At a particular restaurant, each onion ring has 40 calories and each pizza roll has 80
calories. A combination meal with pizza rolls and onion rings is shown to have 800
total calories and 4 more pizza rolls than onion rings. Graphically solve a system of
equations in order to determine the number of onion rings in the combination meal,
x, and the number of pizza rolls in the combination meal, y.

The angle that is adjacent to the angle CED is the angle DEA.

When two angles have a similar vertex and side, they are referred to as neighbouring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.

An adjacent angle is complementary to another if the total of its adjacent angles is 90 degrees.

When the total of two adjacent angles is 180 degrees, they are supplementary to one another.

Two angles are said to be adjacent angles when they share a common vertex.

In the given figure the angle that shares the common vertex to angle CED is angle DEA.

Hence, the angle that is adjacent to the angle CED is the angle DEA.

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Answer:

y=-3x+7

its the same thing  

Step-by-step explanation:

The amount when compounded quaterly and compounded continuously will be $16,979.44 and $17,713.02. And the difference is $733.58

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

[tex]\rm P=P_o \times e^{rt}[/tex]

The initital amount is $15,000 and the interest rate is 4.75% annually.

A. If the interest is compounded quarterly. Then the amount is given as,

[tex]\rm A = \$15,000 \times \left (1 + \dfrac{0.0475}{4} \right)^{42/4}[/tex]

A = $15,000 x 1.1319

A = $16,979.44

B. if the interest is compounded continuously. Then the amount is given as,

[tex]\rm A = \$ 15,000 \times e^{0.0475 \times (42 / 12)}[/tex]

A = $15,000 x 1.1808

A = $17,713.02

C. The difference in the amount of interest earned is given as,

Differenece = $17,713.02 - $16,979.44

Differenece = $733.58

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}[/tex]

(a) f(x) =  [tex]log_2(x)[/tex] is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2

(e) v(t) = [tex]5^t[/tex]is an exponential function

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is a trigonometric function.

(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = [tex]5^t[/tex] is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  [tex]log_2(x)[/tex]    

(b) g(x) = ∜x    

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex]    

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex]                    

(e) v(t) = [tex]5^t[/tex]    

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex]

The probability of having a 4 in a 30 roll is 5 times

The expected value, μ, of rolling a 4 on a fair number cube (with faces numbered 1 to 6) can be found by using the formula μ = np, where n is the number of trials (30 in this case) and p is the probability of success for an individual trial (rolling a 4).

The probability of rolling a 4 on a fair number cube is 1/6. Therefore, the expected value of rolling a 4 30 times can be calculated as follows:

μ = 30 * (1/6) = 5

So, Mr. Jackson can expect to roll a 4 approximately 5 times in 30 rolls of his number cube.

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Answer: 154.28 feet

Step-by-step explanation:

Answer:

100 liters is equal to 100,000 milliliters.

Step-by-step explanation:

Answer:

61

Step-by-step explanation:

√(2+3)^2+(2+4)^2

=√5^2+6^2

=√25+36

=√61

So the number is 61

Answer:

53/63

Step-by-step explanation:

It is already in simplest form

The required  sum of the first n odd numbers is equal to n².

The first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. When we add up the first few of these numbers, we get the following sums:

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

We can see that the nth odd number is equal to 2n - 1. And the sum of the first n odd numbers is equal to n². This can be verified geometrically by considering a square with sides of length n.

The sum of the first n odd numbers can be thought of as the sum of the diagonal elements of the square, which forms a square of length n.

Thus, the sum of the first n odd numbers is equal to n².

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the measurement of the ∠R will be 101 degrees.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.

Given TPRS is a parallelogram. in that ∠T = (4x +1) and ∠S = (3x +4)°

Since in a parallelogram, opposite angles are equal Thus,

∠P = ∠S = 3x + 4

∠R = ∠T = 4x +1

Since we know the sum of all angles of a quadrilateral is 360°

3x +4 + 4x +1 + 3x +4 + 4x +1 = 360

14x + 10 = 360

14x = 350

x = 350/14

x = 25

Thus,

∠R = 4x +1

∠R = 4 *25 + 1

∠R = 101°

therefore, the measurement of the ∠R will be 101 degrees.

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To find the instantaneous speed of an object, we must make the time interval very small, so that the speed does not change appreciably.

How to find the speed?

Speed is a scalar quantity which tells how fast an object is moving, regardless of its direction.

To find the instantaneous speed of an object, we must make the time interval very short, so that the speed does not change appreciably. The formula for the instantaneous speed of an object is given by the limit as time approaches zero of the change in distance divided by the time over which that change occurs. The formula for average speed is simply the total distance traveled divided by the total time elapsed.

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The statement is true. Matrix multiplication is not commutative, so the product of the transposes of the matrices must be applied in the same order as the initial product, not in a reverse order.

The statement that the transpose of a product of matrices equals the product of their transposes in the same order is true. Matrix multiplication is not commutative, which means that the order in which the matrices are multiplied matters. That is, for two matrices A and B, AB does not necessarily equal BA. Thus, when taking the transpose of a product of matrices, the order in which the transposes of the matrices are multiplied must be the same as the order in which the original matrices were multiplied. Otherwise, the result will not be the same. For example, if two matrices A and B are multiplied to give AB, the transpose of AB will be (AB)^T = B^T A^T, not A^T B^T. This is why the product of the transposes must be applied in the same order as the initial product.

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17 students played cricket more than basketball.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

Pie chart showing the preference of the students is given below.

Total number of students = 300

We know that total degree of the circle = 360°

Students who played cricket = 90°

Number of students who played cricket will be (90° / 360°)th of 300.

Number of students who played cricket = (90° / 360°) × 300

                                                                   = 75

Students who played basketball = 70°

Number of students who played basketball = (70° / 360°) × 300

                                                                         = 58.33 ≈ 58

Students played cricket - Students played basketball = 75 - 58 = 17

Hence there are 17 students more in cricket than that in basketball.

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A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel. Hence, the vertices ABCD form a parallelogram.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel.

B. The opposite sides of the parallelogram are parallel and equal, and their slopes are equal.

C. The given vertices of a parallelogram are:

A(-2, 0), B(0, 9), C(2, 0) and D(0, -9).

Calculate the slope of segment AB and CD.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

For AB:

m = (9 - 0) / (0 + 2) = 9/2

For CD:

m = (-9 - 0) / (0 - 2) = 9/2

Since the slopes of the segments AB and CD are equal the two lines are parallel to each other. Hence, the vertices ABCD form a parallelogram.

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The function that describes the sequence maps each index or position to its corresponding value.

A sequence space is a vector space that contains endless sequences of real or complex numbers. It is used in functional analysis and related mathematical fields. It is, in essence, a function space whose constituents are functions from the natural numbers to the field K of real or complex numbers.

The notation f(2) = 4 indicates that a term in a sequence defined by a function has a value of 4 when the term's index or position is 2.

Because sequences are a collection of ordered pairs with the first element being the index or position of the term and the second being the term's value, they can be characterised as functions. The function that represents the series maps each index or location to its associated value, and these ordered pairs can be seen as points on a coordinate plane.

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The probability that daily production is between 28 and 45.9 liters is 0.024.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Given that, x₁=28, x₂=45.9, μ=38 and σ =4.3

We know that, Z=(x-μ)/σ

Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample

z =(38-28)/4.3= 2.32 and probability on the z-table is 0.9896

z = (38-45.9)/4.3 = -1.83 and probability on the z-table is 0.9656,  

Now, P(2.32<z<-1.83) = 0.9896-0.9656

= 0.024

Therefore, the probability that daily production is between 28 and 45.9 liters is 0.024.

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The equation 15 - x = 7 models the scenario because it represents the decrease in the number of cats that the zoo now nurses. It can be read as "15 (the number of cats originally) minus x (the number of cats moved) equals 7 (the number of cats the zoo now nurses)".

Answer:

Step-by-step explanation:

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Answer:

The first one is 3/5 & The second one is 3/8 & The the third one is 1/8

Step-by-step explanation:

Hope this helps :)

The total number of seeds Frank is going to plant is 6b + 6 seeds.

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

Graden 1 = b

Graden 2 = 5b + 6

Frank is going to plant b seeds in one garden and 5b + 6 seeds in another garden.

The total number of seeds Frank is going to plant is:

b + (5b + 6) = 6b + 6

So Frank is going to plant 6b + 6 seeds.

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Answer:

60

Step-by-step explanation:

15x3=45

5x3=15

15+45=60