Calling card A charges a connect fee of 69¢ plus 1.9¢ perminute. Calling card B has no connect fee but charges 6¢ perminute.

Which system of equations can be used to determine the number of minutes (x) where the price (y) is the same for both cards?

No, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.

To form a triangle considering three lengths of sides, the sum of the lengths of any two sides must be greater than the length of the third side.

Checking the above condition

1. The sum of 7.5,8.5 is 16, which is greater than 14.5. So, the condition is satisfied.

2. The sum of 7.5, 14.5 is 22, which is greater than 8.5. So, the condition is satisfied.

3.  The sum of 8.5 and 14.5 is 23, which is less than 7.5. The condition is not satisfied.

Since the sum of the two shorter sides 8.5 and 14.5 is not greater than the longest side 7.5 these three sides with given lengths cannot form a triangle.

Therefore, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.

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The angle ABC in the circle is 70 degrees.

The intercepted arc is the arc that is inside the inscribed angle and whose

endpoints are on the angle. The arc angle is half the the inscribed angle.

The intercepted arc that is formed is equal to the inscribed angle,

multiplied by two (intercepted arc measure = inscribed angle × 2).

Therefore, let's find the arc angle ABC as follows:

∠ ABC = 1  /2 (360 - 120 - 100)

∠ ABC = 1  /2 (360 - 220)

∠ ABC = 1  /2 (140)

Therefore,

∠ ABC = 70 degrees

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The preparation of the income statement of Buildex Company's adjusted trial balance is as follows:

Buildex Company

Services revenue           $70,500

Interest revenue                 5,700

Total revenue                $76,200

Expenses:

Depreciation expense   $4,700

Wages expense            52,000

Insurance expense         4,400

Supplies expense           2,700

Utilities expense              1,700

Total expenses          $65,500

Net income                 $10,700

The income statement is a financial statement that shows the financial performance of a business over a period.

In the income statement, the total expenses are deducted from the total revenue to compute the profit or loss.

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Use the following selected accounts and amounts with normal balances from Buildex Company's adjusted trial balance to prepare its income statement for the year ending December 31. Hint: Not all accounts need to be used.

Cash                        $10,400           Depreciation expense $4,700

Building                   185,000           Wages expense          52,000

Accounts payable      9,400           Insurance expense        4,400

Services revenue    70,500           Supplies expense          2,700

Interest revenue        5,700           Utilities expense             1,700

Answer:

2

Step-by-step explanation:

Ujeli had 11 pencils and she kept 3 so 11-3 = 8

so that means that the remaining pencil were dived by 4 (8÷2) = 2

The correct options regarding the inequality are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

Based on the time constraint, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 scarves * 3 hours/scarf = 12 hours.

Phil can use at most 900 yards of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can knit 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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Answer:

∫(1 - 25x²) dx

Step-by-step explanation:

The equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.

To find the equation of a line with a slope of 1/4 that passes through the point (3,0), we can use the point-slope form of the equation of a line.

The point-slope form of a line is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Substituting the values into the formula, we have:

y - 0 = 1/4(x - 3)

Simplifying:

y = 1/4(x - 3)

Distributing 1/4 throughout the expression:

y = 1/4x - 3/4

Therefore, the equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.

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Answer:

Step-by-step explanation:

Answer:

-7/4

Step-by-step explanation:

we can see that every time the value of x increases by 4, the value of y decreases by 7.

let's pick two sets of coordinates (first two will be fine).

that is (-4, 6) and (0, -1)

Slope = (change in y values) / (change in x values)

= (-1 - 6) / (0 - -4)

= -7 / (0 + 4)

= -7/4.

so our slope (gradient) is -7/4

Answer:

13cm

Step-by-step explanation:

The area of a trapezoid is given by the formula:

Area = ½*(b1+b2)*h

where:

In this problem, we are given that b1 = 6 cm, b2 = 15 cm, and Area = 136.5 square centimeters.

Plugging these values into the formula, we get:

136.5 = ½*(6 + 15)*h

Solving for h, we get:

136.5=10.5h

h = 136.5/10.5=13centimeters

Therefore, the height of the trapezoid is 13 centimeters.

52.8 square inches of paper to cover the entire Pyramid.

The amount of paper needed to cover the entire pyramid, we need to determine the total surface area of the pyramid.

The pyramid consists of a square base and four triangular faces.

1. Base Surface Area:

The surface area of the square base can be calculated by finding the area of a square with sides measuring 4.4 inches. The formula for the area of a square is side length squared:

Base Surface Area = (4.4 in)² = 19.36 in²

2. Triangular Faces Surface Area:

Each triangular face of the pyramid has a base of 4.4 inches and a height of 3.8 inches. The formula for the area of a triangle is 1/2 times the base times the height:

Triangular Face Surface Area = 1/2 * (4.4 in) * (3.8 in) = 8.36 in²

Since the pyramid has four triangular faces, the total surface area of the triangular faces is:

Total Triangular Faces Surface Area = 4 * (8.36 in²) = 33.44 in²

3. Total Surface Area:

To calculate the total surface area of the pyramid, we add the base surface area to the total triangular faces surface area:

Total Surface Area = Base Surface Area + Total Triangular Faces Surface Area

                         = 19.36 in² + 33.44 in²

                         = 52.8 in²

Therefore, it would take approximately 52.8 square inches of paper to cover the entire pyramid.

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The summation of 5 to power of n (where n starts from 1) is determined as 625.

The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.

The given summation expression include;

∑5ⁿ

where;

So we are going to sum the number 5ⁿ 4 times.

The expression becomes;

5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ

where;

n = 1

The summation becomes;

5⁴ⁿ = 5⁴ = 625

Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.

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The probability that she selects the route of three specific capitals is 3/43

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

States = 43

Capitals = 3

The probability is then calculated as

P = Capitals/States

substitute the known values in the above equation, so, we have the following representation

P = 3/43

Hence, the probability is 3/43

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The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.

To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.

The total number of students surveyed is 12 + 25 + 17 + 6 = 60.

The number of students who chose dinosaurs or planets is 25 + 17 = 42.

Therefore, the relative frequency will then be 42 / 60 = 0.7.

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The two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

To determine which expressions are less than 7/8, we can compare them individually to 7/8 and evaluate their values.

Let's consider each expression one by one:

7/8 x 9/19:

To compare this expression to 7/8, we multiply the fractions:

(7/8) x (9/19) = 63/152.

Since 63/152 is less than 7/8, this expression is less than 7/8.

7/8 x 3/4:

Multiplying the fractions:

(7/8) x (3/4) = 21/32.

Since 21/32 is less than 7/8, this expression is less than 7/8.

7/8 x 9/9:

The fraction 9/9 simplifies to 1, so the expression becomes:

(7/8) x 1 = 7/8.

Since 7/8 is equal to 7/8 (not less than), this expression is not less than 7/8.

7/8 x 4/3:

Multiplying the fractions:

(7/8) x (4/3) = 28/24.

We can simplify 28/24 to 7/6.

Since 7/6 is greater than 7/8, this expression is not less than 7/8.

Therefore, the two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

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The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.

Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.

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Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, making option A the correct answer.

The correct answer is A. Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. It represents the likelihood of an event occurring based on mathematical calculations and assumptions.

To provide a detailed explanation, let's break down the components of the definition:

Favorable outcomes: These are the outcomes that meet the desired criteria or event you are interested in. For example, if you are rolling a fair six-sided die and you want to find the probability of rolling a 3, the favorable outcome would be a single outcome where the die shows a 3.

Total number of possible outcomes: This refers to the complete set of all possible outcomes in the given situation. In the case of the fair six-sided die, there are six possible outcomes (numbers 1 to 6) since each face of the die represents a different number.

Theoretical probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio provides an estimate of the probability of the event occurring under ideal, theoretical conditions. It assumes that each outcome is equally likely to occur.

It's worth noting that theoretical probability is based on mathematical calculations and assumptions, and it may not always reflect the actual probability observed in real-world scenarios. However, it serves as a foundation for understanding and analyzing probabilities in various contexts, such as in mathematics, statistics, and decision-making processes.

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Answer:

The correct answer is 2.

Answer:

Step-by-step explanation: you are sped that is the answer black n

The coordinate of vertices of DEF are;

D = ( -4, -3)

E = ( -7, 4)

F =( -7, -3)

Here, we have,

Reflection in the y-axis: The reflection of point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse  (x,y)→( -x,y) .

First, triangle ABC is reflected across the y axes.

So, we have:

(x,y)→( -x,y)

then, translated down 5 units.

so, transformation rule on ABC, we have:

(x,y)→( -x , y - 5)

so, the coordinate of vertices of DEF are;

D = ( - 4, 2 - 5) = ( -4, -3)

E = ( -7, 9 - 5) = ( -7, 4)

F = (-7 , 2 - 5) = ( -7, -3)

Hence, the coordinate of vertices of DEF are;

D = ( -4, -3)

E = ( -7, 4)

F =( -7, -3)

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The solution to the equation 1/3a = -15 is a = -45

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

1/3a = -15

Multiply 3 to both sides of the equation

so, we have the following representation

3 * 1/3a = -15 * 3

When the products are evalated, we have

a = -45

Hence, the solution to the equation is a = -45

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1. The function representing the population of bacteria after t minutes is P(t) = 4900× [tex]e^{(0.08(t/60)}[/tex]

2. The percentage rate of change per minute is approximately 0.13%.

The general form of an exponential growth function ⇒ P(t) = P0 ×[tex]e^{(rt)}[/tex]

P(t) is the population at time t,

P0 is the initial population,⇒4900

r is the growth rate  ⇒ 8%

t is the time.

Therefore, our function in terms of hours (t) becomes:

P(t) = 4900 × [tex]e^{(0.08t)}[/tex]

To find per minute, there are 60 minutes in an hour,

∴ t becomes  t/60

P(t) = 4900× [tex]e^{(0.08(t/60))}[/tex]

We know the rate of change per hour is 8%, so the rate of change per minute will be 8% divided by 60, which is

[tex]e^{(0.08/60)-1}[/tex] × 100 = 0.13%.

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Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

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The regression equation is: y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

To compute the regression equation based on the given data, we can use the formulas for slope (b1) and y-intercept (bo):

b1 = (NΣXY - ΣXΣY) / [tex](N\sum X^2 - (\sum X)^2)[/tex]

bo = (ΣY - b1ΣX) / N

Where:

N = Number of data points (in this case, 11)

ΣX = Sum of all X values (prices)

ΣY = Sum of all Y values (average number of pounds sold per day)

ΣXY = Sum of the product of X and Y values

[tex]\sum X^2[/tex] = Sum of the squares of X values

Using the provided data:

Ex = 210

Xy = 450

Zcy = 10387

Zz = 7275

Xy = 42471

Let's calculate the required values:

N = 11

ΣX = Ex + Zcy + Zz = 210 + 10387 + 7275 = 17872

ΣY = Xy = 450

ΣXY = Xy = 450

[tex]\sum X^2 = (Ex)^2 + (Zcy)^2 + (Zz)^2 = (210)^2 + (10387)^2 + (7275)^2 = 239208144[/tex]

Now, substitute these values into the formulas to find b1 and bo:

[tex]b1 = (11 \times450 - 17872 \times 450) / (11 \times239208144 - (17872)^2)[/tex]

= -14112250 / 2050445128

≈ -0.0068824

bo = (450 - (-0.0068824 [tex]\times[/tex] 17872)) / 11

= (450 + 122.7790368) / 11

≈ 36.8881

Therefore, the regression equation is:

y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

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The complete question may be like:

Over a period of one year, retailer sells widgets at 11 different prices. He Calculates the average number of oiunds sold per day at each different price. From theese data, the following are calculated. Ex = 210, Xy = 450, Zcy = 10387, Zz? 7275 Xy? 42471 Compute the regression equation , SELEC A) y 0.20261x + 0.549951 B) y = 0.549951x + 30.410021 C) y = 0.20261. + 30.410021 D) none of these =b1x + bo.

The distance between the side AB are 314.2 ft.

In a triangle ABC AC = 200 ft, m ∠A = 72°, and m ∠B = 37°. we need to find the measure of the side AB,

So,

Using sine law.

Sin A / CB = Sin B / AC = Sin C / AB

Using the angle sum property of a triangle we find the value of angle C,

∠C = 180° - (∠A + ∠B)

∠C = 180° - (72° + 37°)

∠C = 180° - 109°

∠C = 71°

So,

Sin 37° / 200 = Sin 71° / AB

AB = 200 / Sin 37° × Sin 71°

AB = 314.2 ft

Hence the distance between the side AB are 314.2 ft.

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The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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Answer: $127.50

Step-by-step explanation: if we pull up our handy dandy calculator and do 15% of 150 it will output 22.50, 150 - 22 = 127.50 which brings the total to $127.50

The values of x and y in simplest radical form are :

5) x = 3 and y = 3√3

6) x = 5√3 and y = 10√3

7) x = 21 and y = 14√3

Given are three right angled triangles, whose angles are 30° - 60° - 90°.

The measures of sides for a 30° - 60° - 90° triangle is in the ratio 1 :√3 :2.

That is if length of the shorter leg which is the side opposite to 30° is k, then the length of the longer leg, which is the side opposite 60° will be √3k and the length of the hypotenuse, which is the side opposite to 90° will be 2k.

5) Using the above fact, here,

2k = 6

⇒ k = 6/2 = 3

So, x = 3 and y = 3√3

6) √3 k = 15

k = 15 /√3 = 5√3

So, x = 5√3 and y = 2 × 5√3 = 10√3

7) k = 7√3

So, x = √3 × 7√3 = 21

y = 2 × 7√3 = 14√3

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