if a right triangle has sides of length a, b and c, and if c is the largest, then it is called the hypotenuse. the length of the hypotenuse can be calculated with this formula: c

Answer: 155

Step-by-step explanation: 0.18x=28 divide each side by 0.18.

The number of hours spent walking dogs is 3 hours and 5 hours was spent landscaping.

The first step is to form a system of equations using the information provided in the question:

x + y = 8 equation 1

6x + 13y = 83 equation 2

Where:

The elimination method would be used to solve the equations.

Multiply equation 1 by 6

6x + 6y = 48 equation 3

Subtract equation 3 from equation 2:

7y = 35

Divide both sides of the equation by 7:

y = 35 / 7

y = 5

Substitute for y in equation 1:

x + 5 = 8

8 - 5 = x

x = 3

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Answer: 0.17193742185

Step-by-step explanation:

Answer:

0.171937422

Step-by-step explanation:

Applying the corresponding angles theorem, m<DEG = 33°.

The Corresponding Angles Theorem states that if two lines are cut by a transversal, then corresponding angles are equal. This means that if two lines intersected by a transversal form a pair of corresponding angles, then those angles are congruent (have the same measure).

Given that:

m<HBC = 33 degrees

m<ABE = m<HBC [vertical angles are congruent]

m<ABE = 33° [substitution property]

Therefore, based on the corresponding angles theorem, we have:

m<DEG = m<ABE

Substitute:

m<DEG = 33°

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The improved high-speed mixer that allows bakers to produce cookies in less time will result in an increase in production, a decrease in cost, an increase in demand, and an increase in price of chocolate chip cookies.

Point A to Point B illustrates an increase in the production of chocolate chip cookies. This can be calculated using the formula: Change in Output = Output at Point B - Output at Point A. For example, if the output of chocolate chip cookies at Point A is 25 cookies per hour, and the output at Point B is 40 cookies per hour, then the change in output is 40-25=15 cookies per hour.

Point C to Point B illustrates a decrease in the cost of production of chocolate chip cookies. This can be calculated using the formula: Change in Cost = Cost at Point C - Cost at Point B. For example, if the cost of production at Point C is $2 per cookie, and the cost at Point B is $1 per cookie, then the change in cost is $2 - $1 = $1 per cookie.

Point C to Point D illustrates an increase in the demand for chocolate chip cookies. This can be calculated using the formula: Change in Demand = Demand at Point D - Demand at Point C. For example, if the demand for chocolate chip cookies at Point C is 100 cookies per hour, and the demand at Point D is 150 cookies per hour, then the change in demand is 150 - 100 = 50 cookies per hour.

Point A to Point D illustrates an increase in the price of chocolate chip cookies. This can be calculated using the formula: Change in Price = Price at Point D - Price at Point A. For example, if the price of chocolate chip cookies at Point A is $1 per cookie, and the price at Point D is $2 per cookie, then the change in price is $2 - $1 = $1 per cookie.

The improved high-speed mixer that allows bakers to produce cookies in less time will result in an increase in production, a decrease in cost, an increase in demand, and an increase in price of chocolate chip cookies.

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Answer:

hi !!

Step-by-step explanation:

34.70 - 34.70/100*10 = 34.70 - 3.47 = $31.23

Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).

The diameter of a circle is equal to the number of inches in a pizza's size.

The area of a circle is calculated using the formula: [tex]\pi r^{2} = \pi (d/2)^{2}[/tex].

Assume that a pizza's calories are evenly distributed over its surface (even though we know there is a crust ring around the outsize). C calories per square inch, as an illustration.

The number of calories in a 6-inch pizza is

[tex]CA_{6} = C\pi (6/2)^{2} =9C\pi =590[/tex]      [eq1]

Calories in a 16-inch pizza are calculated as follows:

[tex]CA_{16}=C\pi (6/2)^{2} =64C\pi[/tex]

The number of calories in one of those pizza's eight slices is:

[tex]X=CA_{16} /8=8C\pi[/tex]   [eq2]

math:

[tex]C\pi =590/9[/tex]   [from eq1]

[tex]X=8(C\pi )[/tex]    [from eq2]

[tex]X=8(590/9)[/tex]

[tex]X=524[/tex]        [estimated]

Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).

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Deandre invested $22,000 in the 10% account and $30,000 - $22,000 = $8,000 in the 5% account.

percentage, a relative value indicating hundredth parts of any quantity.

Let's call the amount Deandre invested in the 10% account x.

The amount he invested in the 5% account is $30,000 - x.

The interest he received from the 10% account is 0.10x and the interest he received from the 5% account is 0.05($30,000 - x).

The total interest received is $2600, so we can set up the equation:

0.10x + 0.05($30,000 - x) = $2600

0.10x + 0.05 * $30,000 - 0.05x = $2600

0.10x - 0.05x + 0.05 * $30,000 = $2600

0.05x = $2600 - 0.05 * $30,000

0.05x = $2600 - $1,500

0.05x = $1100

x = $1100 / 0.05

x = $22,000

Hence, Deandre invested $22,000 in the 10% account and $30,000 - $22,000 = $8,000 in the 5% account.

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Answer:

4.5t - 12.5

Step-by-step explanation:

12.5(0.2t − 1) + 21t

12.5(0.2t) + 12.5(-1) + 2t

2.5t - 12.5 + 2t

4.5t - 12.5

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]9000 = P\left(1+\frac{0.04}{4}\right)^{4\cdot 4} \implies 9000=P(1.01)^{16} \\\\\\ \cfrac{9000}{(1.01)^{16}}=P\implies \boxed{7675.39\approx P}[/tex]

The format of the equation that shown below:

We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k.

Given:

The General form of Vertex form is

y = a(x - h)² + k

where (h, k) are the vertex.

For Example, Pick a point on the graph other than the vertex.  Let's say you see the line pass through (1,5) and the vertex is at (3,4)

First the vertex gives

y = a (x - 3)² + 4

Put the values (1,5) into this equation.

5 = a (1 - 3)² + 4

Solve for a

5 = a x (-2)2 + 4

5 = 4a + 4

1 = 4a

1/4 = a

and, the vertex form of parabola is y = 1/4(x - 3)² + 4.

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Answer: w=-7/4, x = 3 , z = 8.
You were only incorrect on one which I will provide an image on how I solved that one so you can maybe see what you did wrong. hope it helps !

Answer:

1.D

2.D

3.D

4.A

5.A

6.B

7.A

8.B

hope those are right

Step-by-step explanation:

1.D

2.D

3.B

4.A

5.A

6.B

7.A

8.B

The mean of sample a is equal to the mean of the population, it is likely that the sample is representative of the population, but it is not a guarantee of it.

If the mean of sample a is equal to the mean of the population, then it can be concluded that sample a is representative of the population. The mean of a sample is an estimate of the population mean, and if the sample mean is equal to the population mean, it indicates that the sample was randomly selected and is representative of the population.

However, it is important to note that the equality of the sample mean and the population mean does not guarantee that all other statistics, such as the standard deviation or the distribution shape, are equal. Sampling variability and the size of the sample can also impact the similarity between the sample and population statistics.

In conclusion, if the mean of sample a is equal to the mean of the population, it is likely that the sample is representative of the population, but it is not a guarantee of it. Further statistical analysis is needed to determine the representativeness of the sample and its similarity to the population.

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The actual distance between Spice Island and Kay Island is 85 miles.

Distance is a numerical measurement of how far apart two points or objects are. In mathematics, distance is often used in geometry to describe the length of a line segment connecting two points in a given space. It can also be used to describe the difference between two quantities or values. In physics, distance is a scalar quantity that measures the amount of space between two objects. It is often used to describe the separation between two points in a given direction.

There are various ways to calculate distance, depending on the type of space and the number of dimensions involved. In a one-dimensional space, such as a number line, distance can be calculated as the absolute value of the difference between two points. In a two-dimensional space, such as a plane, distance can be calculated using the Pythagorean theorem. In a three-dimensional space, such as our physical universe, distance can be calculated using the Euclidean distance formula.

Distance is an important concept in many fields, including mathematics, physics, engineering, computer science, and economics. In transportation and logistics, distance is used to determine the time and cost of moving goods and services from one location to another. In sports, distance is used to describe the length of a race or the distance traveled by a projectile.

If the scale on the map is 1 inch = 25 miles, this means that 1 inch on the map represents 25 miles in real life. To find the actual distance between the two islands, we need to multiply the distance on the map by the scale factor. So, the actual distance between the two islands is:

3.4 inches * 25 miles/inch = 85 miles

So the actual distance between Spice Island and Kay Island is 85 miles.

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The equation of the relation between x and y is y= 2x

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

The table of values

On the table of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

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Complete question

Without performing any algebraic manipulations, can you define the relation between x and y?

X (input) 7 8 9 10

y (output) 14 16 18 20

The exact values of trigonometric functions cosine and tangent are 4 / 5 and 3 / 4, respectively.

In this question we must determine the exact value of two trigonometric functions on the basis a given value of another trigonometric function, whose quadrant is also known. According to the statement, sine is in the first quadrant, then both cosine and tangent are also positive. The value of cosine can be found by means of following trigonometric formula:

cos θ = √(1 - sin² θ)

cos θ = √[1 - (3 / 5)²]

cos θ = 4 / 5

And the exact value of tangent can be found by this formula:

tan θ = sin θ / cos θ

tan θ = (3 / 5) / (4 / 5)

tan θ = 3 / 4

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The claim of Carly is correct that the sum of the deviations for a data set will always be 0.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Sum of the deviations of a data set is always 0.

This is because that the sum of the positive deviations is equal to the sum of the negative deviations.

Let a data set be 3, 2, 4, 5, 1

Mean = (3 + 2 + 4 + 5 + 1) / 5 = 3

Values     Deviations

3               3 - 3 = 0

2               2 - 3 = -1

4               4 - 3 = 1

5               5 - 3 = 2

1                1 - 3 = -2

Sum of the deviations = 0 - 1 + 1 + 2 - 2 = 0

Hence the sum of the deviations for a data set will always be 0.

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The square is shown in the complex plane, where each vertex can be represented as a complex number.

If we let the first vertex be 0, then the next vertex [tex]$a$[/tex] is at a distance of 1 unit along the real axis. The complex number representing [tex]$a$[/tex] is [tex]$1 + 0i$[/tex]. The vertex [tex]$b$[/tex] is at a distance of 1 unit along the imaginary axis, so its complex representation is [tex]$0 + 1i$[/tex]. Finally, the vertex [tex]$c$[/tex] is at a distance of 1 unit along the negative real axis, so its complex representation is [tex]$-1 + 0i$[/tex].

To find [tex]$b/a$[/tex], we divide the complex number representing [tex]$b$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$b/a = (0 + 1i) / (1 + 0i) = 0 + 1i$[/tex].

Similarly, to find [tex]$c/a$[/tex], we divide the complex number representing [tex]$c$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$c/a = (-1 + 0i) / (1 + 0i) = -1 + 0i$[/tex].

So, the values of [tex]$b/a$[/tex] and [tex]$c/a$[/tex] in rectangular form are [tex]0 + 1i[/tex] and [tex]-1 + 0i[/tex], respectively.

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Answer:

224 millimeters

or

2.24 cm

Step-by-step explanation:

Scale is 8 millimeters = 1 meter

So 28 meters = 28 x 8 millimeters = 224 millimeters

224 millimeters = 224/10 cm = 22.4 cm

Answer:

Step-by-step explanation:

y = mx +c

1 = m0 + c

1=0+c

c=1

5-1=4

3-1=2

4/2=2

m=2

y=2x+1

The polynomial function for the cars manufactured in thousands since 1990, where x represents the number of years since 1990 the fourth option

P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3

A polynomial consists of an expression that has two or more terms of (the same) variables with different powers or index.

The possible table in the question, obtained from a similar question on the internet is presented as follows;

Year;              [tex]{}[/tex]                1991     1993       1995        1997         1999

Cars Manufactured; [tex]{}[/tex]      1.4       11.4         39.8         96.2         190.2

(thousands)

The details in the table indicates that we get;

When x = 1991 - 1990 = 1, P(x) = 1.4

Which, based on the coefficients of x³, x², and x, corresponds with the first and the fourth polynomial.

p(x) = 0.5·x³ + 0.2·x² + 0.3·x + 0.4...(1)

p(1) = 0.5 × 1³ + 0.2 × 1² + 0.3 × 1 + 0.4 = 1.4

P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3...(4)

p(1) = 0.2 × 1³ + 0.5 × 1² + 0.4 × 1 + 0.3 = 1.4

When x = 1993 - 1990 = 3, we get in equation (1);

p(3) = 0.5 × 3³ + 0.2 × 3² + 0.3 × 3 + 0.4 = 16.6

The polynomial in equation (4) indicates that we get;

p(3) = 0.2 × 3³ + 0.5 × 3² + 0.4 × 3 + 0.3 = 11.4

Therefore, the polynomial in the fourth equation best represents the polynomial function for the cars manufactured in thousands where x represents the years since 1990

Verifying, we get;

When x = 5; p(5) = 0.2 × 5³ + 0.5 × 5² + 0.4 × 5 + 0.3 = 39.8

When x = 7; p(7) = 0.2 × 7³ + 0.5 × 7² + 0.4 × 7 + 0.3 = 96.2

When x = 9; p(9) = 0.2 × 9³ + 0.5 × 9² + 0.4 × 9 + 0.3 = 190.2

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Answer:

169.65

Step-by-step explanation:

The surface area of each cone is approximately 113.1 square feet. Half of this surface area is painted red, so approximately 56.55 square feet of each cone is painted black. The total surface area painted black for all three cones is approximately 169.65 square feet.

The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

=> y = -2/1

=> y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

=> x + 3 = 0

=> x = -3

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The quadratic function from the table of values is y = x^2 + 5

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

x     y

0     5

2     9

12    149

A quadratic function can be represented as

y = a(x - h)^2 + k

Where

Vertex = (h, k)

In this case, the vertex is the minumum

So, we have

(h, k) = (0, 5)

So, we have

y = ax^2 + 5

Using the other points, we have

a(2)^2 + 5 = 9

So, we have

a = 1

So, the function is y = x^2 + 5

The average gas mileage for new vehicles sold does not decrease based on the data in the table

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Complete question

A mathematician used data of the average gas mileage of new vehicles sold in Greece for the years 2012 to 2022 to create a quadratic function that models the data, where x is the number of years since 2010 and y is the average gas mileage, in miles per gallon (mpg). Some of the values are shown in the table of values.

During what years was the average gas mileage for new vehicles sold in Greece decreasing?​

x     y

0     5

2     9

12    149

Answer:

The experimental probability of drawing a spade is 0.15. This is calculated by dividing the number of spades drawn (3) by the total number of cards drawn (20).

Experimental probability = Number of successful outcomes / Total number of trials

= 3 / 20

= 0.15

The graph of the function is added as an attachment

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

2x−y=−8​

Make y the subject

y = 2x + 8

The above equation is a linear equation

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

This means that the slope is 2 and the y-intercept is 8

Next, we plot the graph of the equation

See attachment for the graph

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a. Inverse of 100B is [tex]100B^{-1}[/tex]

b. To obtain the inverse of B', double the corresponding entries in the first row of [tex]B^{-1}[/tex].

c. To obtain the inverse of B', divide the corresponding entries in the first column of [tex]B^{-1}[/tex] by 2.

a. Inverse of 100B is [tex]100B^{-1}[/tex] by simply taking the mathematical Inverse.

b) To find the inverse of B', we can first write B' in terms of B as follows:

c) To find the inverse of B', we can first write B' in terms of B as follows:

In summary, the inverse of a matrix can change when the original matrix is altered by scalar multiplication or the addition of a multiple of a row or column. However, if we know the inverse of the original matrix, we can use it to find the inverse of the modified matrix.

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The trigonometry ratios are tan(∅) = 2/3√10 and

csc(∅) = 7√10/20

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

0°≤ ∅ ≤ 180°

Also, we have

cos(∅) = -3/7

The tangent is calculated as

tan(∅) = √[1/cos²(∅) - 1]

Substitute the known values in the above equation, so, we have the following representation

tan(∅) = √[1/(-3/7)² - 1]

So, we have

tan(∅) = √[49/9 - 1]

This gives

tan(∅) = √40/9

So, we have

tan(∅) = 2/3√10

Also, we have

cos²(∅) + sin²(∅) = 1

So, we have

(-3/7)² + sin²(∅) = 1

Evaluate

sin²(∅) = 1 - (-3/7)²

sin²(∅) = 1 - (9/49)

sin²(∅) = 40/49

Take the inverse of both sides

csc²(∅) = 49/40

So, we have

csc(∅) = 7/(2√10)

Rationalize

csc(∅) = 7√10/20

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