

To subtract fractions, we need to have a common denominator. The smallest number that both 5 and 10 divide into is 10, so we can convert both fractions to have a denominator of 10:

(26/5) x (2/2) = 52/10

37/10

Now we can subtract the fractions:

52/10 - 37/10 = 15/10

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5:

15/10 = (15/5) / (10/5) = 3/2

Therefore, 5 1/5 - 3 7/10 simplified and subtracted equals 3/2 or 1 1/2.

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

The answer is (0,1)

Step-by-step explanation:

Answer:

13 and 1/2

Step-by-step explanation:

1/2 gets 4 1/2

1 1/2 could be tbroken down to

1/2+1/2+1/2  each half gets you 4 1/2

so 4 1/2+4 1/2 +4 1/2 =13 1/2

Answer: LKM and MKN

Step-by-step explanation: If you do is 180-90= 90

90/2 because complementary angles are angles that add up to 90 degrees. 90/2= 45

1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, the amount paid for the month of June is approximately $252.75, and the amount paid for the entire year is approximately $6,144.

To calculate the amount paid for the month and the year, we need to consider the number of days covered by the insurance policy. Let's break it down step by step:

Step 1: Determine the number of days covered in June.

Since the policy doesn't go into effect until June 16th, there are 15 days remaining in June that will be covered by the insurance policy.

Step 2: Calculate the daily rate.

To find the daily rate, we divide the total cost of the insurance policy by the number of days in a year:

Daily rate = 6,144 / 365

Step 3: Calculate the amount paid for June.

The amount paid for June can be found by multiplying the daily rate by the number of days covered:

Amount paid for June = Daily rate * Number of days covered in June

Step 4: Calculate the amount paid for the year.

To calculate the amount paid for the year, we simply multiply the daily rate by 365 (the total number of days in a year):

Amount paid for the year = Daily rate * 365

Now let's perform the calculations:

Step 2: Daily rate

Daily rate = 6,144 / 365 ≈ 16.85 (rounded to two decimal places)

Step 3: Amount paid for June

Amount paid for June = 16.85 * 15 ≈ 252.75 (rounded to two decimal places)

Step 4: Amount paid for the year

Amount paid for the year = 16.85 * 365 ≈ 6,144 (rounded to two decimal places)

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Answer:

Step-by-step explanation:

The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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Both equations give the correct terms, so we can conclude that the pattern rule is:  \(an^2 - 131n + 80\) , where \(a=63\)  .

To find the pattern rule for the given sequence 12, 59, 294, 1469, 7344, we need to observe the differences between consecutive terms. Let's find the differences between each pair of terms:

\(59 - 12 = 47\)

\(294 - 59 = 235\)

\(1469 - 294 = 1175\)

\(7344 - 1469 = 5875\)

The differences are not constant, so we need to find the differences between these differences:

\(235 - 47 = 188\)

\(1175 - 235 = 940\)

\(5875 - 1175 = 4700\)

Now, the second differences are constant (equal to 940), which suggests that the pattern rule is a quadratic equation. Let's assume the pattern rule is of the form:

\(an^2 + bn + c\)

where n is the term number (starting with n=1 for the first term).

To find the coefficients a, b, and c, we can use the first three terms of the sequence. Let's substitute n=1,2,3 into the equation and equate it to the corresponding terms:

\(a + b + c = 12 (for n=1)\)

\(4a + 2b + c = 59 (for n=2)\)

\(9a + 3b + c = 294 (for n=3)\)

We can solve these equations simultaneously to get the values of a, b, and c:

\(a = 63\)

\(b = -131\)

\(c = 80\)

Therefore, the pattern rule for the sequence is:

\(an^2 - 131n + 80\)

where a=63.

To check if this pattern rule works for the other terms of the sequence, we can substitute n=4 and n=5:

\(a(4^2) - 131(4) + 80 = 1469\)

\(a(5^2) - 131(5) + 80 = 7344\)

Therefore, Both equations give the correct terms, so we can conclude that the pattern rule is:

\(an^2 - 131n + 80, where a=63.\)

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As a result, length of a side is around 1347.1 inches to the nearest 10th of an inch.

The Law of Sines, which states that the ratio of the length of a side to the sine of the angle opposite that side is equal for all sides and angles in a triangle, can be used to determine the length of side an in ABC.

The following equation can be created by applying the Law of Sines:

C/sin(31°) = a/sin(74°)

If we are aware that c = 720 inches, we can use a calculator to determine sin(31°):

sin(31°) ≈ 0.51504

As a result, we can find a:

A is equal to sin(74°)*c/sin(31°)

a ≈ 0.96231 * 720 / 0.51504 \sa ≈ 1347.11

With a 10th-inch precision, we obtain:

1354.7 inches

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Answer:

its actually 1343.8

Step-by-step explanation:

Answer:

Both are not possible because they are both not teaching the 0 like any normal graph should

Step-by-step explanation:

Answer:

so the one on the right would be consistent and independent because they intersect and are not the same line. They have different y- intercepts and different slopes

Answer:

Step-by-step explanation:

What two number multiply to equal 6*(-12) and add to equal -1? That is -9 and +8.

\(6q^2-9q+8q-12\)

Now factor by grouping

\((6q^2-9q)+(8q-12)\\3q(2q-3)+4(2q-3)\\(3q+4)(2q-3)\)

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

Let y = the amount in Adrianna's savings account

Let x = the number of weeks passed

y = 5x + 20

The number of days until I need to go to the store for sausages again is

7.5 days.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of packages = 6

Number of sausages in each package = 2(1/2)

Total sausages.

= 6 x 2(1/2)

= 6 x 5/2

= 3 x 5

= 15

Number of sausages the dog eats each day = 2

The number of days the sausages will be used.

= 15/2

= 7.5

Thus,

The number of days is 7.5 days.

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No, there are x values which map to more than 1 y-value.

Given that Matthew examines the relation as shown in the below.

{(4, -11), (3,1), (0,1), (2,6), (3, -1)}

We need to check whether the relation is a function or not,

So, we know that,

A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.

If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.

Here we can see that the y values are repeated, so it is not a function.

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Answer:

g(x) = 3 (x + (-5)) (x + (-9))

Zeros: (5 and 9)

Step-by-step explanation:

3a² -42a +135 = 3 (a² - 14a +45) = 3 (a-5) (a-9)

3 (a-5) (a-9) = 0

a = 5 or a = 9 ..... Zeros

Answer:

$45

Step-by-step explanation:

The sale price changed from $80 to 60, then with the coupon another 25% was taken off leading it to come to a price of $45

$80 x .75 = 60

$60 x .75 = 45

(.75 is for the price of the original value that he will be paying later)

Answer:

10.25

Step-by-step explanation:

Answer:

$10.25 because $51.25 divided by 5 equals $10.25 which is the unit price of each scarves.

Step-by-step explanation:

Answer:

Leigh Anne has the grater rate of pay by 0.30

Step-by-step explanation:

Jerry: $11.75 per hour

Anne: $12.05 per hour

Answer:

The minimum sample size needed is \(n = (\frac{1.96\sqrt{\sigma}}{4})^2\). If n is a decimal number, it is rounded up to the next integer. \(\sigma\) is the standard deviation of the population.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?

A sample of n is needed, and n is found when M = 4. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(4 = 1.96\frac{\sigma}{\sqrt{n}}\)

\(4\sqrt{n} = 1.96\sqrt{\sigma}\)

\(\sqrt{n} = \frac{1.96\sqrt{\sigma}}{4}\)

\((\sqrt{n})^2 = (\frac{1.96\sqrt{\sigma}}{4})^2\)

\(n = (\frac{1.96\sqrt{\sigma}}{4})^2\)

The minimum sample size needed is \(n = (\frac{1.96\sqrt{\sigma}}{4})^2\). If n is a decimal number, it is rounded up to the next integer. \(\sigma\) is the standard deviation of the population.