The spring concert at a certain high school sold 155 tickets. Students were charged ​$4 each and adults $8 each. The income from the sale of tickets was ​$980. How many students and how many adults bought​ tickets? Use algebra to solve this problem.

Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.

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Answer:

x = 52.7°

Step-by-step explanation:

To find the value of x in the given right triangle, we can use the tangent trigonometric ratio.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The unknown angle is x, so θ = x.

The side opposite the angle measures 21 units, so O = 21.

The side adjacent the angle measures 16 units, so A = 16.

Substitute the values into the ratio and solve for x:

\(\tan x=\dfrac{21}{16}\)

     \(x=\tan^{-1}\left(\dfrac{21}{16}\right)\)

     \(x=52.6960517...\)

     \(x=52.7^{\circ}\; \sf (nearest\;tenth)\)

Therefore, the value of x is 52.7°.

The equation for the missing angle is

Tan x = 21 / 16

The problem will be solved using Trigonometry - SOH CAH TOA

SOH for Sin = Opposite / Hypotenuse

CAH for Cos = Adjacent / Hypotenuse

TOA for Tan = Opposite / Adjacent

The given part is

opposite  = 21

Adjacent = 16

using TOA

Tan x = 21 / 16

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Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

In this exercise we have to use the knowledge of Taylor Polynomial to calculate the requested function, this way we will have;

the least integer for n is 2    

The function given in this exercise corresponds to:

\(f(x) = ln(1+x)\)

knowing that the x point will be centered on:

\(x=0\\Pn(0,2)\\Error < 0.01\)

By rewriting the equation we have to:

\([[Max(f^{(n+1)} (c))]/(n + 1)!] *0.2^{(n+1)} < 0.01\)

So doing the derivatives related to the first function given in the exercise we have to:

\(f(x) = ln(1+x)\)

Following this we have to:

\(Max|f^{(n+1)} (c)| < n!\)

Thus, error is;

\((n!/(n + 1)!) * 0.2^{(n + 1)} < 0.01\)

\((1/(n + 1))* 0.2^{(n + 1)} < 0.01\)  

Let's try n = 1

\((1/(1 + 1)) *0.2^{(1 + 1)} = 0.02\)

This is greater than 0.01 and so it will not work. Let's try n = 2

\((1/(2 + 1)) * 0.2^{(2 + 1)} = 0.00267\)

This is less than 0.01. So,the least integer for n is 2.

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Answer: 43%,

Step-by-step explanation:

i did it in my search bar but its just 112 percent of 378 which is 43

Answer:

x = −3,3i, −3i

Step-by-step explanation:

Answer:

HA= None VA= 5/3

Step-by-step explanation:

The HA is none because the bottom part is missing x squared so you add x squared and it will be 2/0 which means it's not possible which means HA= none. VA is 5/3 because you set the denominator to 0 so you add 5 then divide by 3 so the answer for VA is 5/3

The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.

The given function is,

y = 1/2 x + 2.

Also, the domain of the function is {-4, -2, 0}.

Since, the domain of the functions defines the values of x,

And range defines the value of y in function.

The value of y at x = -4

y = 1/2(-4) + 2 = -2 + 2 = 0

At x = -2,

y = 1/2(-2) + 2 = -1 + 2 = 1

At x= 0,

y = 1/2 (0) + 2 = 2

The values of y are 0, 1 and 2.

Hence, the range of the function is {0, 1, 2}.

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Answer:

864

Step-by-step explanation:

AT= 2Area base+ph

AT= 2(12*12) +(12*4)12

AT=2 (144)+576

AT= 288+576

AT=864"

Answer: C is the correct answer!I don't feel like explaining. sorry.Please let me know if I am wrong.

Answer:

\(option \: b) \: \: \: 5 \sqrt{5} cm\)

Step-by-step explanation:

Given,

Base of the triangle = 10

Hypotenuse of the triangle = 15

So, according to Pythagoras Theorem,

\( {c}^{2} - {a}^{2} = {b}^{2} \)

\( {15}^{2} - {10}^{2} = {b}^{2} \)

\(225 - 100 = {b}^{2} \)

\(125 = {b}^{2} \)

\(b = \sqrt{125} \)

\(b = \sqrt{5 \times 5 \times 5} \)

\(b = 5 \sqrt{5} cm \: (ans)\)

Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.

The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.

If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:

P = (2b + t) - d

Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).

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Answer:

There are 12 sections on the spinner, and out of the 12 sections, 5 of them are red.

If he spins the spinner 48 times, he should expect 5x4, or 20 of the spins to land on red.

Let me know if this helps!

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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Answer:

Each bag had weighed about 1 1/2 (or 1.5) pounds.

Step-by-step explanation:

6 divided by 4 should end in a result of the unit weight 1.5 lbs.

Answer:

3, 4

Step-by-step explanation:

i divided 6 and 8 by 2 and got 3,4

boom magic

Answer:

The last two.

\( - 5x + 3 \: and \: - 2x + 3 - 3x\)

Step-by-step explanation:

Simplify the first set of parentheses to get

\( - 5 \frac{1}{3} x\)

Simplify the second set of parentheses by distributing the negative. It will change the signs in the parentheses.

\( \frac{1}{3} x + 3\)

Add (really subtract since the signs are different) the like terms.

\( - 5x + 3\)

Step-by-step explanation:

xy=360

x-y=75

(x-y)^2+2xy=(x+y)^2-2xy hence we have for x+y= ((x-y)^2+4xy)^0.5 which somehow equals 84.1

Answer:

I think it is 1594323

Step-by-step explanation:

3^17−3^15+3^13=116385579

and divide that by 73 it equals 1594323

so 1594323 times 73 equals 116385579

i don't know i am not good at this stuff

3¹³(3⁴-3²+1)

3¹³.73

I hope this helps

These triangles can be proven congruent by using ASA RULE.

What is congruent triangles and its rules ?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.

Main Body:

In ΔTUV and ΔTWV

VT =VT                 ----(1)

∠VTU=∠TVW      -----(2)

As TUVW is a parallelogram

so, ∠T = ∠U

hence, ∠TVU =∠VTW    ----(3)

taking equation 1, 2,3

therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

A

Step-by-step explanation:

DE is the shortest side because it's is opposite to the smallest angle (<F)

180 - 60 = 3X +2X + 5,

X = 23

<F = 2*(23) +5 = 51

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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The that will represent the exponential function is given in image

What are exponential functions, exactly?

A mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is referred to as the function's base and must be greater than zero. The most commonly used exponential function basis is the transcendental number e, which is approximately equivalent to 2.71828.

Exponentially increasing growth

In Exponential Growth, the amount expands incredibly slowly at first, then rapidly. With the passage of time, the rate of change quickens. The rate of growth quickens as time passes. The fast growth is supposed to indicate a "exponential ascent".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the proportion of increase.

Now,

As the function y=10x² represents the number of gummies after x months

the the graph will be  

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Answer:

B is the answer

Vertically opposite angles

Answer:

The correct option is b) \(P(D|A)=P(A|D)P(D)\).

Step-by-step explanation:

The probability of selecting the different types of tires are:

P (A) = 0.40

P (B) = 0.15

P (C) = 0.45

The defective rate for the different types of tires are:

P (D|A) = 0.02

P (D|B) = 0.01

P (D|C) = 0.05

The formula to compute the probability that the tire is defective given that it is Brand A tire as follows:

\(P(D|A)=P(A|D)P(D)\)

Answer:

  52920

Step-by-step explanation:

You have described the Least Common Multiple (LCM) of the three numbers. That can be found by considering their unique factors. The LCM is the product of the unique factors, 2³, 3³, 5, 7².

  315 = 3×3×5×7

  378 = 2×3×3×3×7

  392 = 2×2×2×7×7

The LCM will be ...

  2×2×2×3×3×3×5×7×7 = 52920

The smallest natural number divisible by 314, 378, and 392 is 52920.

Answer: 68y+106=36-y

Answer:

- 1

Step-by-step explanation:

( x + 4 )² + 38 = 47

( x + 4 )² = 47 - 38

( x + 4 )² = 9

( x + 4 )² = 3²

Square root on both sides,

x + 4 = 3

x = 3 - 4

x = - 1