(L5) Theorem 5.5B states that if the measure of one angle of a triangle is greater than the measure of another angle, then the side __________ he angle with the greater measure will be longer than the side opposite the angle with the __________ measure.

hi

Sales  taxes  = 390 *0.074 = 28.86  

Total cost :  390+28.86 =  418.86

Answer:

$60.

Step-by-step explanation:

Cost price=  $50

Selling price = $80

Percentage markup = Gain/Cost price x   100%

=30/50x100

=$60.

Answer:

25

Step-by-step explanation:

math

The concept of the radius helps us understand the distance between the center of the circle and any point on its circumference.

Mathematicians use the term "radius" to label any line segment from the center of a circle to any point on the circle  is likely due to the historical development of geometry and the influence of Latin and Greek languages. and it helps to describe the size and properties of the circle.

The concept of the radius helps us understand the distance between the center of the circle and any point on its circumference. It is a fundamental measurement in geometry and is used in various mathematical formulas and equations involving circles.

In geometry, the study of circles and their properties has a long history that dates back to ancient times. The ancient Greek mathematicians, including Euclid, made significant contributions to the development of geometry. The Greek language was widely used in mathematics during that period.

The term "radius" itself originates from Latin and means "spoke of a wheel." It refers to the line segment from the center of a circle to any point on the circle, which resembles the spoke of a wheel radiating outwards. The concept of the radius played a fundamental role in understanding the properties of circles and their relationships with other geometric figures.

When mathematicians formalized the study of circles and developed a standard terminology, the term "radius" was adopted to describe this important line segment. Since mathematics often draws from historical and cultural influences in naming concepts, it is likely that the term "radius" was chosen to maintain consistency with its historical usage and to evoke the visual image of lines radiating from a center.

While the term "radius" may have originated from the analogy to a wheel spoke, its adoption and usage in mathematics have become established conventions that provide a concise and universally understood way to refer to this key element of a circle.

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The time it takes for Mrs. Jardine to bake more cookies compared to Mrs. How is of 6 hours.

The linear functions in this problem are defined in the slope-intercept format, as follows:

y = mx + b.

In which:

Miss Hoy can bake two dozen cookies every four hours. Mrs. Jardine can bake one dozen cookies every one hour, then the slopes are given as follows:

Assuming Mrs. Hoy gets a 36 cookie head start, the functions are given as follows:

Mrs. Jardine will have baked more cookies when:

12x > 6x + 36

6x > 36

x > 36/6

x > 6 hours.

Hence after 6 hours.

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The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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The region of integration D is a triangular region bounded by the lines y = x, x = 3, and the curve y = x^2. To evaluate the double integral ∬ D dxdy, we set up the limits of integration and find the integral to be 4.5.

(a) To sketch the region of integration, D, we can plot the given lines and curve on a coordinate system. The line y = x forms the boundary on one side, the line x = 3 forms the boundary on the other side, and the curve y = x^2 forms the upper boundary of the triangular region D. The region D will be the area enclosed by these lines and curve.

(b) To evaluate the double integral ∬ D dxdy, we need to determine the limits of integration. Since the region D is bounded by the lines y = x and x = 3, the limits of integration for x will be from x = 0 to x = 3. For each value of x within this range, the corresponding y-values will vary from y = x to y = x^2. Therefore, the limits of integration for y will be from y = x to y = x^2.

Setting up the integral:

∬ D dxdy = ∫[0,3] ∫[x,x^2] 1 dy dx

Now we can integrate with respect to y first and then with respect to x:

∬ D dxdy = ∫[0,3] ∫[x,x^2] 1 dy dx

         = ∫[0,3] [y] [x,x^2] dx

         = ∫[0,3] (x^2 - x) dx

Evaluating the integral:

∬ D dxdy = ∫[0,3] (x^2 - x) dx = [x^3/3 - x^2/2] [0,3]

                                = (3^3/3 - 3^2/2) - (0/3 - 0/2)

                                = 27/3 - 9/2

                                = 9 - 4.5

                                = 4.5

Therefore, the value of the double integral ∬ D dxdy is 4.5.

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Answer:

n < 5

Step-by-step explanation:

in the number line n is less than 5

there is a hollow circle so it means n < 5

if it is a full circle it would be n <= 5

Answer:

ONe is postive and the other is negetive

Step-by-step explanation:

The value of 'a' in the given expression is 11/2.

The square root formula can be used to calculate the square root of any number. The square root of any number is the value that, when multiplied by itself, yields the original number. Each number has two square roots, one positive and the other negative. For example, the number four has two square roots, -2 and 2.

Given \($32 \sqrt{2}=2^a$\)

We can write 32 as:

32 = 2 × 2 × 2 × 2 × 2

32 = \(2^{5}\)

We can write \($\sqrt{2}=2^{1 / 2}$\).

Now,

\($$\begin{array}{r}32 \sqrt{2}=2^a \\2^5 \cdot 2^{1 / 2}=2^a \\2^{5+1 / 2}=2^a \\2^{1 / 2}=2^a \\\end{array}$$\)

Therefore, the value of a = 11/2.

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Answer:

who tell me how to start?

The slope and y-intercepts of each line, respectively, are:

5. m = -2; b = 6       6. m = 5/3; b = 10/3       7. m = -1/4; b = 4

Slope of a line is calculated as, m = change in y / change in x.

5. Given (2, 2) and (3, 0):

Slope of the line (m) = change in y / change in x = 2 - 0 / 2 - 3

m = 2/-1

m = -2

To find the y-intercept (b), substitute m = -2 and (x, y) = (2, 2) into y = mx + b:

2 = -2(2) + b

2 = -4 + b

2 + 4 = b

b = 6

6. Given (1,5) and (4, 10):

Slope of the line (m) = change in y / change in x = 10 - 5 / 4 - 1

m = 5/3

To find the y-intercept (b), substitute m = 5/3 and (x, y) = (1, 5) into y = mx + b:

5 = 5/3(1) + b

5 - 5/3 = b

b = (15 - 5)/3

b = 10/3

7. Given (8, 2) and (-8, 6):

Slope of the line (m) = change in y / change in x = 6 - 2 / -8 - 8

m = 4/-16

m = -1/4

To find the y-intercept (b), substitute m = -1/4 and (x, y) = (8, 2) into y = mx + b:

2 = -1/4(8) + b

2 = -2 + b

2 + 2 = b

b = 4

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The area between -2 and 2 is approximately 0.9545. Therefore, the percentage of times between 2 and 4 hours is 95%.

To find the percentage of times between 2 and 4 hours, we need to first standardize the values using the formula z = (x - mu) / sigma, where x is the value we are interested in (2 and 4), mu is the mean (3), and sigma is the standard deviation (0.5).

For 2 hours: z = \(\frac{(2 - 3)}{0.5}\) = -2

For 4 hours: z =\(\frac{(4 - 3)}{0.5}\) = 2


Next, we can use a standard normal distribution table or calculator to find the area under the curve between -2 and 2. This area represents the percentage of times between 2 and 4 hours.

According to the table, the area between -2 and 2 is approximately 0.9545. Therefore, the percentage of times between 2 and 4 hours is 95%.

So the answer is: 95%.

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Answer:

i need points

Step-by-step explanation:

ndm

Answer: 3.50

Step-by-step explanation:

4 ounces x 3 tenders = 12ounces so 3 dollars. then 4 ounses so 50 cents. so 3.00 + 0.50= 3.50

To design a 64k x 8 PROM (Programmable Read-Only Memory) using 16k x 4 PROM, we need 8 ICs (Integrated Circuits) of PROM with a 2-to-4 decoder and 4 lines and 2 columns.

In a 16k x 4 PROM, each memory location stores 4 bits of data, and there are 16k (16384) memory locations. To achieve a 64k x 8 memory capacity, we need four times the number of memory locations, which is 4 x 16384 = 65536 memory locations.  To address these 65536 memory locations, we require 16 bits of address lines. The 2-to-4 decoder is used to decode these 16 address lines into 2^16 = 65536 unique combinations. Each combination represents a specific memory location in the 64k x 8 PROM.

With 2 lines and 2 columns for each IC, we need 8 ICs in total to accommodate the required memory capacity. Each IC can handle 4 lines and 2 columns, resulting in a total of 8 lines and 2 columns.To design a 64k x 8 PROM using 16k x 4 PROM, we need 8 ICs of PROM with a 2-to-4 decoder and 4 lines and 2 columns. Each IC can handle 16k memory locations, and by combining them, we achieve a memory capacity of 64k x 8.

Note: It's worth mentioning that there are alternative ways to achieve the same memory capacity, such as using different decoder configurations or varying the number of lines and columns per IC. The specific design choice may depend on factors such as cost, space constraints, and specific requirements of the application.

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer:

\(\sqrt[3]{3}\)

Step-by-step explanation:

Our expression is: \(\frac{1}{3} \sqrt[3]{81}\).

Let's focus on the cube root of 81 first. What's the prime factorisation of 81? It's simply: 3 * 3 * 3 * 3, or \(3^3*3\). Put this in for 81:

\(\sqrt[3]{81} =\sqrt[3]{3^3*3}=\sqrt[3]{3^3} *\sqrt[3]{3}\)

We know that the cube root of 3 cubed will cancel out to become 3, but the cube root of 3 cannot be further simplified, so we keep that. Our outcome is then:

\(\sqrt[3]{3^3} *\sqrt[3]{3}=3\sqrt[3]{3}\)

Now, let's multiply this by 1/3, as shown in the original problem:

\(\frac{1}{3}* 3\sqrt[3]{3}=\sqrt[3]{3}\)

Thus, the answer is \(\sqrt[3]{3}\).

~ an aesthetics lover

Answer:

£48

Step-by-step explanation:

Area of walls = area of four rectangular walls + area of two triangular shape at front and back

Area of a rectangular wall = l *w = 8 * 4 = 32 m²

Area of 4 rectangular walls = 4 *32 = 128 m²

Triangle:

Base = 6m

height = h = 7 - 4 = 3 m

Area of triangle = (1/2)*b*h

                          \(= \dfrac{1}{2}*6*3 = 3*3 = 9 \ m^{2}\)

Area of 2 triangles = 2*9 = 18 m²

Area of four walls = 128 + 18 = 146 m²

Number of paint tins required = 146 ÷ 25 = 5.84 = 6

6 tins are required.

Cost of 6 tins = 8 * 6 = £48

The linear function that models the data is y=3/5x - 2/5 which has the form y=mx+b, where m is the slope and b is the y-intercept.

This can be written in the form y = mx + b where m and b are constants and x is a variable. The graph of a linear function is a straight line that goes through the origin.

To calculate the linear function, we must first calculate the slope. The slope is the numerical change in y (rise) divided by the numerical change in x (run).

Subtracting the y-values for x=-9 and x=-8, we get

-29/5 - (-26/5) = -3/5.

Similarly, subtracting the x-values for x=-9 and x=-8, we get

-9 - (-8) = -1.

Now, -3/5 / -1, we get the slope, m, of 3/5.

Next, we must calculate the y-intercept, b.

To do this, we can use either of the points given.

Using the points (x=-9, y=-29/5), we can substitute the x and y values into the linear equation, y=mx+b.

-29/5 = 3/5(-9) + b, which can be simplified to

-29/5 = -27/5 + b.

Adding 27/5 to both sides, we get b = -2/5.

Therefore, the linear function that models the data is y=3/5x - 2/5.

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A rectangular prism has 6 faces, 8 vertices and 12 edges.

What is rectangular prism?

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.

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The formula expressing the radius of the circle, r (in cm), in terms of the number of seconds, t, since the circle started shrinking is r = r₀ - kt, where r₀ is the initial radius and k is the rate at which the circle is shrinking.

The formula r = r₀ - kt represents the relationship between the radius of the circle and the time elapsed since it started shrinking. Here's an explanation of the variables:

r represents the radius of the circle at any given time t.r₀ represents the initial radius of the circle when it started shrinking .k represents the rate at which the circle is shrinking, indicating how much the radius decreases per unit of time.t represents the number of seconds that have elapsed since the circle started shrinking.

By subtracting kt from the initial radius r₀, we can determine the current radius of the circle at any given time t. The term kt represents the amount by which the radius decreases over time, based on the rate of shrinkage defined by the value of k.

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the local time in Anchorage when the image was taken was 5:00 PM, and the local day was Dec. 2, 2011.

To determine the local time and day in Anchorage when the satellite image was taken, we need to consider the time difference between the Prime Meridian (0 degrees longitude) and Anchorage, Alaska (approximately 150 degrees west longitude).

Each time zone is approximately 15 degrees wide, representing a one-hour difference in local time. Anchorage is in the Alaska Standard Time (AKST) zone, which is typically UTC-9 (nine hours behind UTC) during standard time.

Given that Anchorage is about 150 degrees west of the Prime Meridian, we can calculate the time difference as follows:

150 degrees / 15 degrees per hour = 10 hours

Therefore, when the image was taken at 0300Z (3:00 AM), Dec. 3, 2011, at the Prime Meridian, the local time and day in Anchorage were:

3:00 AM - 10 hours = 5:00 PM, Dec. 2, 2011

So, the local time in Anchorage when the image was taken was 5:00 PM, and the local day was Dec. 2, 2011.

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Each term in pattern B can be found by dividing the corresponding term in pattern A by 3.

The given table is :

Pattern A           30          24             18           12

Subtract 6

Pattern B           10           8               6             4

Subtract 2

As we observe the table when pattern A is divided by pattern B the result is 3

30/10= 24/8=18/6=12/4 =3

or when we divide pattern A numbers with 3 we get the pattern B values.

Hence,  each term in pattern B can be found by dividing the corresponding term in pattern A by 3.

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We can rewrite m^91 + 2m^90 as (m+2m^90)^2 - m^90.

We are looking for values of m such that m+2m^90 is an integer.

For m = 30, m+2m^90 = 30 + 230^90 = 30 + 2(30^90) = 60, which is an integer.

For m = 24, m+2m^90 = 24 + 224^90 = 24 + 2(24^90) = 48, which is also an integer.

For the other values of m, m+2m^90 is not an integer. Therefore, the only values of m for which m^91 + 2m^90 is the square of an integer are m = 24 and m = 30.

To sketch the area represented by g(x) = ∫1xt4 dt, we need to first understand what this function is representing.

g(x) represents the area under the curve of the function t^4 from t = 1 to t = x. This means that for any value of x, g(x) is equal to the area under the curve of t^4 from t = 1 to t = x. To sketch this area, we can start by plotting the curve of t^4 on a graph. We can then shade in the area under the curve from t = 1 to t = x for any given value of x. As we increase x, the shaded area will increase accordingly.

Since this is a "long answer" response, it's also worth noting that we can use calculus to find the exact value of g(x) for any given value of x. Taking the integral of t^4 from t = 1 to t = x, we get: g(x) = ∫1xt^4 dt = [(1/5)t^5]1x = (1/5)x^5 - (1/5)
This means that g(x) is a function of x, and the value of g(x) for any given x can be found by plugging in x to the equation (1/5)x^5 - (1/5).

So, to summarize, the area represented by g(x) is the area under the curve of t^4 from t = 1 to t = x. This area can be sketched by shading in the area under the curve from t = 1 to t = x on a graph. We can also use calculus to find the exact value of g(x) for any given value of x.

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The 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

To construct a 95% confidence interval for the mean weight of the bags of that specific brand of candies, we can use the following formula:

Confidence Interval = Sample Mean ± (Critical Value)× (Standard Deviation / √Sample Size)

First, let's calculate the critical value. Since the population distribution is assumed to be normal and the sample size is small (n = 16), we can use a t-distribution instead of a z-distribution.

The critical value can be obtained from the t-distribution table or using statistical software. For a 95% confidence level with 15 degrees of freedom (n - 1 = 16 - 1 = 15), the critical value is approximately 2.131.

Now, we can plug in the given values into the formula:

Sample Mean = 2.5 ounces (given)

Standard Deviation = 0.1 ounces (known)

Sample Size (n) = 16 (given)

Critical Value = 2.131 (from t-distribution)

Confidence Interval = 2.5 ± (2.131)× (0.1 / √16)

Calculating the standard error (Standard Deviation / √Sample Size):

Standard Error = 0.1 / √16 = 0.1 / 4 = 0.025

Confidence Interval = 2.5 ± (2.131) × (0.025)

Calculating the bounds of the confidence interval:

Lower Bound = 2.5 - (2.131) ×(0.025)

Upper Bound = 2.5 + (2.131)×(0.025)

Lower Bound ≈ 2.5 - 0.0539 ≈ 2.4461 ounces

Upper Bound ≈ 2.5 + 0.0539 ≈ 2.5539 ounces

Therefore, the 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

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Answer:

\(\displaystyle x \approx 9.2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:  

Step 1: Define

Angle θ = 35°

Opposite leg = x

Hypotenuse = 16

Step 2: Solve for x

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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Answer:

x = 8

Step-by-step explanation:

7x-3x= 32

4x=32

/4    /4

x= 8

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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