Judith wants to buy a sleeping bag. The original price is $140. What is the sale price?

The greatest possible third term is when the sum of four positive integers that form an arithmetic sequence is $46 is 15

The sum of the first n terms of an arithmetical sequence is given by

n/2[2a +(n-1 d])

Where a is the first term and d is the common difference. In this situation, n=4 and the sum is 46, substituting these values,

4a +6d = 46

2a+3d=23, ……………………………………………………………..1

The nth term is given by a+(n-1)d, and we are looking at the 3rd term

so: a +2d must be a maximum

from (1): 3d=23–2a as all terms are integers, 23–2a must divisible by 3

This means that that a can only be 1, 4, 10or giving values of d, as 7, 5,1 respectively and the third term can be : 15, 14, 12 among these 15 is the largest.

Therefore if the sum of four positive integers that form an arithmetic sequence is $46$. of all such possible sequences, then the greatest possible third term will be 15

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Answer:

81.68 mm

Step-by-step explanation:

C = πd = π · 26 ≈ 81.68141 mm

Answer:

p = ± 5

Step-by-step explanation:

Given

p² - 25 = 0 ( add 25 to both sides )

p² = 25 ( take the square root of both sides )

p = ± \(\sqrt{25}\) = ± 5

Answer:

p= +/- 5

Step-by-step explanation:

p² -25 =0

or, (p+5) (p-5) =0 {a²-b²= (a+b)(a-b)}

either,. or,

p+5=0 p-5=0

or, p= -5 p=5

Answer:

X < 5, or 5 > X

Step-by-step explanation:

Open up the parenthesis on the left side

-8 < 32 - 8x

Isolate -8x

- 8 - 32 < -8x
We can rewrite the inequality to make it easier to solve

-8x > -8 - 32

-8x > -40

Now solve for X, keep in mind you must switch the inequality sign when dividing by negatives

x < 5

Answer:

D

Step-by-step explanation:

Undefined terms are words that are not formally defined.

Hope this helps!

Answer:

14.88 km

Step-by-step explanation:

add both base 1 and base 2 together divide them by 2 then multiply by the height.

Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh

Now, According to the question:

The surface area of a triangular prism is also known as the total surface area. Therefore, it is calculated using the formula, Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh; where:

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The derivative of y with respect to x is sinh⁻¹(x/2) + x / (2√(4 + x²)) - 2x.

To find the derivative of y with respect to x, we need to use the chain rule and the derivative of inverse hyperbolic sine function:

dy/dx = (d/dx) [x sinh⁻¹(x/2) - (4 + x²)]

First, we need to find the derivative of the first term, using the chain rule:

(d/dx) [x sinh⁻¹(x/2)] = sinh⁻¹(x/2) + x (d/dx) sinh⁻¹(x/2)

Now, we need to find the derivative of sinh⁻¹(x/2), which is given by:

(d/dx) sinh⁻¹(u) = 1 / √(1 + u²) * (du/dx)

where u = x/2, so du/dx = 1/2:

(d/dx) sinh⁻¹(x/2) = 1 / √(1 + (x/2)²) * (1/2)

Substituting this back into the first term, we get:

(d/dx) [x sinh⁻¹(x/2)] = sinh⁻¹(x/2) + x / (2 √(1 + (x/2)²))

Now, we can substitute this and the derivative of the second term into the expression for dy/dx:

dy/dx = sinh⁻¹(x/2) + x / (2 √(1 + (x/2)²)) - 2x

Simplifying this expression, we get:

dy/dx = sinh⁻¹(x/2) / 2 + x / (2 √(1 + (x/2)²)) - 2x

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Answer:

c because it will be half of it meaning you have to multiply rhem

The angle at the center subtend by the chord of the circle will be 50°. Then the correct option is C.

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angle that the very same arc subtends at any point around the circle's periphery is the double of the angle that same arc subtends at the center.

The angle at the periphery is 25°.

Then the angle at the center of the circle will be double of the angle subtend at the periphery.

Central angle = 2 × 25°

Central angle = 50°

The angle at the center subtend by the chord of the circle will be 50°.

Then the correct option is C.

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Answer:

The piece-wise function is;

\(f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}\)

Step-by-step explanation:

The flat rate for renting the car = $35 per day

The amount charged as insurance fee per day for renting the car for 3 days or less = $10

The insurance fee charged per day when the car is rented for more than 3 days = $5

Let the number of days = x

Therefore, we have;

For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x

For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x

Therefore;

The charge rate for renting the car for less than or equal to 3 days = 45·x

The charge rate for renting the car for more than 3 days = 40·x

The piece-wise function can be presented as follows;

\(f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}\)

Answer:

1 skateboard will cost $73 and the other will cost $72

Step-by-step explanation:

Skateboard A (Original) = X

Skateboard B (+$1) = X + 1

Solving for X

(x + 1) + x = 145

2x + 1 - 1 = 145 - 1

2x = 144

2/2 = x  

144/2 = 72

x = 72

Answer:

The equation is

2.7x - 5.4

Step-by-step explanation:

Gas is priced at $2.70 per gallon. My gas tank has 2 gallons currently in the tank. Write an equation to how much

the money I will spend to fill up my tank.

Let the total gallons that would fill your tank = x

The tank currently has 2 gallons

A gallon =>$2.70

Therefore, our equation is

=(x - 2) × 2.70

= 2.7x - 5.4

Answer:

4760

Step-by-step explanation:

Simple interest= principal× time ×rate/100

=3500×4×9/100

= 1260

Amount that will be in the bank after 4years= 3500+1260

=4760

Answer:

8 / 5

Step-by-step explanation:

Since 2/5 gallons cover 1/4 of the deck you would have to multiply 2/5 times 4 to so how much it would take to cover the whole deck so your answer is 8/5 gallons

Answer:

you answer would be halves...I think lol

Answer:

halves

Step-by-step explanation:

To simplify the question, it's really asking you to find how many spaces (jumps) are in between each whole number.

If you count the number of jumps between two whole numbers, you get two.

This means they are halves.

The average food cost percentage in North American restaurants is 33.3%, but it can vary significantly among different establishments. Some restaurants are successful with a lower food cost percentage of 25.0%.

In North American restaurants, the food cost percentage refers to the portion of total sales that is spent on food supplies and ingredients. On average, restaurants allocate around 33.3% of their sales revenue towards food costs. This percentage takes into account factors such as purchasing, inventory management, waste reduction, and pricing strategies. However, it's important to note that this is an average, and individual restaurants may have widely differing formulas for success.

While the average food cost percentage is 33.3%, some restaurants have managed to maintain a lower percentage of 25.0% while still achieving success. These establishments have likely implemented effective cost-saving measures, negotiated favorable supplier contracts, and optimized their menu offerings to maximize profit margins. Lowering the food cost percentage can be challenging as it requires balancing quality, portion sizes, and pricing to meet customer expectations while keeping costs under control. However, with careful planning, efficient operations, and a focus on minimizing waste, restaurants can achieve profitability with a lower food cost percentage.

It's important to remember that the food cost percentage alone does not determine the overall success of a restaurant. Factors such as customer satisfaction, service quality, marketing efforts, and overall operational efficiency also play crucial roles. Each restaurant's unique circumstances and business model will contribute to its specific formula for success, and the food cost percentage is just one aspect of the larger picture.

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Answer:

15•4 mm

Step-by-step explanation:

using sine rule

a÷ sinA=c ÷sinC

15•4÷sin90=0•5÷sinC

sinC =0•5 × sin90 ÷ 15•4

C =1•9°

A+B+C= 180

90+B+1•9=180

B= 88•2°

b÷sinB = a÷sinA

b÷sin88•2= 15•4÷sin90

b=sin88•2 ×15•4 ÷sin90

b =15•39

to 1 dp

b =15•4 mm

The sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

Acute angles are angles whose measures are greater than 0° and less than 90°. According to the statement, we must find at least a value such that sin θ = cos θ:

sin θ = cos θ                     Given

sin θ / cos θ = 1                 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property

tan θ = 1                            Definition of tangent

θ = π / 4                            Inverse trigonometric function / Result

In a nutshell, the sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

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To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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The correct option is C. a designed experiment is one for which the analyst controls the specification of the treatments and the method of assigning the experimental units to each treatment. An observational study is one for which the analyst observes the treatments and the response on a sample of experimental units.

In a designed experiment, the analyst has control over the treatments being studied and the method of assigning the experimental units to each treatment. This allows them to actively manipulate and control the variables of interest.

On the other hand, in an observational study, the analyst simply observes the treatments and the response on a sample of experimental units without actively controlling or manipulating any variables. The distinction lies in the level of control the analyst has over the experimental setup and data collection process.

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The approximate side length of a square on the quilt = 6.32 inch

In this question,

Taynia makes a quilt using fabric squares.

We have been given the side length of each fabric square is the square root of the area.

Here, the area of each fabric square is 40 square inches.

We need to find the approximate side length of a square on the quilt.

Let A be the area.

A = 40 square inches

To find the side length, we need to take the square root of 40.

Let s be the side length.

⇒ s = √A

⇒ s = √40

⇒ s = 6.32 inch

Therefore, the approximate side length of a square on the quilt = 6.32 inch

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Answer:

26.

Step-by-step explanation:

1 day/24 hours, makes 4 revolutions.

4 x 6 = 24,

1/2 of 4 = 2.

24+2 = 26.

26 revolutions, if my answer is wrong someone please correct me.

Answer:

For 2 circle 1, 3, 4, and 5

To construct a confidence interval for the population proportion of Americans over 40 who smoke, we can use the formula:

Confidence Interval = Sample Proportion ± (Critical Value) x Standard Error

where the sample proportion is the number of individuals who don't smoke divided by the total sample size (806/1089), the critical value can be found using a normal distribution table or calculator with the given confidence level (85%), and the standard error can be calculated using the formula:

Standard Error = √[ (Sample Proportion x (1 - Sample Proportion)) / Sample Size ]

Plugging in the given values, we get:

Sample Proportion = 806/1089 = 0.740
Sample Size = 1089
Standard Error = √[(0.740 x 0.260) / 1089] = 0.016
Critical Value (using a normal distribution table or calculator) = 1.440

Therefore, the 85% confidence interval for the population proportion of Americans over 40 who smoke is:

0.740 ± (1.440 x 0.016) = 0.740 ± 0.023

Rounding to three decimal places, the confidence interval is (0.717, 0.763). This means that we can be 85% confident that the true proportion of Americans over 40 who smoke falls between 71.7% and 76.3%.

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Answer:

\(6\frac{2}{3}\)

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Answer:

the answer is 60

Step-by-step explanation:

so you see that there's 20 percent right, you find what number u can add it by to get 100, so 80+20=100 so u do that and put it in a decimal form which is 0.8 and you multiply it by the price so 0.8 x 75= 60

Los jugadores pueden sentarse en las sillas de 60 formas diferentes.

Dado que en un juego de habilidad participan 5 jugadores que bailan alrededor de 3 sillas mientras suena una canción, para determinar de cuántas formas diferentes pueden sentarse los 5 jugadores en las 3 sillas se debe realizar el siguiente cálculo:

Por lo tanto, los jugadores pueden sentarse en las sillas de 60 formas diferentes.

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Answer:

Los jugadores pueden sentarse en las sillas de 60 formas diferentes.

Step-by-step explanation:

Answer:

$100

Step-by-step explanation:

Given data

Principal = 500

Interest= 5%

Time = 4years

Applying the simple interest expression

SI= PRT/100

substitute

SI= 500*5*4/100

SI= 10000/100

SI= 100

Hence the interest after 4 years is $100