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Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.

According to the question,

We have the following information:

Amira is younger than Marques.

Their ages are consecutive integers.

The sum of Amira's age and 2 times Marques's age is 38.

Now, let's take Amira's age to be x years.

Then, Marques's age will be (x+1) years.

So, we have:

x + 2(x+1) = 38

x + 2x + 2 = 38

3x+2 = 38

3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)

3x = 36

x = 36/3

x = 12 years

Hence, Amira's age is 12 years.

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Using the spring's force we know that 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.

So, F is the 4 lb force required to maintain the spring's stretched position.

The labor of extending a spring is denoted by the formula:

So, calculate:

Therefore, 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.

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Answer:

Step 4

Step-by-step explanation:

You cannot combine non-like terms like 2x and 15

They have to be left as is

Steps would be:

2.  5x +15-3x   →  Distributive property
3.   2x+15        →  Combining like terms

And that's it. You cannot go any further

the difference in mean life expectancies for the two groups is within 1 year of the true difference is 1729

Health issues can arise from substances other than chemicals like bleach. The way you clean your house and the environment in which you live both matters. Scientists caution that performing these tasks could have a detrimental effect on your health.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score.

Given data:

σ₁ = σ₂ = 15

n₁ = n₂ = n

Margin of error = 1

Confidence level = 95% = α = 1 - 0.95 = 0.05

z score of α / 2 = 0.05 / 2 = 1.96 , n₁ = n₂ = ?

For the difference of mean test, the margin of error will be:

E = z score  α / 2 [tex]\sqrt \frac{(SD1)^{2} }{n1}+\sqrt \frac{(SD2)^{2} }{n2}[/tex]

[tex]1 = 1.96 \sqrt\frac{(15)^{2} }{n} + \sqrt \frac{(15)^{2} }{n}[/tex]   [∵ n₁ = n₂ = n]

[tex]1 = 1.96 * 15 \sqrt \frac{2}{n}[/tex]

1 = 41.58 / √n

√n = 41.58 / 1 = 41.58

On squaring both sides:

n = 1728.90 ≈ 1729

∴ n₁ = n₂ = 1729

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The sequence is given by the following formula:

Finally, the answers are 41 and 49.

Answer:

a) Yes, the graph is proportional.  It is linear and it goes through the point (0,0)

b) No shells cost no dollars

c)  3 shells cost 1.20

Step-by-step explanation:

To graph this, you only need 2 points.  You have the points (0,0).  You can put a point at (0,0) and at the point ( (3, 1.20) and then draw a line through those 2 points.

Using the normal distribution, the 98th percentile of the distribution of scores is of 2084.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean of the scores is given as follows:

[tex]\mu = 1468´[/tex]

The 20th percentile is of 1216, meaning that when X = 1216, Z = -0.84, hence the standard deviation is calculated as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{1216 - 1468}{\sigma}[/tex]

[tex]0.84\sigma = 252[/tex]

[tex]\sigma = \frac{252}{0.84}[/tex]

[tex]\sigma = 300[/tex]

The 98th percentile is X when Z = 2.054, hence it is calculated as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

2.054 = (X - 1468)/300

X - 1468 = 300 x 2.054

X = 2084.

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The equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.

The number of chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.

The number of chirps per minute = x

The outside temperature in degrees Fahrenheit = f

Then the linear equation will be

x = 4f - 148

Given that x = 100 chirps per minutes

Substitute the values in the equation

100 = 4f -148

4f = 100+148

4f = 248

f = 248/4

f = 62 degrees Fahrenheit.

Hence, the equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.

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THE DOMAIN & RANGE OF THE FUNCTION g(x)=|x + 4| is

This is further explained below.

Generally, The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

[tex](-\infty, \infty)[/tex]

Set-Builder Notation:

[tex]$\{x \mid x \in \mathbb{R}\}$[/tex]

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

[tex]$[0, \infty)$[/tex]

Set-Builder Notation:

[tex]$\{y \mid y \geq 0\}$[/tex]

Determine the domain and range.

Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]

Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]

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My first step is to draw a picture

We know that the length is 2 times the width

L = 2w

We are given a width of 4.6 yards

L = 2(4.6) = 9.2 yards

We can find the area by using the formula

A = l*w

A = 9.2 * 4.6

A =42.32 yd^2

Answer: 26

Step-by-step explanation:

[tex]f(-2)=-2(-2)^2 -(-2)+3=13\\\\2f(-2)=2(13)=26[/tex]

The remainder when 14 is divided by 3 is 2

What is remainder?

When we divide a number by another number if at the end if we have a number less than quotient and we can not divide further we say that the remaining number is remainder.

We are given a number as 14 and we divide 14 by 3

And on dividing 14 by 3 we get the quotient as 4 and remainder as 2.

Hence the remainder we get on dividing 14 by 3 is 2.

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The correct inequality to solve for x will be;

⇒ $20.03x + $125.99 < $200.00

Where, 'x' is the number of shirts.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Lisa buy new clothes for spring under $200.00

She spent $125.88 for buying some shirts that has each cost $20.80.

Let the number of shirts = x

Then, We can formulate for the given condition is;

The inequality for solution of the value of x is,

⇒ $20.03x + $125.99 < $200.00

Because we can solve for x, which is the number of shirts Lisa can buy with the money she has left.

Therefore,

The correct inequality to solve for x will be;

⇒ $20.03x + $125.99 < $200.00

Where, 'x' is the number of shirts.

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The equivalent expression of the perimeter in two terms is 44 + 4x

From the question, the area of the garden is given as

A = 15(2x + 7)

The area of a rectangle is calculated using

A = LW

Where

Length = L

Width = W

This means that

L = 15

W = 2x + 7

The perimeter of the rectangular garden is then calculated as

P = 2 * (L + W)

So, we have

P = 2 * (15 + 2x + 7)

Evaluate

P = 2 * (22 + 2x)

This gives

P = 44 + 4x

Hence, the perimeter is 44 + 4x

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Complete question

Shawn designs a rectangular garden as shown below. He will design both rock sections to have the same width (x). A. Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Shawn's garden.

The area in, square feet, of Shawn’s garden is found be calculating 15(2x + 7).

Answer:

Your answer would be

(a) FPUGT.

Given:

Let x be the cost of the Buffalo Bills jersey.

Let y be the cost of the Miami Dolphin jersey.

According to the question, we have

9x+3y=899.40.......(1)

12x+2y=1139.30.....(2)

From (1),

Substitute equation (3) in equation (2), we get

Then the value of y is,

Hence, the cost of the Buffalo Bills jersey is $89.95, and the cost of the Miami Dolphin jersey is $29.95.

We will have that the expression has the solution of:

Therefore the solution is D. -5.

When we elevate to the power of 3 -5 will be equal to -125.

Answer:

100 is perfect square

Step-by-step explanation:

in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100

The ratio of blue color to red paint in the mixture is 5 :3.

Ratio expresses the relationship between two or more numbers. It shows the frequency of one value compared to the frequency of another value. The sign that is used to measure ratio is :.

In order to determine the ratio, count the number of blue tiles and the number of red tiles.

Number of blue tiles = 10

Number of red tiles = 6

The ratio of blue to red is 10 : 6. When expressed in its simplest form, it is 5 : 3.

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ANSWER

EXPLANATION

The given translation

This means the shape will be translated 3units to the right and 2 units up.

That is;

The true statements about the constraints in this situation are:

In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:

2x + 0.50y = 120

Where:

When x = 40 and y = 60, we have:

2x + 0.50y = 120

2(40) + 0.50(60) = 120

80 + 30 = 120

110 ≠ 120 (Not a solution).

When x = 30 and y = 120, we have:

2x + 0.50y = 120

2(30) + 0.50(120) = 120

60 + 60 = 120

120 = 120 (True solution).

Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.

When x = 0 and y = 240, we have:

2x + 0.50y = 120

2(0) + 0.50(240) = 120

0 + 120 = 120

120 = 120 (True solution).

Therefore, if we buy no beans we can buy 240 pounds of rice.

When x = 0 - 5 and y = 240 + 20, we have:

2x + 0.50y = 120

2(0 - 5) + 0.50(240 + 20) = 120

-10 + 130 = 120

120 = 120 (True solution).

Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.

When x = 0 + 10 and y = 240 - 60, we have:

2x + 0.50y = 120

2(0 + 10) + 0.50(240 - 60) = 120

20 + 90 = 120

110 = 120 (Not a solution).

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EXPLANATION

The area of the figure can be obtained by applying the following relationship:

Where b=base and height=h

In order to find the height, we need to apply the trigonometric relationship:

Multiplying both sides by 6.4:

Solving the argument:

Switching sides:

Now that we have the height, we can compute the area as follows:

The answer is 53.24 squared inches.

Answer:

A 20% B. 45%

Step-by-step explanation:

A 40,000/200000=.2 0r 20%

b. 90,000/200000=.45 or 45%

Answer:

Step-by-step explanation:

13.

m1 is 120 because angle 120 and angle 1 are tranversal angle

So now we know that angles m1 and m2 are vertically opposite angle

Then m2 = 120

m1 = 120

m2 = 120

14.

angle 1 and 105 have the sum of 180 because they are Interior angles on the same side of the transversal

So angle 1 equals 180-105=75

angle 2 and angle 1 are on a line so the sum of the 2 angles are 180

So: 180 - 75 = 105

m1 = 105

m2 = 75

Frank first get charged an overdraft fee on Wednesday

Frank has $66.50 in his account as of Sunday.

He made a debit of $60.33 on Monday (66.50 - 60.33), leaving him with a balance of $6.17. He added $80.75 to the account on that same Monday (6.17 plus 80.75). He has $86.92 left over as of Monday.

Frank had a balance of $86.92 on Tuesday when he made a $54.45 debit (86.92 - 54.45). The remaining balance is $32.47.

Frank had a balance of $32.47 at the beginning of the day on Wednesday. He subsequently made withdraw of $49.20. debit(32.47 - 49.20). Frank has overdrawn and will be assessed an overdraft fee following the debit because his balance is -$16.73. Frank still has a negative balance even after making a deposit of $15.

Therefore, Frank was therefore assessed an overdraft fee on Wednesday.

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Angle ZWY has a measure of 13 degrees.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.

Given,

Angle WXY has a measure of 133 degrees

Angle ZYX has a measure of 34 degrees

Angle ZWY:

= 180 - 133 -34

= 13

Angle ZWY has a measure of 13 degrees.

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The multiplication we need to make is:

To answer this question we need to use the following rules for multiplications with signs:

We can see that in our expression we have the last case: a negative number multiplied by a positive number. In this case, the negative number is -6 and the positive number is 1.

So, we know from the rule that the result will be negative.

And finally, we multiply just the numbers: 6 by 1 is 6.

In summary, the result is:

Answer: -6

Answer:

-6

Step-by-step explanation:

hope this helps

If the tank contains 12 gallons and then the car consumes 10, we can know how much gasoline is left by substracting 12 with 10:

12 - 10 = 2

Then, 2 gallons of gasoline is left in the tank

Since there is still gasoline because 12 is higher than 10, then we represent this amount with a positive value.

The degree of a monomial is the power of the variable in the monomial

The degree of a monomial is defined as the highest power of the variable term in the monomial

As a general rule, a monomial has only one term

An instance of a monomial is

ax^n

Using the definition above, the degree of the monomial is n

Simlarly, the degree of x^2 is 2

This is because 2 is the power of the variable term

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