Tell whether the sequence is arithmetic. If it is, identify the common difference.
0, 7, 14, 21, ...
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The sequence is arithmetic and has a common difference of [_]
OmB. The sequence is not arithmetic.

Answer: What do those numbers mean

Step-by-step explanation:

The level can be attained  by light reflections.

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The probability that a household in Maryland has an annual income of 100000 or more is 0.2373

Given Data;

Maryland had the greatest mean yearly household income of any state, according to Money magazine (time website). Consider a normal distribution with a mean of 75847 and a standard deviation of 33800 for the annual household income in Maryland.

Population Mean (μ) = 75847

Population Standard Deviation (σ) = 33800

'X' follows a normal distribution with a population mean and population standard deviation.

Here,

X ~ N ( μ = 75847 ,σ = 33800 )

Z =(X - μ)/σ

To get the probability that a household in Maryland has an annual income of 100000 or more.

Now, we have to compute P (X > 100000)

P (X > 100000) = 1 - P( (X-μ)/σ < (100000-75847)/33800 )

                         = 1 - p(z < 0.715 )

                         = 1 - 0.7627

                         = 0.2373

The required probability is 0.2373

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In 27 minutes, Daquin completed 30% of his schoolwork. He must therefore finish another 70% of her homework.

We must multiply both sides of the equation by 3 to see how long it takes Daquin to finish 10% of the homework. It takes her 9 minutes.

We simply need to multiply our time estimate by seven to determine how long it will take her to complete the remaining 70% of her homework.

9 minutes are required for 10% of the homework.

63 minutes are required to complete 70% of the homework.

% finished equals 30%

Duration: 27 minutes

70% of the homework is still to be done.

Time required for the remaining task is 70/30 divided by 27 is equal to 63 minutes.

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The percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.

According to the question,

We have the following information:

Total number in a class including sophomores and juniors = 28

Number of juniors in the class = 16

Now, we have the number of sophomores in this class:

Total number in the class- Number of juniors in the class

28-16

12

Now, we can easily find the percent of sophomores in the class by following the given steps:

Number of sophomores*100/Number of sophomores and juniors

1200/28

42.86%

Hence, the percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.

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Step-by-step explanation:

the triangle above is an isosceles triangle,

two sides and angles are equal

AC=AD

triangle ACB=triangle ABD(because it is an isosceles triangle )

The function rule in slope-intercept form is y = -4x - 2

Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:

y = mx + c

Where:

From the graph of this line, we have the following data points:

Point (x, y) = (-1, 2)

Point (x, y) = (0, -2)

In Mathematics, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-2 - 2)/(1 - 0)

Slope, m = -4/-1

Slope, m = -4

Note: The y-intercept occurs at the point where the x-value is equal to zero (0).

Now, we can write the function rule for this line in slope-intercept form as follows:

y = mx + c

y = -4x - 2

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Considering the proportional relationship graphed, it is found that:

A. The constant is of 20.

B. A pair on the graph is given as follows: C. ) (45, 900); the machine caps 900 bottles in 45 seconds.

A proportional relationship is a linear function with intercept zero in which the output variable y is given by the multiplication of the input variable x and the constant k, as follows:

y = kx.

Considering point (15, 300) on the graph presented, the constant is calculated as follows:

300 = 15k

15k = 300

k = 300/15

k = 20.

The input and the output are given as follows:

Hence option C is the correct option for item 2.

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The linear equation:

-28 = y/7

Can be solved by multiplying both sides by 7, to get y = -196

Here we want to solve the equation:

-28 = y/7

And we want to solve this for the variable y.

To do so, we need to isolate said variable in one side of the equation, now remember that we can multiply both sides of the equation by the same number.

Then we can multiply both sides by 7 so we get:

-28*7 = (y/7)*7

-196 = y

The correct option is the last one.

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Answer:

8:00

Step-by-step explanation:

Calculate time

It is 5:15 now.

Subtract 15 minutes

5:00

Subtract 9 hours

subtract 5 hours

12:00

Then subtract 4 hours

8:00

Answer:

24

Step-by-step explanation:

Start by finding the unit price. Unit price is the term for finding the price of one unit of an item, often used in word problems. We find this by dividing the cost of an item after a certain amount is sold, by that amount.

[tex]96/8 = \$12[/tex]

Now, we know the unit price is 12. Divide the end value of everything you sold by the unit price, 12.

[tex]288/12 = 24[/tex]

Therefore, you sold 24 candles.

Hope this helps!

Dimensions of the area enclosed is 800 * 800 and the maximum area = 6,40,000 square yards.

Given:

Liana has 3200 yards of fencing to enclose a rectangular area.

Let l and b be the length and width.

we know that:

perimeter of rectangle = 2(l+b)

2l + 2b = 3200

l+b = 1600

b = 1600 - l

Area of rectangle A = lb

= l*1600-l

= 1600 l - l^2

Apply derivative:

dA/dl = 1600 - 2l

1600 - 2l = 0

1600 = 2l

l = 1600/2

l = 800

l+b = 1600

b = 1600 - 800

= 800

Area = 800*800

= 6,40,000

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The measure of the exterior angle of the triangle is 144 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, the measure of the two remote interior angles of a triangle are x - 10 and 4x + 4. The exterior angle of the triangle measures 3x + 54 .

Let's solve for the exterior angle.

x - 10 + 4x + 4 = 3x + 54

5x - 6 = 3x + 54

5x - 3x = 54 + 6

2x = 60

x = 60 / 2

x = 30

Therefore,

exterior angle = 3x + 54 = 3(30) + 54 = 90 + 54 = 144 degrees

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Answer:

27/31

Step-by-step explanation:

The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)

The problem will be solved using SOH CAH TOA

let the distance between the 150 ft long guy wire and the radio antenna be x

let the distance between the 180 ft long guy wire and the radio antenna be y

cos 65° = x / 150

x = cos 65° * 150

x = 63.39 ft

The height of the antenna

sin 65° = height of antenna / 150

height of antenna = sin 65 * 150

height of antenna = 135.95

using Pythagoras theorem

(length of guy wire)² = (height of the antenna)² + (anchor distance)²

(anchor distance)² = 180² - 135.95²

anchor distance = √(180² - 135.95²)

anchor distance = 117.97

The anchor points distance apart

= 63.39 + 117.97

= 181 (to the nearest foot)

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Using re-grouping to solve 21 x 43, the four products that would be calculated and then added is: 800 + 40 + 60 + 3.

Given data:

21 x 43

Now let make use of re-group to find the for product

21 x 43

So,

20 +1 = 21

40 + 3 =43

Hence,

(20+1) × (40+3)

Expand

(20 × 40) + (1 × 40) + (20 ×3) + (1 ×3)

800 + 40 + 60 + 3

= 903

Check:

21 x 43 = 903

800 + 40 + 60 + 3 =903

Therefore the correct option is C.

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Answer:

Step-by-step explanation:

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Ace

12K answers

42.2M people helped

Answer:

1,008 calories

Step-by-step explanation:

504 calories in eight ounces

How many calories are there in one pound

1 pound = 16 ounces

504 calories = 8 ounces

x calories = 1 pound

Recall, 1 pound = 16 ounces

504 calories : 8 ounces = x calories : 16 ounces

504 / 8 = x / 16

Cross Multiply

504 * 16 = 8 * x

8,064 = 8x

Divide both sides by 8

x = 8,064 / 8

= 1,008

x = 1,008 calories

Therefore, there are 1,008 calories in one pound

Answer:

67.859 g

Step-by-step explanation:

123.9 g - 56.041 g

= 123.900 g - 56.041 g

= 67.859 g

Answer:

Step-by-step explanation:

67.859

The evaluation of the rational algebraic expression  are presented as follows;

1.  [tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]

2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2 + 2\cdot x \cdot y + y^2}{x \cdot y}[/tex]

3. [tex]\dfrac{3 \cdot x + 1}{x^2+2\cdot x +1} +\dfrac{5}{2\cdot x + 8} =\dfrac{11\cdot x^2 +36\cdot x +13}{2\cdot x^3 + 12\cdot x^2 + 18\cdot x+ 8}[/tex]

A rational algebraic expression is an algebraic expression that consists of a quotient and divisor that consists of variables and numbers.

1. [tex]\dfrac{1}{3} + \dfrac{2}{5}[/tex]

[tex]\dfrac{1}{3} + \dfrac{2}{5} = \dfrac{5\times 1 + 2 \times 3}{3\times 5} =\dfrac{5 + 6}{15}[/tex]

[tex]\dfrac{5 + 6}{15} = \dfrac{11}{15}[/tex]

Therefore, we get;

[tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]

2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y}[/tex]

[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}[/tex]

[tex]\dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}= \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]

Therefore;

[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]

3. [tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}[/tex]

[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8} = \dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)}[/tex]

[tex]\dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)} = \dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]

[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}=\dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]

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Answer:

3 ¹/₃ years

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 500=3000 \times 0.05 \times t[/tex]

[tex]\sf \implies 500=150t[/tex]

[tex]\sf \implies t=\dfrac{500}{150}[/tex]

[tex]\implies \sf t=3\frac{1}{3}[/tex]

Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.

Answer:

-1/3

Step-by-step explanation:

m = y2-y1/x2-x1                     formula for slope

m = 7-9/8-2                          Plug in the numbers

m = -2/6                                Subtract 7-9 and 8-2

m = -1/3                                 Simplify

The measures of the angles BCA and ABD are equal because they are both right angles.

The line segment BD is a tangent to the circle with diameter AB. We need to find out the reason why the measure of angle BCA must be equal to the measure of angle ABD. The diagram is attached below.

Since AB is the diameter of the circle, it makes an angle equal to 180 degrees at the center of the circle. So the measure of the angle BCA is half of the angle produced by the diameter.

∠BCA = (1/2)×180° = 90°

Since the line BD is tangent to the circle, it will be perpendicular to the diameter. Hence, the angle formed by the diameter and the tangent must be the right angle.

∠ABD =  90°

Hence, both the angles are equal to each other.

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Answer:

Step-by-step explanation:

It is assumed 30% is the discount.

Original price is $150.99, discount is 30%, sale price is:

The length and width of a rectangle that maximises the enclosed area are 162.5 yards. The maximum area is 26,406.25 square yards.

In the given question we have to find the maximum area of the rectangular area.

A farmer with 650 meters of fencing wants to enclose a rectangle plot that border on a river.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 650

Divide by 2 on both side we get

x+y = 325................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 325-x.

Now putting the value of y

A = x(325-x)

A = 325x-x^2

On differentiating

dA/dx = 325-2x

Putting dA/dx=0

325-2x=0

Subtract 325 on both side we get

-2x= -325

Divide by -2 on both side we get

x = 162.5 yards

Now putting the value of x in the y=325-x

y=325-162.5

y=162.5 yards

So the maximum area is

A= 162.5*162.5

A= 26,406.25 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 162.5 yards. 26,406.25 square yards is the maximum area.

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Answer:

Step-by-step explanation:

(2 1/2) : (1/4) = 10/1 =10

The solution to the system of equations will be;

⇒ (2, 0)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first equation is,

y = - 2x + 4

And, A line goes through (0, 4) and (2, 0).

Now,

For the second linear equation;

The coordinates are,

(-4, -3) (0, -1) , (2, 0) , (6, 2)

Hence, The equation of line passes through the points (-4, -3) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (0 - (-4))

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3)= 1/2 (x - (-4))

⇒ y + 3 = 1/2 (x + 4)

⇒ y = 1/2x + 2 - 3

⇒ y = 1/2x - 1

Now, We find the value of system of equations;

y = - 2x + 4

y = 1/2x - 1

Solve both above equation, we get;

1/2x - 1 = - 2x + 4

1/2x + 2x = 4 + 1

5/2x = 5

x = 2

And, y = 1/2 (2) - 1 = 0

Thus, The solution to the system of equations will be;

⇒ (2, 0)

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Answer:

A

Step-by-step explanation:

The frequency of data value 1 that is 10 will be 6 as "Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency."

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event. The relative frequency is calculated by dividing each frequency by the total number of data values. Therefore, the frequency is calculated by multiplying the relative frequency by the total number of data values.

Here,

Value                                           Relative frequency

10                                                  0.15

20                                                 0.30      

30                                                 0.45

40                                                 0.10

data 1 value=10

Dividing each frequency by the total number of data values gives the relative frequency.

So, multiplying the relative frequency by the total number of data values gives the frequency.

40*0.15=6

Since "multiplying the relative frequency by the total number of data values gives the frequency," the frequency of the data value 1 that is 10 will be 6.

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No, The scatter plot does not show a linear association

A graph is way of presenting data used by several disciplines.

There are many types of graphs and scatter plot is one of them.

scatter plot can be defined as set of dots plotted on a horizontal and vertical axis.

scatter plots can demonstrate the degree of connection, if any, between the values of observed quantities or events, they are crucial in statistics

The scatter plot does not show a straight line graph or a linear function. tracing the line shows a inverted shape of "s" which is not associated with linear functions.

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Yes, there is causation between the two given variables, as the weight is related at some point with the amount of calories consumed.

For two variables x and y, we say that there is causation when, if we modify one of the variables, the other changes in response.

Correlation just means that the variables are related in some way (maybe both have a causation relationship with the same other variable)

So causation implies correlation.

Correlation does not imply causation.

In this case, we have the example:

x = The number of additional calories consumed

y =  amount of weight gained.

Clearly, we have causation between x and y as larger is the value of x, larger will be the value of x.-

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