"Solve for x. Enter as a decimal not as a fraction. Round to the nearest hundredth if necessary."

3.

We know that Hobby Land sells art supplies two different ways.

We can represent the situation with a system of equations

Where x is the cost of one easel and y represents the cost of one paint set.

Now, we must solve the system of equations.

We can multiply equation (1) by -4

Then, we can add (3) + (2)

Now, we can solve the equation for y

Finally, to find x we can replace the value of y in the equation (1)

So, the cost of one easel is $64.

Solution as either an ordered pair:

- (64, 75).

The Function is the equation of a line

Step1: we pick any two-point in the of the table and substitute them into the formula below

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Let us pick the point (4,25) and (8,50)

where

Step-by-step explanation:

13.

a/7 + 5/7 = 2/7

a/7 = 2/7 - 5/7 = -3/7

a = -3

14.

6v - 5/8 = 7/8

6v = 7/8 + 5/8 = 12/8

v = 12/8 / 6 = 2/8 = 1/4

15.

j/6 - 9 = 5/6

j - 54 = 5

j = 5 + 54 = 59

16.

0.52y + 2.5 = 5.1

0.52y = 5.1 - 2.5 = 2.6

y = 2.6/0.52 = 5

17.

4n + 0.24 = 15.76

4n = 15.76 - 0.24 = 15.52

n = 15.52/4 = 3.88

18.

2.45 - 3.1t = 21.05

-3.1t = 21.05 - 2.45 = 18.6

t = 18.6/-3.1 = -6

we have the following:

x is small pizzas

y is medium pizzas

therefore, the answer is:

2 small pizzas and 5 (2+3) medium pizzas

Answer:

Approximately 5.2 meters

Step-by-step explanation:

This formation will make a right triangle. The ground to the point in the tree is one of the legs. The base of the tree to the base of ladder is another leg and the length of the ladder is the hypotenuse. In this case, we already have the hypotenuse and one of the legs, so we need to find the value of another leg.

We can do so by using the Pythagorean Theorem which is [tex]a^2+b^2=c^2\\[/tex].

a and b represent the values of the two legs, and c is the hypotenuse. Since we already have the hypotenuse, we can change this equation a bit to find the other leg.

Let's assign the missing value, b in the theorem.

The new equation will be [tex]b^2=c^2-a^2[/tex].

We can insert the values for c and a and solve for b.

The new equation will be [tex]b^2 = 14^2-13^2[/tex].

[tex]b^2=196-169[/tex]

[tex]b^2=27[/tex]

[tex]\sqrt{b^2} =\sqrt{27}[/tex]

The square root of [tex]b^2[/tex] cancels out.

The approximate square root of 27 is 5.19 which we can round to 5.2.

Mean will increase because 87 is greater than 83 and 78, then the eman will be greater

Answer

Option D is correct.

R' (1.5, 2)

Explanation

A dilation means the size is increased or decreased. If the scale factor is less than 1, then the size is decreased, but if the scale factor is more than 1, it means the figure is enlarged.

Dilating about the origin just multiplies the coordinates by the scale factor. So, dilating (x, y) about the origin by a scale factor k, gives new coordinates (kx, ky).

For this question, we need to dilate R (3, 4) by a scale factor, r = ½

R' = [½(3), ½(4)] = (1.5, 2)

Hope this Helps!!!

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.

In the given question,

We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

..............< p <...............

We have to construct the 90% confidence interval.

From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.

So the total number of cell phone owners aged 18 - 24 is 240.

So n=240

From them 108 have an android phone.

So x=108

Estimation of sample proportion([tex]\hat p[/tex]) = x/n

Now putting the value

Estimation of sample proportion([tex]\hat p[/tex]) = 108/240

Estimation of sample proportion([tex]\hat p[/tex]) = 0.45

Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone

C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]

As we know that

[tex]\hat p=0.45[/tex]

Now finding the value of [tex]z_{\alpha /2}[/tex]

We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90

So [tex]\alpha[/tex] = 1-0.90

So [tex]z_{\alpha /2}=z_{0.10 /2}[/tex]

[tex]z_{\alpha /2}=z_{0.05}[/tex]

From the standard z table

[tex]z_{0.05}[/tex] = 1.645

Now putting the value in the

C.I. =  [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})[/tex]

Simplifying

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})[/tex]

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})[/tex]

C.I. = [tex](0.45 \pm 1.645\sqrt{0.001031})[/tex]

C.I. = [tex](0.45 \pm 1.645\times0.0321)[/tex]

C.I. = [tex](0.45 \pm 0.053)[/tex]

We can write it as

C.I. = {(0.45+0.053),(0.45-0.053)}

C.I. = (0.503,0.397)

Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

0.503 < p < 0.397.

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In order to solve the problem we will first create equations to represent the volume of water on the gallons through the weeks. The output of the functions will be the volume of each and the entry will be the number of weeks passed.

For the first one:

While on the second one:

In order to calculate the number of weeks it'll take until they have the same volume of water we need to find the "week" which would make them equal. So we will equate both expressions and solve for that variable.

It'll take 69 weeks for the tanks to have the same volume.

We can see the pairs (-1, 4) and (1, 4), so the function is not invertible.

Remember that a function is only invertible if it is one-to-one.

This means that each output can be only mapped from a single input (the outputs are the values of g(x) and the inputs the values of x).

In the table, we can see the pairs (-1, 4) and (1, 4).

So both inputs x = -1 and x = 1 have the same output, this means that the function is not one-to-one, so it is not invertible.

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The distance​ d(P,Q) is equal to 7.1 units and the coordinates of the midpoint M of the segment PQ are (-9.5, 24.5).

Mathematically, the distance between two (2) points that are located on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the given parameters into the formula, we have;

Distance, d(P, Q) = √[(-7 + 12)² + (27 - 22)²]

Distance, d(P, Q) = √[5² + 5²]

Distance, d(P, Q) = √[25 + 25]

Distance, d(P, Q) = √50

Distance, d(P, Q) = 7.1 units.

Midpoint on x-coordinate is given by:

xm = (x₁ + x₂)/2

xm = (-7 - 12)/2

xm = -19/2

xm = -9.5

Midpoint on y-coordinate is given by:

ym = (y₁ + y₂)/2

ym = (27 + 22)/2

ym = 49/2

ym = 24.5

Therefore, the coordinates of the midpoint M are equal to (-9.5, 24.5).

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Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.

Let's call:

A = The event of the driver wearing a seat belt in a car accident.

B = The event of the driver dying in a car accident

The conditional probability is calculated as follows:

The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.

The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.

From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:

The probability of B is:

The required probability is:

Simplifying the common denominators:

To know the expression that is less than 1 when x=4

we will need to check each expression

As for the first one;

anything raise to the power of zero will give 1, since the o affects all that is in the bracket, then the expression is 1

Hence it is not less than 1

For the second expression;

The value is less than 1

For the third expression;

substituting x=4 in the above expression

The above is the same as;

Postulates and Theorems of Parallel Lines

First, we need to know what type of angles are <3 and <7. Following the definition:

If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.

Angles 3 and 7 are corresponding angles and they are told to be congruent.

Now we apply the postulate that reads:

The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate

By solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.

So, the total pounds Sarah needs to blend:

Now form an equation as:

Then, solve equation for 'x' as follows:

Therefore, by solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.

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We are given the following the following inequality:

|x - 5| >= 1

When we have a inequality in the format:

|f(x)| >= a

There are two possible solutions.

Either f(x) <= -a or f(x) >= a

In this question:

|x - 5| >= 1

x - 5 <= -1

x <= -1 + 5

x <= 4

Or

x - 5 >= 1

x >= 1 + 5

x >= 6

In interval notation, the answer is:

The solution on the number line is:

We have the sequence: 40, 20, 10, 5,...

Each term is half the previous term, so it is a geometrical sequence with common ratio r = 0.5.

We can not complete the sequence, as it becomes infinitely smaller and does not have a last term.

But we can write the three next terms to complete the blank spaces: 2.5, 1.25, 0.625.

We can start by writing the recursive formula. We know that each term is half the value of the previous term, so we wil have:

From this recursive formula, we can deduce the explicit formula (in terms of n) as:

Answer:

a) Geometric sequence with r = 0.5.

The sequence first terms are: 40, 20, 10, 5, 2.5, 1.25, 0.625.

b) The recursive formula is a(n) = 0.5*a(n-1).

The explicit formula is a(n) = 40*0.5^(n-1).

The standard form is a standard method of writing numbers such that we have it in the form:

where

Given the system of equations:

The two equations appear to be just the same, thus, we are only given one system of equations.

Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.

We have a rigth triangle, where we have to find the measure of x.

We can use trigonometric ratios to relate the lengths of the sides and the measure of x.

The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:

Answer: x = 51.4°

A) We need to find the rate of change of the function first.

The rate of change or slope of the line is:

Where x and y are the coordinates of a point in line.

In order to calculate the slope we can take the poinst:

x1 = -6, y1 = 4

x2 = -2, y2= 1

Using the formula of above we find that the slope is:

Now, in order to find the value of y-intercept of the line we can use formula:

Which is the function of the line. From the formula of above we don't know the value of b (the y-intercept).

But we know that the formula must be valid for a point in the line. We can find the value of b replacing the coordinates of a point in the line, let's choose: x = -6 and y = 4, so:

Now we use the value of m of above:

And from the last equation we can see that:

So, the equation of the line is:

And the y-intercept is obtain replacing x = 0, so the y-intercept is: y = -1/2

b) From the stepts of above we already know an equation that represents the function! It is:

c) Now, we need to use the last equation to find y = n in the table. We know from the table that the value x for that value of y is x = 3, so we replace that value in the equation of the line:

So the value of n is:

Let's call x to the bags of peanuts. One bag has a variable cost of $1.83, then the variable cost of x bags is 1.83x dollars.

The total cost of production for the corporation is obtained by adding fixed and variable costs. In this case, the total cost is 18,200 + 1.83x dollars.

The revenue for the corporation of 1 bag is $3.43, then of x bags is 3.43x dollars.

When the revenue and the total cost are equal, the breakeven point is reached, in this case:

18,200 + 1.83x = 3.43x

18,200 = 3.43x - 1.83x

18,200 = 1.6x

18,200/1.6 = x

11375 = x

The cost of production of 11375 bags is:

Total Cost = 18,200 + 1.83*11375

Total Cost = 18,200 + 20816.25

Total Cost = 39016.25

Pete’s breakeven point is (11375, 39016.25), or, 11375 bags and $39,016.25

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

ratio = 25:5 (students:teachers)

teachers = 155

students = ?

Step 02:

Carlos is correct.

The answer is:

There are 775 students.

Carlos is correct.

Mike set the variables to find in the wrong way.

ANSWER:

A rotation of 90° and then a translation left 2, up 4.

STEP-BY-STEP EXPLANATION:

Since r (90, 0) is the first and means a 90 ° rotation and that T (-2, 4) is a translation of 2 units to the left (because it is negative) and 4 units up (because it is positive) , the answer is the option "A rotation of 90° and then a translation left 2, up 4."

Answer:

$35.5

Explanation:

If Bobby purchased 15 gallons of gas and each gallon cost $2.25, the total cost of the gallons of gas is:

15 x $2.25 = $33.75

Adittionally, Bobby bought a soda for $1.75, so he spend a total of:

$33.75 + $1.75 = $35.5

So, he spends $35.5

Using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.

Recall:

Perimeter of a rectangle (P) = 2(L + W) (relationship between the width, length and perimeter)

Given:

Width (W) = 3.6 cm

Perimeter (P) = 48 cm

Length (L) = ?

Using the relationship between the dimension of a rectangle and its perimeter, the following equation would be derived:

48 = 2(L + 3.6)

Solve for the value of L

48 = 2L + 7.2

Subtract 7.2 from each side

48 - 7.2 = 2L

40.8 = 2L

Divide both sides by 2

20.4 = L

L = 20.4 cm

Therefore, using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.

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The cost price of dealer is $512.

We have to find the dealer's cost of refrigerator.

We know that mark up is on dealer's cost.

We have been given the markup as 5%

Let the dealer's cost of refrigerator be x,

Now, we know that there is a markup on it

So, we will calculate the marked up price

Marked up price = (Cost price * Markup percent)/100 + cost price

Marked up price = x*5/100 + x

Marked up price = 5x/100 + x

Marked up price = x/20 + x = (x+20x)20

Marked up price = 21x/20

We know that marked up price is the selling price and we have been given the selling price of the refrigerator

537.60 = 21x/20

537.60*20 = 21x

10752 = 21x

x = 10752/21

x = 512

The dealer's cost price is $512.

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Two lines are parallel if:

Two lines are perpendicular if:

---------------------

Let's rewrite the given equations in the slope-intercept form:

Since:

We can conclude that the lines are parallel.

Given:

The dimensions of a rectangular prism are measured in centimetres.

Required:

What unit will the volume of the prism be measured in?

Explanation:

The volume of the prism will be measured in square centimetres

Final Answer:

Square centimeters