Give one pair of vertical angles and one pair of supplementary angles shown in the figure below.

For the specified functions, there is no answer. By graphing the functions, the answer has been discovered.

The method of graphing a function begins with creating the graph of a pertinent function. The function equation will be satisfied at a point on a curve if it reflects the function at that location.

We are given two functions as f(x) = -x² + 8x - 13 and g(x) = x + 3

The graph of the given functions has been plotted and attached below.

In the graph, the red function represents the f(x) function and the blue line represents the g(x) function.

From the graph, we can see that the two does not meet.

Hence, there is no solution for the given functions.

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(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.

The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.

(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:

N(t) = No e^(-0.088t)

where No is the initial amount of the substance present at t=0.

(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:

N(t) = 400 e^(-0.088t)

To find how much will remain after 3 days, we need to evaluate N(3):

N(3) = 400 e^(-0.088*3) ≈ 323.3 g

Therefore, approximately 323.3 g of the substance will remain after 3 days.

(iii) The rate of change of the amount of the substance after t days is given by:

dN/dt = -0.088N

To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:

dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day

Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.

(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:

N(t) = 200

Substituting No = 400 into the exponential function, we get:

400 e^(-0.088t) = 200

Dividing both sides by 400, we get:

e^(-0.088t) = 0.5

Taking the natural logarithm of both sides, we get:

ln(e^(-0.088t)) = ln(0.5)

Simplifying, we get:

-0.088t = ln(0.5)

Solving for t, we get:

t ≈ 7.88 days

Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.

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Using percentage, the true proportion of registered voters who are Democrats is = 64.

What do you mean by percentage?

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.

It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.

In the question,

Sample size, n = 140.

Now 46% of the registered voters are Democrats.

Now the no. of registered voters =

46% of 140

= 46/100 × 140

= 6440/100

= 64.4

≈ 64

Therefore, 64 is the true proportion of registered voters who are Democrats.

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Answer:

$53.25

Step-by-step explanation:

$[tex]\frac{355}{100}= 1[/tex]%

$[tex]15\frac{355}{100} = 15[/tex]%[tex]= 53.25[/tex]$

Answer:

53.25

Step-by-step explanation:

This expression divides 360 by -1 to get -360.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.

Here are two possible multiplication/division expressions that equal -360:

18 x (-20) = -360

This expression multiplies 18 by -20 to get -360.

360 ÷ (-1) = -360

Therefore, This expression divides 360 by -1 to get -360.

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Answer: The numerator is the percentage change in quantity demanded, which is (Q2 - Q1)/[(Q2 + Q1)/2] = (4500 - 5000)/[(4500 + 5000)/2] = -0.1818

The denominator is the percentage change in price, which is (P2 - P1)/[(P2 + P1)/2] = (3500 - 3000)/[(3500 + 3000)/2] = 0.1429

The numerator divided by the denominator is -0.1818/0.1429 = -1.2727

The price elasticity of demand is greater than 1 in absolute value, which means the demand is elastic.

Using the midpoint formula, we can calculate the price elasticity of demand as:

[(Q2 - Q1)/((Q1 + Q2)/2)] / [(P2 - P1)/((P1 + P2)/2)]

Substituting the given values, we get:

[(-500)/((5000 + 4500)/2)] / [(3500 - 3000)/((3500 + 3000)/2)]

Simplifying, we get:

-0.1818 / 0.1429 = -1.2727

Since the price elasticity of demand is greater than 1 in absolute value, the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price, and the university can expect a relatively large decrease in enrollment due to the tuition increase.

Step-by-step explanation:

The perimeter of the wall in a classroom is 26 meters.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, a wall in a classroom measures, the length is 10 m and the height is 3 m.

So, the perimeter of wall is 2(Length+Height)

= 2(10+3)

= 2×13

= 26 meters

A computer desk has a length of 70 cm and a breadth of 40 cm.

Now, the perimeter of a computer desk is 2(Length+Breadth)

= 2(70+40)

= 220 cm

220 cm can be written as 220/100 = 2.2 meters

Number of computers v=can be placed along wall =15/2.2

= 6.8

≈ 7

Therefore, approximately 7 computers desks place along the wall.

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The given investment realized a loss of $3.75 with 31.25% decrease.

The amount made by selling a product, which should be greater than the product's cost price, is generally referred to as the profit. It is the profit generated by all business activities. In other words, a product is deemed to have made a profit if its selling price (SP) exceeds its cost price (CP). It explains the financial gain realised when the revenue from a company activity outpaces the costs, like as taxes and expenses, involved in maintaining a business activity.

Given : Purchase Price: $12.00

            Selling Price: $8.25

Since the purchase price is more than the selling prize, So the investment has been sold at a loss.

The loss on investment = Purchasing price - Selling price

                                       = $ 12 - 8.25

                                       = $3.75.

% of decrease = (loss/ purchasing price) × 100

                        = 3.75/12 × 100

                        = 31.25 %

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Answer:

there are 24 different choices available to guests when booking their stay at the bed and breakfast.

Step-by-step explanation:

To find the total number of choices available to guests at the bed and breakfast, you can use the multiplication principle of counting.

According to the multiplication principle, if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

Using this principle, we can calculate the total number of choices available to guests by multiplying the number of choices for each option:

Choice of 3 themes for their room: 3 options

Choice of 2 sizes of rooms: 2 options

Choice of 4 breakfast options: 4 options

Total number of choices = 3 x 2 x 4 = 24

Therefore, there are 24 different choices available to guests when booking their stay at the bed and breakfast.

Answer: 545,884,646.36 ft3.

Step-by-step explanation:

The volume of the cylinder is calculated using the formula V=πr2h, where r is the radius of the cylinder and h is the height. The radius of the cylinder can be calculated by dividing the diameter (125 times the height) by 2.

Therefore, the radius = (125 * 1934) / 2 = 118,550 / 2 = 59,275 ft

Plugging in the values of radius and height into the formula, the volume of the cylinder is V = 3.14 * (59,275)2 * 1934 = 545,884,646.36 ft3

Rounding to the nearest hundredth, the volume of the cylinder is 545,884,646.36 ft3.

Answer:

y = −x2 + 2x −5

Step-by-step explanation:

To find the truth set of the equation 4x + 2 = 3(2x), we need to solve for x and then determine the values of x that make the equation true.

Starting with the equation:

4x + 2 = 3(2x)

Distribute the 3 on the right-hand side:

4x + 2 = 6x

Subtract 4x from both sides:

2 = 2x

Divide both sides by 2:

1 = x

Therefore, the truth set of the equation 4x + 2 = 3(2x) is {1}. In other words, the equation is only true when x is equal to 1.

The scale of the map is 1/10,000.

The formula used to find the formula to find the scale is

scale = length on the map / actual length

Given,

Actual length of the golf park = 2.5 km

length on map = 250 mm

Here, we need to convert both lengths into the same units

2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm

we know that,

scale = length on the map / actual length

= 250 mm / 2,500,000 mm

= 1/10,000.

Therefore, the scale of the map is 1/10,000.

i.e, one unit on the map is equal to 10,000 units of length in reality.

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The H.C.F. of 30, 45, and 60 using the division method is 30.

To find the H.C.F. (Highest Common Factor) of the given numbers using division method, we can follow these steps:

Let's apply this method to find the H.C.F. of 30, 45, and 60.

Step 1: We start by dividing the larger number, 60, by the smaller number, 30.

60 ÷ 30 = 2 with a remainder of 0

Step 2: Now, we divide the smaller number, 30, by the remainder, which is 0.

30 ÷ 0 = undefined

Since the remainder is zero, we stop the process here. The last divisor we obtained is 30. Therefore, the H.C.F. of 30, 45, and 60 is 30.

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In response to the supplied query, we may state that Margo will thus interest have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The principle balance divided by the interest rate is the most typical approach to compute interest.

Margo will be required to repay the $2000 she borrowed plus an additional 8% of that sum as interest each year if she borrows the money at an 8% annual interest rate.

principle multiplied by the interest rate equals interest.

where "principal" refers to the initial loan amount and "rate" is the interest rate in decimal form. The interest rate in this situation is 8%, or 0.08 in decimal form.

Margo will so be required to pay the following interest each year:

interest: $160 x ($2,000 x 0.08)

Margo will thus have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

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Based on the relationship between the length and width of the rectangle, the length of the rectangle for the various values of the width is given below:

The relationship between the length and the width of the rectangle is a linear relationship given by the linear equation below:

l = w/3

where;

l is the length of the rectangle

w is the width of the rectangle

When w = 1

l = 1/3

When w = 3

l = 3/3

l = 1

when w = 7

l = 7/3

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Answer:

Step-by-step explanation:

number of minuties for whole cycle

green time+yellow time+ orange time

2+2+2=6

min to seconds==> 1min=60 seconds

so 6*60=360 seconds

Enjoy:)

Answer: b = 8

Step-by-step explanation:

From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.

Let's factor the equation and set each factor equal to zero:

x²(x+3)(x - b) = 0

x = 0 or x + 3 = 0 or x - b = 0

Solving for x in each case, we get:

x = 0 or x = -3 or x = b

Since the sum of the solutions is 5, we can write:

0 + (-3) + b = 5

Simplifying, we get:

b - 3 = 5

Adding 3 to both sides, we get:

b = 8

Therefore, the value of b is 8.

A statement is not true about the dot plot to the right include the following: A. the French Club has a greater mean than the Spanish Club.

In Mathematics, a dot plot is a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

Mean of French Club = 1/12(18 + (19 × 4) + (20 × 4) + (21 × 2) + 22)

Mean of French Club = 1/12(238)

Mean of French Club = 119/6 = 19.83.

Mean of Spanish Club = 1/12(18 + (19 × 2) + (20 × 3) + (21 × 3) + (22 × 3))

Mean of Spanish Club = 1/12(246)

Mean of Spanish Club = 123/6 = 20.5.

Therefore, 19.83 is less than 20.5.

Median of French Club = 20

Median of Spanish Club = (20 + 21)/2 = 20.5.

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14[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex]

= 14[tex]\frac{1}{2}[/tex] x 36[tex]\frac{1}{4}[/tex]

= 504[tex]\frac{1}{8}[/tex]

Answer:

273/2

Step-by-step explanation:

Answer:

48%      hope this helps!

Step-by-step explanation:

188-127= 61 <--(increase)

divide increase by original( 61/127= 0.480)

Multiply by 100 to get percent (0.480x100= 48%)

Answer:

8.52

Step-by-step explanation:

add the two 3.99 making 7.98 then add 3.50 making 11.48 then substract that from 20.00 making the final answer 8.52

The higher the steel wool grade, the less muscle power required.

The faulty inference the employee used to make this decision is that a higher grade of steel wool will be more effective in quickly removing stains. In reality, higher grade steel wool is more abrasive and can actually damage the wood surface, leaving behind scratches and making the problem worse.

Grade 1 steel wool is the finest grade and is typically used for finishing and polishing wood. It is not suitable for removing stains, as it is not abrasive enough to remove the outer layer of the wood where the stain is located. To remove stains from wood, it is recommended to use a lower grade of steel wool or a non-abrasive cleaning solution specifically designed for wood.

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Answer:

Step-by-step explanation:

Let's first find the number of 12-year-olds and 13-year-olds in the band:

Let x be the number of 12-year-olds.

Then the number of 13-year-olds is 1.25x (125% of x).

The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).

Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.

The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:

The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.

10% of 100 is 10, so there are 10 14-year-olds.

Now we can find the portion of the band for each age group:

12-year olds: fraction = 40/100 = 2/5, percent = 40%

13-year olds: fraction = 50/100 = 1/2, percent = 50%

14-year olds: fraction = 10/100 = 1/10, percent = 10%

Check the picture below.

[tex]\sin(24^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{17}}\implies 17\sin(24^o )=y \\\\[-0.35em] ~\dotfill\\\\ \sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{y}}\implies \theta =\sin^{-1}\left( \cfrac{4}{y} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{4}{17\sin(24^o )} \right)\implies \theta \approx 35.3^o[/tex]

Make sure your calculator is in Degree mode.

There is no such point that requires exactly three numbers to specify its location.

A mathematical notion known as the Euclidean plane symbolizes a two-dimensional environment in which points, lines, and forms may be specified and altered. The Greek mathematician Euclid, who originally described the geometry of the plane in his book Elements, is honoured by the name of the object. The Pythagorean theorem is used to calculate distance in the Euclidean plane, while degrees or radians are used to calculate angles.

The plane doesn't have any points that can be precisely located by three integers. Each point in the Euclidean plane may be found using only two integers, namely its x- and y-coordinates.

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Let d be the distance in miles from the airport that a plane should begin descending. According to the problem statement, we can write the equation:

d/3 = 10

To solve for d, we can isolate it by multiplying both sides of the equation by 3:

d = 3 * 10

Therefore, the pilot should begin descending when the plane is 30 miles from the airport.

The answer is (iv) 150. This result can be obtained by applying the alternate segment theorem.

A circle is a shape with all points at an equal distance from the center. It has no sides or angles and is the only two-dimensional shape with this property. It is also the most basic of all shapes, and is found in nature in many forms, such as raindrops, the sun, and even the human pupil. Circles are often used in art, design, and architecture, and are sometimes even used to represent infinity.

This theorem states that if two chords of a circle intersect at right angles, then the angles in the alternate segments of the circle are equal. In this case, the alternate segments are APQ and CQP. Hence, ∠APQ + ∠CQP = 150°.

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XPO's minimum tax credit carryover to 2019 is $20,500.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.

Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.

To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:

Minimum tax credit carryover = $51,000 - $30,500 = $20,500

Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.

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Answer: 32 Ounces

Step-by-step explanation:

The container holds 32 ounces because if there are 2 pounds of peanuts, and 1 pound = 16 ounces, then you multiply 16 by 2.

16 x 2 = 32