How do I solve this?

Answer:

A ratio equal to 56:64 would be 7:8.

Step-by-step explanation:

7:8 is the simplest form

Answer:

Simplify it to get an equivalent ratio, i.e 7:8!

Hope this helps :))

The car is worth $9,832.50 after 3 years of depreciation.

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". For example, 25% means "25 out of 100" or "25/100". Percentages are used to express the relationship between a part and a whole. For instance, if a company has sold 500 out of 1000 products, we can say that the company has sold 50% of its products. Similarly, if a student scores 80 out of 100 marks in an exam, we can say that the student has scored 80% in the exam.

To find the value of the car after 3 years of depreciation, we need to find the amount by which it depreciates each year and subtract it from the previous year's value.

First year depreciation: 8% of $12,500 = 0.08 x 12,500 = $1,000

Value of car after first year: $12,500 - $1,000 = $11,500

Second year depreciation: 10% of $11,500 = 0.10 x 11,500 = $1,150

Value of car after second year: $11,500 - $1,150 = $10,35

Third year depreciation: 5% of $10,350 = 0.05 x 10,350 = $517.50

Value of car after third year: $10,350 - $517.50 = $9,832.50

Therefore, the car is worth $9,832.50 after 3 years of depreciation.

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The calculated length of the arc is 25.00 units in the interval

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

y = x³/12 + 1/x

The interval is given as

[1, 4]

The arc length over the interval is represented as

\(L = \int\limits^a_b {{f(x)^2 + f'(x))}} \, dx\)

Differentiate f(x)

y' = x²/4 - 1/x²

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

\(L = \int\limits^4_1 {{(\frac{x^3}{12} + \frac{1}{x})^2 + \frac{x^2}{4} - \frac{1}{x^2})}} \, dx\)

Integrate using a graphing tool

L = 25.00

Hence, the length of the arc is 25.00 units

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Log4 27 is approximately 2.377 when expressed as a logarithm in base 2.

To evaluate log4 27 using the change of base formula, we need to write it in terms of a common base, such as base 10 or base 2. Let's use base 10:
log4 27 = log10 27 / log10 4

Now we need to find the logarithms of 27 and 4 in base 10:
log10 27 = 1.431
log10 4 = 0.602

Substituting these values into the formula, we get:
log4 27 = 1.431 / 0.602 = 2.38

So log4 27 is approximately 2.38.

To convert log4 27 to a logarithm in base 2, we use the change of base formula again, this time with base 2:
log4 27 = log2 27 / log2 4

Now we need to find the logarithms of 27 and 4 in base 2:

log2 27 = 4.754
log2 4 = 2

Substituting these values into the formula, we get:
log4 27 = 4.754 / 2 = 2.377

Rounding to the nearest thousandth, we get:

log4 27 ≈ 2.377

Therefore, log4 27 is approximately 2.377 when expressed as a logarithm in base 2.

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Based on the given algebraic expression, the value of b in 7.8b - 2.14 = -42.7 is -5.2

7.8b - 2.14 = -42.7

7.8b = -42.7 + 2.14

7.8b = -40.56

b = -40.56 / 7.8

b = -5.2

Check:

7.8b - 2.14 = -42.7

substitute the value of b into the equation

7.8(-5.2) - 2.14 = -42.7

-40.56 - 2.14 = -42.7

- 42.7 = -42.7

In conclusion, the solution to the algebraic expression 7.8b - 2.14 = -42.7 is b = -5.2

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Answer:

\(m=\frac{1}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (2, -1)

Point (-4, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

Area = 26 sq units

Step-by-step explanation:

If you put the points on a graph then you can see what you are working with. The parallelogram you can just count the squares to find the base and height. base = 6 and height = 1.

A = b • h = 6•1 = 6

To find the lengths of the sides for the rectangle you must use distance formula or pythagorean theorem. I have shown this using Pythagorean theorem. The short side of the rectangle is marked x and calculated to have length sqroot10. See image.

The graph shows the length is twice as long. But I showed a separate calculation also using pythag.thm. to find the length of y, the long side is sqroot40.

Area of rectangle is:

A = b•h OR L×W

A=sqrt10×sqrt40

=20 See image.

Add the areas to get your final answer.

Answer:

Robbie's glider

Step-by-step explanation:

Robbie reaches the greater maximum altitude in the first 6 seconds after launch option (C) Robbie's glider is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Melissa and Robbie are flying remote control gliders.

The altitude of Melissa's glider, h(s), in feet, is modeled by this function:

m(s) = 0.4(s³ - 11s² + 31s - 1)

Plug s = 6 seconds in the function m(s)

m(6) = 0.4(6³ - 11(6)² + 31(6) - 1)

m(6) = 0.4(216 - 396 + 186 - 1)

m(6) = 0.4(5)

m(6) = 2 feet

From the graph of Robbie:

At s = 6 seconds

Altitude = 13 feet (approximately)

Thus, Robbie reaches the greater maximum altitude in the first 6 seconds after launch option (C) Robbie's glider is correct.

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Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

look it up

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

:)

Answer:

a. 10560

b. 63360 in.

c. 10000 m

d. 100000 cm

e. 3.107 miles

f. 42.165 km

Step-by-step explanation:

a. 2 miles contain how many feet?

1 mile = 5280 ft

2 miles × 5280 ft / mile = 10560 ft

b. 1 mile contains how many inches?

1 ft = 12 in

1 mile × 5280 ft/mile × 12 in./ft = 63360 in.

c. 10 kilometers contain how many meters?

1 km = 1000 m

10 km × 1000 m/km = 10000 m

d. 1 kilometer contains how many centimeters?

1 km × 1000 m/km × 100 cm/m = 100000 cm

e. How many miles are in a "5k" (five-kilometer) race?

1 in. = 2.54 cm

5 km =

= 5 km × 1000 m/km × 100 cm/m × 1 in. / (2.54 cm) × 1 ft / (12 in.) × 1 mile / (5280 ft)

= 3.107 miles

f. A marathon is 26.2 miles. How many kilometers is this?

26.2 miles =

26.2 miles × 5280 ft / mile × 0.3048 m/ft × km / (1000 m) = 42.165 km

The answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

The given plot displays the distribution of the number of roses purchased per day at a grocery store. The best measure of variability for this data would be the interquartile range (IQR) since it is robust to outliers and provides a measure of the spread of the middle 50% of the data.

To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.

From the plot, we can see that there are a total of 11 data points: one at 1, two at 2, three at 6, three at 7, two at 8, and three at 9. The median (Q2) is 7 since it is the middle value when the data are arranged in order.

To find Q1, we need to find the median of the lower half of the data. Since there is one data point below 6 and three data points at 6, the lower half of the data consists of four points: 1, 2, 6, and 6. The median of this set is (1+2)/2 = 1.5.

To find Q3, we need to find the median of the upper half of the data. Since there are two data points at 8 and three data points at 9, the upper half of the data consists of five points: 8, 8, 9, 9, and 9. The median of this set is (8+9)/2 = 8.5.

Therefore, the IQR is Q3-Q1 = 8.5-1.5 = 7.

Therefore, the answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7

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a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

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Answer:

262.44 cubic metres.

Step-by-step explanation:

First, we can calculate the volume of the cylinder by doing pi * r^2 * h. In this case, r is 5 / 2 and h is 7.

pi * (5/2)^2 * 7 = pi * 25/4 * 7 = pi * 6.25 * 7 = pi * 43.75 = 3.14159265 * 43.75 = 137.4446784 cubic m.

Seconds, we calculate the volume of the cube. It is 5^3 = 5 * 5 * 5 = 25 * 5 = 125 cubic m.

137.4446784 + 125 = 262.4446784, which is about 262.44 cubic metres.

Hope this helps!

Answer:

5*5*5=125

volume of cylinder=137.44

137.44+125=262.44

Step-by-step explanation:

Using linear regression, the best predicted value for systolic blood pressure (y) given age (x) = 64 is approximately 151.63 mmHg.

To determine the best anticipated value for y given x = 64, we can use linear regression.

The correlation coefficient, r, is first calculated using the formula: r = [(xi - X)(yi - Y)] / [sqrt(xi - X)**sqrt(yi - Y)**sqrt(r)]

where X and Y are, respectively, the sample means of x and y.

Using the supplied data, we have:

X = (38+41+45+48+51+53+57+61+65)/9 = 51

Y = (116+120+123+141+142+145+148+150+152)/9 = 136 xi - X - yi - Y = 464 xi - X - yi - Y - xi - xi - xi - xi - xi - xi - xi - xi - xi - xi

The result is: r = 464 / [sqrt(1120) * sqrt(2804)]. ≈ 0.942

Given the strong correlation between the variables, we can apply linear regression to choose the line that best fits the data: y = a + bx, where a denotes the y-intercept and b the slope of the line. The formulas below can be used to determine the values of a and b.

Where Sx and Sy are the sample standard deviations of x and y, respectively, b = r * (Sy/Sx) a = Y - b*X.

Using the supplied data, we have:

sqrt[(xi - X)2/(n-1)] = Sx = sqrt(1120/8) ≈ 11.83

Sqrt[(yi - Y)2/(n-1)] = Sy = sqrt(2804/8) ≈ 9.38

We thus have:

A =Y - b*X - 69.19 b = r * (Sy/Sx)

Therefore, y = 69.19 + 1.28x is the line of best fit.

We add x = 64 to the equation to determine the best anticipated value for y given that x = 64:

y = 69.19 + 1.28(64) ≈ 151.63

As a result, 151.63 mmHg is the value for y that can be best predicted for x = 64.

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Answer:

Thx

Step-by-step explanation:

Yes

The Docx is not accessible, check if its the wrong one.

Answer:

answer in explanation

Step-by-step explanation:

it is function because each domain is associated with only one range.

all the element of x are domain and y are range.

It is a function. cuz every elements of x have unique image on y.

Domain : [ 6 , -8 , 5,0,6 ]

Range : [ 2 , 5 ,8 , 0, 6 ]

I HOPE IT WILL HELP YOU.

Thank you.

^ - ^

Answer:

Five coins are tossed the probability of getting two heads is 5/16.

Step-by-step explanation:

I hope it will be helpful for you.

In a 4 x 4 x 4 design, there are three main effects, three 2-way interactions, and one 3-way interaction.

In a factorial design, the number of main effects and interactions can be determined by examining the number of factors and their levels. In a 4 x 4 x 4 design, there are three factors, each with four levels.

For each factor, there is one main effect. Since there are three factors in the design, there are three main effects.

To determine the number of possible interactions, we consider the possible combinations of factors. In a 4 x 4 x 4 design, we can have 2-way interactions, 3-way interactions, and a 4-way interaction.

2-way interactions: There are three pairs of factors (A-B, A-C, B-C), resulting in three 2-way interactions.

3-way interactions: There is only one combination of three factors (A-B-C), resulting in one 3-way interaction.

4-way interaction: Since there are no additional factors beyond the three factors, there is no 4-way interaction.

Therefore, in a 4 x 4 x 4 design, there are three main effects, three 2-way interactions, and one 3-way interaction.

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The interval in which the graph increasing is (10,∞). The correct option is D.

The absolute value or modulus of a real number x denoted |x| in mathematics, is the non-negative value of x regardless of its sign. Specifically, if x is a positive number,|x|=x.

In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The objects correspond to mathematical abstractions known as vertices, and each pair of related vertices is known as an edge.

The given absolute function is h (x) =lx-10l+6. When we plot the graph of the function it is observed that the graph is increasing from 10 to ∞. The graph is attached with the answer below.

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On solving the provided question, we can say that - sum of the elements of \(S = (45 * 72 * 111 / 999) = 360\)

Both integers and non-integers are often represented using the decimal system. The Hindu-Arabic number system has been extended in a non-integer way using this. Decimal notation is the term used to describe the representation of numbers in decimal form. The term "decimal" is used to refer to the base-10 number system, which is perhaps the most widely used one. There are 10 single digits in the decimal numeral system.

Consider S to be the collection of real numbers that may be expressed as repeating decimals.

The repeating decimal has the form 0.abc cap.

a, b, and c are three separate digits.

If

\(x = 0.abcabc\\1000x = abc.abc\\1000x - x = abc\\999x = abc\\x = abc/999\)

a, b, c are distinct digits

Number of combinations 10 × 9 × 8

\(= 720 combinations\)

each value appear i= 720/10

\(= 72\)

Sum digits from\(0 to 9 = 45\)

sum of the elements of \(S = (45 * 72 * 111 / 999) = 360\)

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When calculating a confidence interval, increasing the sample size while keeping the confidence level constant will result in a narrower (more precise) confidence interval. The correct option is D.

A confidence interval is a range of values that estimates the true value of a population parameter with a certain level of confidence. The margin of error is a measure of the uncertainty associated with the estimate.

When the sample size increases, there is more data available to estimate the population parameter, leading to a more precise estimate. With a larger sample size, the variability in the data is reduced, resulting in a smaller margin of error. As a result, the confidence interval becomes narrower, indicating a more precise estimate of the population parameter.

Therefore, increasing the sample size while keeping the confidence level constant reduces the margin of error and leads to a narrower (more precise) confidence interval, as stated in option D.

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The number of beverages sold at $1.75 is: y ≈ 10

Let's denote the number of beverages sold at $1.25 by x and the number of beverages sold at $1.75 by y. Then we can set up a system of two equations based on the given information:

x + y = 78 (total number of beverages sold)

1.25x + 1.75y = 110.50 (total amount of money collected)

To solve for y, we can use the first equation to express x in terms of y:

x = 78 - y

Then we can substitute this expression for x into the second equation:

1.25(78 - y) + 1.75y = 110.50

Simplifying and solving for y, we get:

97.5 - 0.5y + 1.75y = 110.50

1.25y = 13

y = 10.4

Since y represents the number of beverages sold at $1.75, we need to round it to the nearest whole number. Since we can't sell a fraction of a beverage, we need to round up if the decimal part is greater than or equal to 0.5, and round down otherwise. In this case, 0.4 is less than 0.5, so we round down. Therefore, the number of beverages sold at $1.75 is:

y ≈ 10

So, 10 of the 78 beverages sold cost $1.75. The remaining beverages cost $1.25.

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Answer:

answer given in step by step...

Step-by-step explanation:

13x+13(x+1)+13(x+2)=312

13x+13x+13+13x+26=312

39x+39=312

39x=312-39

39x=273

x=7

first number=13x=13*7=91

second number=13(8)=104

third number=13(9)=117

The cost of one calzone given the information in the table is $8.75 (first option).

The first step is to form a system of equation to represent the information in the question:

16p + 12c = 269 equation 1

20p + 8c = 275 equation 2

Where:

p =cost of pizzas bought

c = cost of calzones bought

The elimination method would be used to determine the cost of one calzone.

Multiply equation 1 by 5 and equation 2 by 4

80p + 60c = 1345 equation 3

80p + 32c = 1100 equation 4

Subtract equation 4 from equation 3

28c = 245

Divide both sides of the equation by 28

c = 245 / 28

c = $8.75

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Answer:

B

Step-by-step explanation:

Answer:

The answer is B because of the graph being 1/2

Answer:

Area = 40 m^2

Step-by-step explanation:

The formula for any triangles is A = h x b / 2

In this problem, h = 8 m and b = 10 m

So area = 8 x 10 / 2 m^2 = 40 m^2