URGENT Complete the table.
It is in the image below


​

The scale factοr is οne-half. The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle. The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure

The ratiο between cοmparable measurements οf an οbject and a representatiοn οf that οbject is knοwn as a scale factοr in mathematics.

Here,

We have tο cοmpare the perimeter and area οf the οriginal figure tο the perimeter and area οf the reduced figure using the scale factοr.

The ratiο οf the length οf the οriginal rectangle tο that οf the reduced rectangle is 6 tο 3 οr a factοr οf 1/2.

The ratiο οf the width οf the οriginal rectangle tο that οf the reduced rectangle is 2 tο 1, οr, again, a factοr οf 1/2. Sο, because this ratiο οf 1/2 is cοnstant, we knοw the tοtal scale factοr is 1/2, making B cοrrect.

16 ×(1/2) = 8, which means that the perimeter οf the scale-factοred, reduced rectangle is "the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle". Sο, C is cοrrect.

Hence,  The scale factοr is οne-half.

The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle.

The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure.

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Answer:

answer is ( J )

Step-by-step explanation:

The word that would indicate that the course is taught at a faster pace than the other science courses is "accelerated." Therefore, the correct answer is J.

Yes, we can solve Curious Georgia's math problem using the concept of combinations.

There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.

We have,

Yes, we can solve Curious Georgia's math problem using the concept of combinations.

Since we cannot backtrack or go out of our way, we need to take exactly 6 blocks to the north and 6 blocks to the east to reach the math classroom.

This means that we need to choose 6 out of the 12 blocks to go north, and the remaining 6 blocks will be used to go east.

The total number of paths we can take is the number of ways we can choose 6 blocks out of the 12 blocks.

This can be calculated using the combination formula:

[tex]^nC_r[/tex] = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects to choose, and ! represents the factorial function

In this case,

we have n = 12 and r = 6.

The number of paths.

= [tex]^{12}C_6[/tex]

= 12! / 6!(12-6)!

= 924

Therefore,

There are 924 different paths we can take from our apartment to the math classroom, each of which is exactly 12 blocks long and does not backtrack or go out of the way.

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The distance traveled by the wheel when it turns 20 times is 150.7964 feet.

What is circumference?

The circumference of a wheel can be calculated as:

Circumference = 2 x π x radius

where π (pi) is a mathematical constant approximately equal to 3.14159.

The distance traveled by a wheel when it turns is equal to the circumference of the wheel multiplied by the number of times it turns.

Given that the radius of the wheel is 1.2 feet, the circumference of the wheel is:

Circumference = 2 x π x radius

Circumference = 2 x 3.14159 x 1.2

Circumference = 7.53982 feet (rounded to 5 decimal places)

Therefore, each time the wheel turns, it travels a distance of 7.53982 feet. To find the distance traveled when the wheel turns 20 times, we can multiply the distance traveled each time by the number of times the wheel turns:

Distance traveled = Circumference x Number of turns

Distance traveled = 7.53982 feet x 20

Distance traveled = 150.7964 feet (rounded to 4 decimal places)

Therefore, the distance traveled by the wheel when it turns 20 times is 150.7964 feet.

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In linear equation,  x = 6 gallons (of 80% alcohol)

y = 3 gallons (of 20% alcohol)

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Let

x = liters of 80% alcohol

y = liters of 20% alcohol

There are two unknowns, we need two equations

x + y = 9. (1)

0.80x + 0.20y = 0.60(x+y) (2)

From (1)

x + y = 9

y = 9-x

Substitute the value of y into (2) and solve for x:

0.80x + 0.20y = 0.60(x+y)

0.80x + 0.20(9-x) = 0.60(x+9-x)

0.80x + 1.8 - 0.20x = 0.60(9)

0.80x + 1.8 - 0.20x = 5.4

 0.6x = 3.6

x = 6 gallons (of 30% alcohol)

Substitute x=6 into (1) and solve for y:

x + y = 9

6 + y = 9

y = 3 gallons (of 60% alcohol)

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The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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Answer:

5.6

Step-by-step explanation:

180/50 is 5.6

Answer: 280

Step-by-step explanation:

The products of each pair of numbers are:

1 x 33 = 33

4 x 30 = 120

8 x 26 = 208

14 x 20 = 280

b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).

The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.

Answer:

a)

[tex]y = 7( {1.03}^{t} )[/tex]

[tex]y = 7( {1.03}^{5} ) = 8.11[/tex]

There were about 8.11 billion subscribers in 2019.

b)

[tex]7( {1.03}^{t}) = 7.5[/tex]

[tex]t = 2.33 \: years \: after \: 2014[/tex]

sometime in 2016

Answer:

Step-by-step explanation:

17.5

Answer: 105m

Step-by-step explanation:

Hope this helps! :)

a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is

[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]

Let us begin by writing the polynomial factors using the supplied zeros:

Because -2 is a zero, the polynomial has a component of (x + 2).

Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).

Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).

Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.

When we add these components together, we get:

[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]

Extending on this, we get:

[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]

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Answer: a

Step-by-step explanation:

The length of AB of the parallelogram is determined as 14.36 inches.

The length of AB of the parallelogram can be determined by applying cosine rule as shown below:

The cosine rule, also known as the law of cosines, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to find the length of an unknown side or the measure of an unknown angle in a triangle when the lengths of two sides and the measure of the included angle are known.

Length AB = Length AD = x

DB² = AB² + AD² - 2(AB x AD) cos (A)

22² = x² + x² - 2x²(cos 100)

484 = 2x² + 0.347x²

484 = 2.347x²

x² = 484/2.347

x² = 206.2

x = √206.2

x = 14.36 inches

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Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance, the actual labor rate per hour for April was $19.35.

1. Actual Labor Rate per Hour:

The labor price variance formula is:

Labor Price Variance = (Actual Labor Rate - Standard Labor Rate) x Actual Hours

We are given that the labor price variance for April was unfavorable and equal to $1,157. We also know that the standard labor rate was $20 per hour. Using the formula above and plugging in the known values, we can solve for the actual labor rate:

-1,157 = (Actual Labor Rate - 20) x 1,780

-1,157 = 1,780Actual Labor Rate - 35,600

1,780Actual Labor Rate = 34,443

Actual Labor Rate = 19.35

Therefore, the actual labor rate per hour for April was $19.35.

2. Standard Hours Allowed for the Output Achieved:

The flexible-budget variance formula is:

Flexible-Budget Variance = (Actual Hours - Standard Hours) x Standard Labor Rate

We are given that the flexible-budget variance for April was favorable and equal to $1,643. We also know that the standard labor rate was $20 per hour.

Using the formula above and plugging in the known values, we can solve for the standard hours allowed:

1,643 = (1,780 - Standard Hours) x 20

1,643 = 35,600 - 20Standard Hours

20Standard Hours = 33,957

Standard Hours = 1,697.85

Therefore, the standard hours allowed for the output achieved in April was 1,697.85.

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The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

A sort of data structure used in computer programming is the vector. It is a collection of data objects that can be any type, such as strings, numbers, or even other vectors. The storage and manipulation of collections of data elements, such as a list of numbers, words, or other data elements, is done using vector data structures. Sorting, searching, and data manipulation can all be done with vector data structures.

The matrix equation Axequalsb's augmented matrix for the linear system is as follows:

[tex]\left[\begin{array}{ccc}1&-2&4\\7&-4&3\\-6&2&5\\-3&16&-29\end{array}\right][/tex]

Part - 2:

Step 1: Write the system's solution as a vector after solving it.

We must first reduce the augmented matrix to its reduced row-echelon form in order to solve this system.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\-5&2&0\\-3&8&1\end{array}\right][/tex]

Step 2: We can now quickly find solutions for the unknowns.

[tex]x_1[/tex] equals

3

[tex]x_2[/tex] equals

8

[tex]x_3[/tex] equals

1

Step 3:

The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

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The rate of water flow is 6 gallons per unit of time.

What is slope?

Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.

a. To find the rate, we need to calculate the amount of water that flows per unit of time.

Method 1: Using the Graph

First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.

From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.

So, the slope of the line is:

slope = change in y-values / change in x-values

     = (60 - 30) / (10 - 5)

     = 6

Therefore, the rate of water flow is 6 gallons per unit of time.

Method 2: Using the Table

We can also find the rate by calculating the differences in y-values and x-values in the table.

x    y   Difference in y   Difference in x   Rate (y/x)

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

5    30        -              -                 -

7    42        12             2                6

10   60       18             3                6

From the table, we can see that the rate of water flow is 6 gallons per unit of time.

b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.

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The probability of picking a jack and spinning an odd number is 2/9.

Let's first list the sample space in set notation for picking a card (jack, queen, or king) and spinning a 3-section spinner with the numbers 5, 8, and 9:

The sample space is {(jack-5, jack-8, jack-9, queen-5, queen-8, queen-9, king-5, king-8, king-9)}

Now, to find the probability of picking a jack and spinning an odd number, we need to count the outcomes that meet these conditions and divide it by the total number of outcomes in the sample space.

There are two outcomes that meet these conditions: jack-5 and jack-9.

So, the probability is the number of favorable outcomes divided by the total number of outcomes:

P(jack, odd number) = 2 (favorable outcomes) / 9 (total outcomes) = 2/9

Thus, the probability of picking a jack and spinning an odd number is 2/9.

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Answer:

We can use the formula for compound interest to calculate the amount of interest Brian will earn:

A = P (1 + r/n)^(nt)

where:

A = the total amount after 7 years

P = the principal amount ($9,411)

r = the annual interest rate (3.48%)

n = the number of times the interest is compounded per year (52 weeks in a year, so n = 52)

t = the number of years (7)

Plugging in the values, we get:

A = $9,411 (1 + 0.0348/52)^(52*7)

A = $9,411 (1.0006692302021135)^364

A = $12,471.36

To find the amount of interest earned, we can subtract the principal amount from the total amount:

Interest = $12,471.36 - $9,411 = $3,060.36

Therefore, Brian will earn $3,060.36 in interest after 7 years. Rounded to the nearest cent, this is $3,060.37.

the cost of day old donuts after the discount is $4.95.

         A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.

       Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.

       The formula to calculate the discount is:

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

the discount is 40% ⇒0.4

customer buys 3 donuts.

price of 1 donut = $2.75

total cost for 3 donuts= $2.75 x 3 = $8.25

discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1

so, for 3 donuts discount = $1.1 x 3 = $3.3

therefore the final price to be paid by customer is

                    =$8.25-$3.3

                    =$4.95

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x = 5.5

we can solve this by using tanø formula i.e p/b

The amount of chalk that is greater is yellow.

Michelle is correct because more than 1/2 the chalk in the bucket is blue.

In order to determine the amount of chalk that is greater between the amount of yellow chalk and amount of green chalk, we would have to find the difference between them as follows;

Difference = 2/6 - 3/12

Difference = (4 - 3)/12

Difference = 1/12 (positive value)

Similarly, we can determine the greater amount of chalk as follows;

2/6 × 2/2 = 4/12

4/12 > 3/12

Total number of chalks = 2/6 + 5/12 + 3/12

Total number of chalks = (4 + 5 + 3)/12

Total number of chalks = 12/12

Total number of yellow and green chalks = 2/6 + 3/12

Total number of yellow and green chalks = (4 + 3)/12

Total number of yellow and green chalks = 7/12 chalks.

1 - 7/12 = 5/12

7/12 - 1/2 = 6/12 (Michelle is correct).

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The equation in the triangle to find x is x + 84 = 180.

Option B is the correct answer.

We have,

The sum of the angles in a triangle is 180.

And,

42 + 42 + x = 180

84 + x = 180

x = 180 - 84

x = 96

Thus,

The equation in the triangle to find x is x + 84 = 180.

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The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.

Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.

P(B|A) is the conditional probability of B given A.

The Bayes theorem gives us:

P(B|A) is equal to P(A|B)*P(B)/P(A).

Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:

P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871

P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.

P(B) = (7C3 * 7C1) / (14C4) = 35/143

P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.

P(A) = 7/14 = 1/2

Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.

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Answer:

Step-by-step explanation:

Hopefully this is right.

Area = r²

Which is pi times the the radius squared

The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.

Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6

My math teacher back in 7th grade gave us this sentence to help us memorize the equations.

Cherry Pie Delicious (C=d), Apple Pie Are Too (A=r²)

Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1

Hope this helps!

For a circle with a radius of 2, the area can be calculated using the formula:

Area = π x r^2

where π is approximately 3.14 and r is the radius.

Plugging in the values, we get:

Area = 3.14 x 2^2

Area = 3.14 x 4

Area = 12.56

Rounding to the nearest tenth, we get:

Area ≈ 12.6

Therefore, the area of the circle with radius 2 is approximately 12.6.

For a circle with a radius of 1, the area can be calculated using the same formula:

Area = π x r^2

Plugging in the values, we get:

Area = 3.14 x 1^2

Area = 3.14

Rounding to the nearest tenth, we get:

Area ≈ 3.1

Therefore, the area of the circle with radius 1 is approximately 3.1.

Answer:

  (a)  52°

  (b)  128°

Step-by-step explanation:

You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].

The inverse sine function is used to find the angle when its sine is known.

  sin(x) = 0.79

  x = arcsin(0.79) ≈ 52°

x ≈ 52° in the domain 0 ≤ x ≤ 90°.

The sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.

  180° -52° = 128°

x = 128° in the domain 90° ≤ x ≤ 180°.

__

Additional comment

The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.

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The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.

The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.

Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.

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To simplify the expression 1/2 x + 3/4 - 5/8 x - 7/8 + 1/8 (x + 1), we'll need to combine like terms.
First, let's distribute the 1/8 to the expression in parentheses:
1/2 x + 3/4 - 5/8 x - 7/8 + 1/8 x + 1/8
Next, we can combine like terms:
(1/2 - 5/8 + 1/8) x + (3/4 - 7/8 + 1/8)
Simplifying the coefficients of x, we get:
(1/2 - 4/8 + 1/8) x + (3/4 - 6/8 + 1/8)
(1/2 - 1/8) x + (3/4 - 5/8)
(4/8 - 1/8) x + (6/8 - 5/8)
3/8 x + 1/8

Therefore, the expression 1/2 x + 3/4 - 5/8 x - 7/8 + 1/8 (x + 1) simplifies to the equivalent expression 3/8 x + 1/8.


I was a bit confused about what you were asking, please correct me if I am wrong!

Answer:

The salary of a paramedic can vary depending on several factors such as location, experience, and employer. According to the Bureau of Labor Statistics, the median annual wage for paramedics and EMTs was $36,650 in May 2020.

Assuming a constant annual income of $36,650 over 30 years, the estimated total income for a paramedic would be:

$36,650 x 30 = $1,099,500

However, it is important to note that this is just an estimate and does not take into account potential salary increases, promotions, or changes in the job market.

The height of the square pyramid with base area 225 cm² and volume 300cm³ is equal to 4 centimeters.

Area of the base of square pyramid = 225 centimeters squared

Volume of the square pyramid = 300 centimeters cubed

Using the formula for the volume of a square pyramid,

V = (1/3) × B × h

where V is the volume,

B is the area of the base,

and h is the height of the pyramid.

Substitute this value into the formula we have,

⇒ 300 = (1/3) × 225 × h

Simplifying the equation , we get,

⇒ 900 = 225 × h

Dividing both sides by 225, we get,

⇒ h = 4

Therefore, the height of the square pyramid is 4 centimeters.

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