figure A is a dilated from point E the center of dilation which figure is a dilation of figure A

The statement that describes the type of solutions of the specified  equation is the third option C.;

C. The equation has two valid solutions and no extraneous solutions

A solution to an equation are values of the variables of the equation that make the equation true.

The possible equation obtained from a similar question on the website can be presented as follows;

4/(3·x + 1) = x/(2·x + 10)

The above equation expressions can be combined into a quadratic equation as follows;

4 × (2·x + 10) = x × (3·x + 1)

8·x + 40 = 3·x² + x

3·x² + x - 8·x - 40 = 0

3·x² - 7·x - 40 = 0

3·x² - 15·x + 8·x - 40 = 0

3·x·(x - 5) + 8·(x - 5) = 0

(3·x + 8)·(x - 5) = 0

x = -8/3 and x = 5

Therefore, the equation has two valid solutions and no extraneous solutions

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The perimeter of the tri9angle MNO is P = 58 units.

The perimeter of the triangle is equal to the sum of the lengths of the sides, we know that:

OM = 23

NM = 18.4

To find the missing side we can use the similar triangle that we have next to it.

We can see that that OM is correspondent to LJ

Then if the scale factor between the triangles is K, we can write:

18.4  = 10*K

18.4/10 = K = 1.84

Now, NO is correspondent to KL, then:

NO = 1.84*9

NO = 16.6

Then the perimeter is:

P = 16.6 + 23 + 18.4

P = 58 units.

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Summary statistics provide a single number to describe data, while tables and graphs visually represent data to facilitate analysis and answer questions.

We have,

Data can be described by a single number using summary statistics. Summary statistics provide a concise representation of the main characteristics of a dataset.

Commonly used summary statistics include measures such as the mean, median, mode, range, variance, and standard deviation.

These single numbers provide insights into different aspects of the data, such as the central tendency, variability, or distribution.

Tables and graphs are effective tools for representing data and answering questions because they provide a visual representation that helps to organize and understand the information.

Tables present data in a structured format, typically using rows and columns, which allows for easy comparison and analysis.

They can display raw data, summary statistics, or both.

Graphs, on the other hand, use visual elements to represent data in a more intuitive and visual manner.

Different types of graphs can be used depending on the nature of the data and the question at hand.

For example, bar graphs can be used to compare categories or discrete data, line graphs can show trends over time, and scatter plots can display the relationship between two variables.

Tables and graphs help to answer questions about data by providing a clear and organized presentation.

They allow us to observe patterns, trends, and relationships, making it easier to draw conclusions and make informed decisions.

Visually representing data, tables, and graphs enhances our ability to analyze and interpret complex information quickly and effectively.

Thus,

Summary statistics provide a single number to describe data, while tables and graphs visually represent data to facilitate analysis and answer questions.

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The number of fluid ounces of iced tea does the bottle hold is 25.

Given that, a bottle holds 750 milliliters of iced tea.

1 fluid ounce has 30 milliliters.

Here, the number of fluid ounces = Total quantity of iced tea/Quantity of fluid in a fluid ounce

= 750/30

= 25

Therefore, the number of fluid ounces of iced tea does the bottle hold is 25.

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The number of square inches or area of gift wrap that the makeup artist will need is 10.8π square inches.

Given that,

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap.

Radius of each lipstick = 0.6 inch

Height of the lipstick = 2.4 inches

Now,

Area of the each lipstick = 2πrh + 2πr², where r is the radius and h is the height.

Area = 2π (0.6) (2.4) + 2π (0.6)²

        = 2.88π + 0.72π

        = 3.6π

Area of the wrap for 3 lipsticks = 3 × 3.6π = 10.8π square inches.

Hence the area is 10.8π square inches.

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Answer:

look at explanation

Step-by-step explanation:

it's a 50/50 chance

The solution is : 22 meters would be saved if it were possible to walk through the pond.

Here, we have,

There is a pond between two points A and B.

To avoid the pond, one must walk to the south from point A to point C (say) by 34 meters and then to the east from point C to point B by 41 meters.

Now, it is clear that Δ ABC is a right triangle with AB as the hypotenuse that is the minimum distance from A to B through the pond.

The two legs of the right triangle are AC and CB.

Applying Pythagoras Theorem,

AB² = AC² + CB²

      = 34² + 41²

      = 2837

⇒ AB = 53 meters (Rounded to the nearest meter)

Therefore, (34 + 41) - 53 = 22 meters will be saved if it were possible to walk through the pond.

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complete question:

To get from point A to point B you must avoid walking through a pond. To

avoid the pond, you must walk 34 meters south and 41 meters east. To the

nearest meter, how many meters would be saved if it were possible to walk

through the pond?

Borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.

To estimate the extra cost per month of borrowing $50,000 for 30 years at 11% instead of 10%, you can follow these steps:

Calculate the monthly payment for each interest rate:

The formula to calculate the monthly payment for a fixed-rate loan is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M is the monthly payment,

P is the principal amount (loan amount),

r is the monthly interest rate (annual interest rate divided by 12),

n is the total number of monthly payments (number of years multiplied by 12).

Let's calculate the monthly payment at 10% interest rate first:

P = $50,000

r = 10% / 100 / 12 = 0.0083333 (monthly interest rate)

n = 30 years * 12 = 360 (total number of monthly payments)

M1 = $50,000 * (0.0083333 * (1 + 0.0083333)^360) / ((1 + 0.0083333)^360 - 1)

Calculate the monthly payment at 11% interest rate using the same formula:

P = $50,000

r = 11% / 100 / 12 = 0.0091667 (monthly interest rate)

n = 30 years * 12 = 360 (total number of monthly payments)

M2 = $50,000 * (0.0091667 * (1 + 0.0091667)^360) / ((1 + 0.0091667)^360 - 1)

Calculate the difference in monthly payments:

Extra cost per month = M2 - M1

Now let's perform the calculations:

M1 ≈ $446.92 (monthly payment at 10% interest rate)

M2 ≈ $491.55 (monthly payment at 11% interest rate)

Extra cost per month = $491.55 - $446.92 ≈ $44.63

Therefore, borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.

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Answer:

  y = 6

Step-by-step explanation:

You want the value of y, given the sides of isosceles triangle DEF are marked as (7y +14) and (9y +2).

The sides of an isosceles triangle are congruent, so we have ...

  FD = FE

  7y +14 = 9y +2

  12 = 2y . . . . . . . . . . subtract 7y+2

  6 = y . . . . . . . . . divide by 2

The value of y is 6.

__

Additional comment

We know this triangle is isosceles for a couple of reasons. One is that the altitude is a perpendicular bisector of the base. Another is that the two smaller triangles are congruent by the SAS (or LL) postulate, making FD = FE by CPCTC.

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The radius of the sphere is 2cm

The circumference of the sphere is about 12.56 cm

cm²

The volume of the sphere is about 33. 5cm³

From the information given, we have that;

We have that the largest cross sectional area of the sphere takes the value

πr²

The circumference of the sphere = 2πr

Equate the expressions;

2πr = πr²

in the ratio of 4: 1

2πr = 4πr²

Divide the values

r =2cm

Substitute the value to determine the circumference of the sphere, we get;

Circumference = 2 × 3.14 × 2

Multiply the values, we get

Circumference = 12.56 cm

The volume of the sphere is represented as;

=4/3 ×  3.14 × (2)³

Multiply the values, we have;

=4/3 × 3.14 ×8

Multiply the values, we get;

= 33. 5cm³

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Answer:

$224.42

Step-by-step explanation:

P is the principal balance

r is the interest rate (as a decimal)

n is the number of times interest is compounded per year

t is the number of years

Input all of this into the equation you have.

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

[tex]A=160(1+\frac{.07}{1})^{1(5)}[/tex]

Do the math.

[tex]A=160(1+.07)^{5}[/tex]

[tex]A=160(1.07)^{5}[/tex]

[tex]A=160(1.403)[/tex]

[tex]A=224.418[/tex]

Answer: 43.75 miles per day.

Step-by-step explanation: All you have to do is divide 350 by 8, when you divide you basically just split the number evenly 8 times, which is what 350 divided by 8 is. He will have to drive 43.75 miles a day.

Answer: Bryan drove the fastest.

Step-by-step explanation: To find out who drove the fastest, we need to calculate the speed of each person. Speed is given by the formula distance/time.

For Doug:

Speed = 28 miles / 2.3 hours = 12.17 miles/hour

For Primo:

Speed = 34 miles / 2.1 hours = 16.19 miles/hour

For Camillo:

Speed = 57 miles / 1.4 hours = 40.71 miles/hour

For Bryan:

Speed = 49 miles / 1.2 hours = 40.83 miles/hour

The perimeter of the shaded figure is 21.42 units.

Given that, radius of two congruent circles is 3 units.

Dimensions of rectangle are length=6 units and width=3 units.

The formula to find the arc length of a circle is θ/360° ×2πr.

Here, arc length = 90°/360° ×2×3.14×3

= 0.25×2×3.14×3

= 4.71

Arc length of two congruent circles = 2×4.71

= 9.42 units

Perimeter = 9.42+6+6

= 21.42 units

Therefore, the perimeter of the shaded figure is 21.42 units.

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The period of the function is 4π, and the amplitude is 2.

Given data ,

Let the function be represented as f ( x ) = y

Now , the value of f ( x ) is

y = 2sin ( 1/2 )x

To find the period and amplitude of the function y = 2sin((1/2)x), we can use the standard form of a sine function: y = Asin(Bx).

In this case, the amplitude (A) is 2.

The amplitude represents the maximum displacement from the midpoint of the sinusoidal function.

To find the period, we can use the formula:

Period = (2π) / |B|.

B = 1/2.

Period = (2π) / |1/2|

P = (2π) / (1/2) = 2π * 2/1 = 4π

Hence , the period of the function is 4π, and the amplitude is 2.

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The area of the sector is 30.375 ft squared.

The  sector of a circle has a diameter of 18 feet and an angle of 3/4π radians.

Therefore, the area of the sector can be found as follows:

area of the sector = ∅ / 2 r²

where

∅ = central angle in radian

r = radius of the circle

Therefore,

∅ = 3 / 4 π

r = 18 / 2 = 9 ft

area of the sector = 3 / 4 π ÷ 2 × 9²

area of the sector = 3 / 8π × 81

area of the sector = 243 / 8π

area of the sector = 30.375 ft²

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The area of the sector is 95.43 square feet.

The area of sector when the angle is given in radians is given by the formula:

Area of sector = (1/2) × r²θ

where θ is the angle subtended at the center and r is the radius of the circle.

We have:

θ = 3π/4

r = 18/2 = 9 feet

Substituting into the formula:

Area of sector = (1/2) × 9² × 3π/4

Area of sector = 95.43 square feet

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Answer:

To find out how many jars Jazmine can fill with her 3 1/3 cups of jam, we need to divide the total amount of jam by the amount of jam that each jar can hold.

First, we need to convert 3 1/3 cups into an improper fraction:

3 + 1/3 = (3 x 3 + 1) / 3 = 10/3

So, Jazmine has 10/3 cups of jam.

Next, we need to convert the jar size of 2/5 cup into a fraction with the same denominator as 10/3:

2/5 = 6/15

Now we can divide the total amount of jam by the amount of jam that each jar can hold:

(10/3) ÷ (6/15)

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:

(10/3) x (15/6)

Simplifying:

(10/3) x (5/2) = (50/6)

So Jazmine can fill (50/6) jars with her 3 1/3 cups of jam.

This is an improper fraction, so we can convert it to a mixed number:

(50/6) = 8 2/6 = 8 1/3

Therefore, Jazmine can fill 8 and 1/3 jars with her 3 1/3 cups of jam.

Step-by-step explanation:

The third root of 11 lies between the whole numbers 2 and 3.

The estimate of a non-exact root of x is done finding two numbers, as follows:

The number for this problem is given as follows:

Cubic root of 11.

For the parameters, we have that:

Hence the third root of 11 lies between 2 and 3, as 2³ < 11 < 3³.

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Answer:f=60a(60)

hope this helps bye

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

The length of the ladder is 4.72 meters and its angle of elevation is 30.4 degrees.

Using the Pythagorean theorem:

Length of the ladder = √(height² + horizontal distance²)

= √(2.35² + 4.10²)

= √(5.5225 + 16.81)

= √22.3325

≈ 4.72 meters

To calculate the angle of elevation (θ), we can use the trigonometric function sine:

sin(θ) = height / length of the ladder

θ = arcsin(height / length of the ladder)

θ = arcsin(2.35 / 4.72)

θ ≈ 30.4 degrees

Therefore, the length of the ladder is 4.72 meters and its angle of elevation is 30.4 degrees.

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The Translation of given question is:

A ladder is being constructed that starts at 4.10 m and reaches a height of 2.35 m. Calculate the length of the ladder and its angle of elevation.

Answer:

Step-by-step explanation:

he correct answer for the domain of function p(x) is:

Domain: [1, ∞)

This means that x can take any value greater than or equal to 1, including 1 itself. The square root function (√x) is defined for non-negative real numbers, so x must be greater than or equal to 0. In this case, since we have √x - 1 in the function, x must be greater than or equal to 1 to avoid a negative value under the square root. Additionally, there are no other restrictions on the domain, so any value of x greater than or equal to 1 is allowed.

Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

The expression that is equivalent to the given variables above would be =y¹²/5. That is option A.

To determine the expression that is equivalent to the given variable above, the following steps needs to be taken as follows;

That is:

= 9x⁵y¹⁶/45x⁵y⁴

Divide the whole numbers using 9 for both the numerator and denominator.

= x⁵y¹⁶/5x⁵y⁴

To solve for x':

= X(5-5 = 0)

To solve for y':

= y(16-4= 12)

Therefore the equivalent = =y¹²/5

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The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

The probability of choosing the expected value of games is

a) P ( G ) = 1/4

b) P ( R ) = 3/8

c) P ( B ) = 1/4

d) P ( Y ) = 1/8

Given data ,

Color Payout

Red $2

Blue $6

Green $6

Yellow $20

Now , game costs $5 to play and you win money based on the color the spinner lands on

On simplifying , we get

The number of yellow spinner = 1

The number of blue spinner = 2

The number of green spinner = 2

The number of red spinner = 3

So , the probabilities are

a) P ( G ) = 1/4

b) P ( R ) = 3/8

c) P ( B ) = 1/4

d) P ( Y ) = 1/8

Hence , the probability is solved

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The correct answer is:

B. cosθ = √5/3 and tanθ = 2/√5

C. cosθ = -√5/3 and tanθ = 2/√5

To solve this question, we can use the given information that sinθ = 2/3 and determine the values of the other trigonometric functions based on that.

Recall the trigonometric identity: sin^2θ + cos^2θ = 1

Since sinθ = 2/3, we can substitute this value into the identity and solve for cosθ:

(2/3)^2 + cos^2θ = 1

4/9 + cos^2θ = 1

cos^2θ = 1 - 4/9

cos^2θ = 5/9

Taking the square root of both sides, we get:

cosθ = ±√(5/9) = ±(√5/3)

Now, let's analyze the given options:

A. secθ = 3/√5 and tanθ = 2/√5

B. cosθ = √5/3 and tanθ = 2/√5

C. cosθ = -√5/3 and tanθ = 2/√5

D. secθ = -3/2 and tanθ = 2/√5

From our calculations, we found that cosθ can be either √5/3 or -√5/3. So, option B and C are valid.

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Answer:

[tex]\Huge \bold{\boxed{\boxed{\text{5\%}}}}[/tex]

Step-by-step explanation:

To calculate the margin of error for the survey, we need to use the formula:

[tex]\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}[/tex]

The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:

[tex]\large \text{Range of values = 32\% - 22\% = 10\%}[/tex]

Substituting this value into the formula, we get:

[tex]\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}[/tex]

Therefore, the margin of error on the survey is 5%.

1. The weight of the patient in kilograms is 27.216 kg. (60 lb * 0.4536 kg/lb = 27.216 kg)

2. The total dosage of medication required for the patient is 13.608 mg. [tex](0.5 mg/kg \times 27.216 kg = 13.608 mg)[/tex]

3. The patient should be administered 1.3608 mL of the stock medication. (13.608 mg / 10 mg/mL = 1.3608 mL)

To calculate the necessary values based on the given information, let's follow the steps below:

Determine the weight of the patient in kilograms:

Given that the patient weighs 60 lb, we can convert this to kilograms using the conversion factor of 1 lb = 0.4536 kg.

Weight (in kg)[tex]= 60 lb \times 0.4536 kg/lb = 27.216 kg.[/tex]

Calculate the total dosage of medication required for the patient:

The medication order is 0.5 mg/kg, and the patient weighs 27.216 kg.

Total dosage [tex]= 0.5 mg/kg \times 27.216 kg = 13.608 mg.[/tex]

Determine the amount of stock medication required in milliliters (mL):

The stock medication is available in a concentration of 10 mg/mL.

To find the volume required, we need to divide the total dosage by the concentration of the stock medication.

Volume (in mL) = Total dosage (in mg) / Concentration (in mg/mL) = 13.608 mg / 10 mg/mL = 1.3608 mL.

Therefore, based on the given information, the weight of the patient is 27.216 kilograms, the total dosage of medication required is 13.608 milligrams, and 1.3608 milliliters of the stock medication should be administered to the patient.

Please note that when administering medication, it is crucial to follow the guidance of a healthcare professional and consider other factors such as the specific medication instructions, patient's condition, and any allergies or contraindications.

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Question: A patient weighs 60 lb, and the medication order is 0.5 mg/kg. The stock medication is available in a concentration of 10 mg/mL.

Based on this information, calculate the following

What is the weight of the patient in kilograms? (1 lb = 0.4536 kg)

What is the total dosage of medication required for the patient?

How many milliliters (mL) of the stock medication should be administered to the patient?

Please provide the necessary calculations and steps to find the answers based on the given information.

The export will reach $11.2 billion in 5.4 years or in the year 2013 from the given function.

Given that,

The value of China's exports of automobiles and parts (in billions of dollars) is approximately,

f(x) = 1.8208 e^(0.33872x)

We have to find the value of x, when f(x) = $11.2 billion

11.2 = 1.8208 e^(0.33872x)

6.15 = e^(0.33872x)

Taking logarithms on both sides,

ln (6.15) = 0.33872x ln (e)

ln (6.15) = 0.33872x

x = 5.36 ≈ 5.4 years.

The value will reach 11.2 billion after 5.4 years which is in the year 2013.

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