Alex is buying a sweater that originally costs $35 and a pair of jeans that originally cost $28. If the sweater is marked down 30% and the jeans are marked down 15%, find the total cost, including 8% sales tax.

The smaller number is 25, and the larger number is 68. The larger number is 18 more than twice the smaller number, and their sum is 93.

To solve this word problem using the 3-step process, we need to find the two numbers given that the larger number is 18 more than twice the smaller and the sum of the two numbers is 93.
Step 1: Let's assign variables to the unknown numbers. Let's say the smaller number is "x" and the larger number is "y".
Step 2: Translate the given information into equations. From the problem, we know that the larger number is 18 more than twice the smaller. So, we can write the equation as: y = 2x + 18.
We also know that the sum of the two numbers is 93. So, we can write another equation as: x + y = 93.
Step 3: Solve the system of equations. We have two equations:
y = 2x + 18
x + y = 93
We can solve this system of equations by substitution method or elimination method. Let's use substitution.
Substitute the value of y from the first equation into the second equation:
x + (2x + 18) = 93
3x + 18 = 93
3x = 93 - 18
3x = 75
x = 75 / 3
x = 25
Now, substitute the value of x back into the first equation to find y:
y = 2(25) + 18
y = 50 + 18
y = 68
So, the smaller number is 25 and the larger number is 68.

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The area under the curve over [2,5] is 24.

Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.

Let us consider n subintervals. Therefore, width of each subinterval would be:

$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty  }{ R } \\&= \lim _{ n\rightarrow \infty  }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$

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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.

Therefore, the area under the curve over [2,5] is 21.

From the given data, we can see that the width of the interval is:

Δx = (5 - 2) / n

= 3/n

The endpoints of the subintervals are:

[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]

Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5

The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:

Δx = (5 - 2) / n

= 3/n

Therefore,

Δx = 3/3

= 1

So, the subintervals are: [2, 3], [3, 4], [4, 5]

The right endpoints are:3, 4, 5. The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, Δx is 1, f(x) is 2x

∴ f(c1) = 2(3)

= 6,

f(c2) = 2(4)

= 8, and

f(c3) = 2(5)

= 10

∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx

= 6(1) + 8(1) + 10(1)

= 6 + 8 + 10

= 24

Therefore, the Riemann sum is 24.

To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.

∴ Area = ∫2^5f(x)dx

= ∫2^52xdx

= [x^2]2^5

= 25 - 4

= 21

Therefore, the area under the curve over [2,5] is 21.

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Answer:

It is geometric and the common ratio is 1/5 or .2

Step-by-step explanation:

It is geometric because it involves multiplication rather than addition.

25/125 = 1/5 or .2

Helping in the name of Jesus.

Answer:

This is a geometric sequence with a common ratio of 1/5.

To see why, divide any term by the previous term:

25 / 125 = 1/5

5 / 25 = 1/5

So each term is 1/5 of the previous term, which means the sequence is geometric with a common ratio of 1/5.

The other two angle measures of a right triangle with side lengths 5, 12, and 13 can be found using trigonometric ratios. Let's label the sides of the triangle as follows:

- The side opposite the angle we are looking for is 5.
- The side adjacent to the angle we are looking for is 12.
- The hypotenuse is 13.

To find the first angle, we will use the inverse tangent function (tan^(-1)). The formula is:
Angle = tan^(-1)(opposite/adjacent)

Plugging in the values, we get:
Angle = tan^(-1)(5/12)

Using a calculator, we find this angle to be approximately 22.6 degrees (rounded to the nearest degree).

To find the second angle, we will use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, the second angle can be found by subtracting the right angle (90 degrees) and the first angle from 180 degrees.
Second angle = 180 - 90 - 22.6

Calculating this, we find the second angle to be approximately 67.4 degrees (rounded to the nearest degree).

Therefore, the other two angle measures of the right triangle are approximately 23 degrees and 67 degrees.

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Answer:

Step-by-step explanation:

1. Imagine a triangle with base side 36 feet and Kate at the right with the angle of elevation, 24 degrees. We can use tangent:

tan 24 = o/a ; tan(24) = o/36 ; 36(tan(24)) = o ; o = 16 feet

This is how tall the screen is.

2. We do a similar operation:

tan(74) = o/a ; tan(74) = 555/a ; a = 555/tan(74) ; a = 159.1 feet

Hope this helps!

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

x² - 9

Step-by-step explanation:

   (x + 3)(x - 3)

= x(x - 3) + 3(x - 3)     Distributive  property

= x² - 3x + 3x - 9

= x² +( -3x + 3x) - 9       Associative

= x² + 0x - 9                   Addition    

= x² - 9                        

Answer:

see attached

Step-by-step explanation:

Answer:

17,224 ft^3 to nearest cubic foot.

Step-by-step explanation:

Volume of grain it can hold

= volume of hemisphere + volume of the cylinder

= 1/2 * 4/3 * 3.14 * 11^3 + 3.14 * 11^2 * 38

= 2786.23 + 14437.72

= 17223.95

Answer:

the answer will be a negative answer

Step-by-step explanation:

Answer:

2hours 20minutes

Step-by-step explanation:

hope this helps

Answer:

 52°, 90°

Step-by-step explanation:

The two acute angles in a right triangle are complementary, because the third angle is 90°. For acute angles A and B, we must have ...

  90° + A + B = 180°

  A + B = 90° . . . . . subtract 90°; definition of complementary angles

  B = 90° - A

For angle A = 38°, this tells us ...

  B = 90° -38° = 52°

The other two angles in the triangle are 90° and 52°.

A test for two proportions and the null hypothesis would be the best test statistic to assess the variance in bacon consumption from 2011 to 2016.

The null hypothesis for the test is that the proportion of adults who consumed at least 3 pounds of bacon in 2011 is equivalent to the proportion of adults who consumed at least three pounds of bacon in 2016.

A potential explanation would be that the percentage of adults who ate at least 3 pounds of bacon in 2011 and 2016 differed.

Additionally, the test statistic may be likened to a chi-squared distribution with one degree of freedom; hence, it is necessary to compute the test statistic's p-value in order to establish whether the null hypothesis can be ideally rejected or not.

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Step-by-step explanation:

look it is very easy.

use formula of simple interest

Answer: 50.9091 percent

Answer:

y=-15

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Answer:The blue triangle is a dilation of the black triangle. What is the scale factor of the dilation?

Step-by-step explanation:

If Clare's average number of strokes per hole is 3, it means that the total number of strokes she took in the round divided by the number of holes she played is equal to 3.

Let's say Clare played n holes in total and took a total of s strokes in the round. Then we can write:

s/n = 3

Multiplying both sides by n, we get:

s = 3n

This means that Clare took 3 strokes per hole on average, and a total of 3n strokes in the round. If she were to redistribute the strokes on different greens, the total number of strokes would still be 3n, and her average number of strokes per hole would remain 3.

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To find the first derivative of f(x), we need to integrate the second derivative with respect to x once.

f'(x) = ∫ f''(x) dx = ∫ x(x-a)(x-b)^2 dx

f'(x) = ∫ (x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2) dx

f'(x) = 1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C

where C is the constant of integration.

To find the second derivative of f(x), we need to differentiate f'(x) with respect to x.

f''(x) = d/dx [1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C]

f''(x) = 1 x^4 - 1(a+b)x^3 + 1(a^2+3ab+b^2)x^2 - 1ab(a+b)x + 1ab^2

f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2

Therefore, the second derivative of f is given by f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2.

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

the sum of two positive integer to always be positive

1/3

本题已由中国数学会官方解答（现有会员：2人）

Answer:

75.86 %

Step-by-step explanation:

\( \frac{44}{58} \times 100\)

75.86 %

Answer: 1/12 is the answer

Step-by-step explanation: 3 , 4

1 of those colors so , 1/3 x 1/4 = 1/12!!

i hope that helps <3

Answer:the cone is 9 cm

Step-by-step explanation:

Let h be the height of the cone.

Diameter = 8 cm

Radius = 4 cm

Volume = 48π cm3

31​π×(4)2×h=48π

Answer:

9cm

Step-by-step explanation:

The average speed of a train travelling 240 km in 4 hours is 60 km/h.

Distance = 240 km

Time = 4 hours

Speed = Distance/Time

Speed = 240 km/4 hours

Speed = 60 km/h

The average speed of a train is calculated by dividing the total distance travelled by the total time taken to travel that distance. In this case, the train has travelled a total distance of 240 km in 4 hours. We can calculate the average speed of the train by dividing 240 km by 4 hours. This gives us an average speed of 60 km/h. This means that the train travelled an average speed of 60 km/h for the entire journey. This speed is the average speed of the train, which means that it could have been travelling faster or slower than this at different times during the journey.

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An equilibrium phase diagram can be used to determine phase transitions, phase presence, and phase compositions at different conditions.

An equilibrium phase diagram can be used to determine the below mentioned parameters:

A) It can determine where phase transitions will occur. Phase transitions refer to changes in the state or phase of a substance, such as solid to liquid (melting) or liquid to gas (vaporization). The phase diagram provides information about the conditions at which these transitions take place, such as temperature and pressure.

B) It can determine what phases will be present for each condition of chemistry and temperature. The phase diagram shows the different phases or states of a substance (such as solid, liquid, or gas) under different combinations of temperature and pressure. It provides a visual representation of the stability regions for each phase, indicating which phase(s) will be present at a given temperature and pressure.

C) It can determine the chemistry and amount of each phase present at any condition. The phase diagram gives information about the composition (chemistry) and proportions (amount) of different phases present under specific conditions. It helps identify the coexistence regions of multiple phases and provides insight into the equilibrium compositions of each phase at various temperature and pressure conditions.

In summary, an equilibrium phase diagram is a valuable tool in understanding the behavior of substances and can provide information about phase transitions, phase stability, and the chemistry and amounts of phases present at different conditions.

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Answer:

\(\frac{3}{16} x^{3}-\frac{9}{4}x+6 = y\)

Step-by-step explanation:

Lets start with the easiest part of this question - simply plugging in to get easier equations:

\(-8a+4b-2c+d=9\\\)

\(8a+4b+2c+d=3\)

Something that now immedietly pops out is that many of the terms would cancel if we added them together. We get the following results by adding the two equations together:

\(8b+2d = 12\)

Now lets look at the other bit of inromation the question gives you -- that the two points are horizontal tangents. Taking the derivative of the standard form of a cubic, we get:

\(y' = 3ax^2+2bx+c\)

Since the points are both horizontal tangents, y' will be equal to 0 at the points. Thus, plugging in we get:

\(y'(-2) = 0 = 12a-4b+c\)

\(y'(2) = 0 = 12a+4b+c\)

We again see a simple subtracting opportunity that will cancel out two terms:

\(-8b = 0\)

\(b = 0\)

Now going back to the equation we got by adding the two equations that we got from simply plugging our points in:

\(d = 6\)

Now that we have b and d, we can now plug them back into our step one and derivative equations in order to get a simple system:

\(-8a - 2c=3\)

\(12a+c=0\)

Solving for a and c, we get:

\(a = \frac{3}{16}\)

\(c = \frac{-9}{4}\)

Thus, finally, our answer is:

\(\frac{3}{16} x^{3}-\frac{9}{4}x+6 = y\)

Attached is desmos, which you can use to check.