Lisa walked 1 1/4 miles on Tuesday and 2 2/3 miles on Wednesday. What was the total distance, in miles , Lisa walked during those 2 days?

Answer:

17

Step-by-step explanation:

if the sequence is 3n+5

we do 3x4(since we are working out the 4th term) +5

3x4=12  12+5=17

The only set of side lengths that can form a triangle is 9, 4, 8.

Option A is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check if each of the given sets of side lengths satisfies this condition:

A.

9, 4, 8

9 + 4 > 8 ✓

9 + 8 > 4 ✓

4 + 8 > 9 ✓

All three inequalities are true, so these side lengths can form a triangle.

B.

14, 7, 6

14 + 7 > 6 ✓

14 + 6 > 7 ✓

7 + 6 > 14 ✗

The last inequality is false, so these side lengths cannot form a triangle.

C.

3, 8, 1

3 + 8 > 1 ✓

3 + 1 > 8 ✗

8 + 1 > 3 ✓

The second inequality is false, so these side lengths cannot form a triangle.

Therefore,

The only set of side lengths that can form a triangle is A. 9, 4, 8.

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Answer:

Anime is animation from japan

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Step-by-step explanation:

-13 x 4 = -52

-52 x 0.5 = -25

-2 x 0.5 = -1

-1 + -25 = -26

Answer:

-----------------------

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

the largest length of the squares will be 120m.

The largest possible length will be equal to the greatest common factor between the dimensions of the rectangular plot, so we need to find the GCF between 600 and 720.

If we decompose both numbers, we get:

600 = 2*2*2*3*5*5

720 = 2*2*2*2*3*3*5

Then the greatest common factor is: (2*2*2*3*5) = 120

So the largest length of the squares will be 120m.

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The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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Answer: it's A

Step-by-step explanation:

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer:

A

Step-by-step explanation:

All the values of x that solve the given system of equations are as follows:

x = 17/2.

A system of equations is when multiple variables are related by equations, which are solved to find the values of each variable. Usually, these relations are linear, but they may also be quadratic, as is the case in this problem.

For this problem, we are given two equations, as follows:

From the second equation, we have that:

x = 9 - 3y.

Replacing in the first, we have that:

(9 - 3y)² - 9y² = 72.

9y² - 54y + 81 = 72.

54y = 9.

y = 9/54

y = 1/6, as 9/9 = 1, 54/9 = 6.

Hence the solution for x of the system of equations is found by replacement, as follows:

x = 9 - 3y = 9 - 3/6 = 9 - 1/2 = 18/2 - 1/2 = 17/2.

The solution is x = 17/2.

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Answer:

Y(0,13)

X(13,0)

Answer:

\((a)\) \(P(x) = 0.02x^2 +50x - 100\)

\((b)\) \(Average = 0.02x + 50 - \frac{100}{x}\) and \(Marginal = 0.04x + 50\)

\((c)\) \(Average = 59.8\) and \(Marginal = 70\)

(d) See Explanation

Step-by-step explanation:

Given

\(p(x) = 100\)

\(C(x) = -0.02x^2 +50x +100\)

Solving (a) Profit function; P(x)

\(P(x) = xp(x) - C(x)\)

This gives:

\(P(x) = x*100 - (-0.02x^2 + 50x + 100)\)

\(P(x) = 100x + 0.02x^2 - 50x - 100\)

Collect like terms

\(P(x) = 0.02x^2 - 50x +100x - 100\)

\(P(x) = 0.02x^2 +50x - 100\)

Solving (b): Average profit function and Marginal profit function

\(Average = \frac{P(x)}{x}\)

This gives:

\(Average = \frac{0.02x^2 + 50x - 100}{x}\)

Break down the fraction

\(Average = \frac{0.02x^2}{x} + \frac{50x}{x} - \frac{100}{x}\)

\(Average = 0.02x + 50 - \frac{100}{x}\)

\(Marginal = \frac{dP}{dx}\)

\(P(x) = 0.02x^2 +50x - 100\)

Differentiate

\(\frac{dP}{dx} = 2 * 0.02x + 50 - 0\)

\(\frac{dP}{dx} = 0.04x + 50\)

Hence:

\(Marginal = 0.04x + 50\)

Solving (c): Average profit and Marginal profit if x = a

\(a = 500\)

So:

\(x =500\)

Substitute 500 for x

\(Average = 0.02x + 50 - \frac{100}{x}\)

\(Average = 0.02 * 500 + 50 - \frac{100}{500}\)

\(Average = 59.8\)

\(Marginal = 0.04x + 50\)

\(Marginal = 0.04*500 + 50\)

\(Marginal = 70\)

Solving (d): Interpret the values in (c)

\(Average = 59.8\)

They make a profit of 59.8 for the first 500 items

\(Marginal = 70\)

From the 501st item, the profit is 70

Answer:

d) The additional training did not significantly lower the defect rate

Step-by-step explanation:

Let proportion of defective chips be = x

Null Hypothesis [H0] : Additional training has no impact on defect rate             x = 8% = 0.08

Alternate Hypothesis [H1] : Additional training has impact on defect rate          x < 8% , x < 0.08  

Observed x proportion (mean) : x' = 27 / 450 = 0.06

z statistic = [ x' - x ]  / √ [ { x ( 1-x ) } / n ]

( 0.06 - 0.08 ) /  √ [ 0.08 (0.92) / 450 ]

= -0.02 / √ 0.0001635  

= -0.02  / 0.01278

z = - 1.56

Since calculated value of z, 1.56 < tabulated value of z at assumed 0.01 significance level, 2.33

Null Hypothesis is accepted, 'training didn't have defect rate reduction impact' is concluded

Answer:

f(x) = (x-4)² +28

Step-by-step explanation:

f(x) = x²- 8x + 44

in vertex form :

f(x) = (x -4)² + 28

Using relations in a right triangle, it is found that the length of AC is of 14 cm.

The relations in a right triangle are given as follows:

Researching this problem on the internet, we have that:

Hence the hypotenuse is found as follows:

sin(A) = 48/h

0.96 = 48/h

h = 48/0.96

h = 50 cm.

The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:

\(x^2 + 48^2 = 50^2\)

\(x^2 = \sqrt{50^2 - 48^2}\)

x = 14 cm.

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you will need 180 mL of the 55% alcohol mixture to create a 25% alcohol solution.

How to solve the question?

To find out how much of the 55% alcohol mixture is needed to create a 25% alcohol solution, we can use the formula:

(amount of pure alcohol in the 10% mixture + amount of pure alcohol in the 55% mixture) / total volume of solution = desired alcohol concentration

Let x be the amount of the 55% alcohol mixture needed.

First, we need to calculate the amount of pure alcohol in the 10% mixture. We know that the 10% mixture contains 10% alcohol, which means that there are 0.10 x 360 = 36 mL of pure alcohol in the mixture.

Next, we need to calculate the amount of pure alcohol in the 55% mixture. We know that the 55% mixture contains 55% alcohol, which means that there are 0.55 x x = 0.55x mL of pure alcohol in the mixture.

The total volume of the solution will be 360 mL + x mL.

Using the formula above, we can set up the equation:

(36 + 0.55x) / (360 + x) = 0.25

Simplifying the equation, we get:

36 + 0.55x = 0.25(360 + x)

36 + 0.55x = 90 + 0.25x

0.3x = 54

x = 180 mL

Therefore, you will need 180 mL of the 55% alcohol mixture to create a 25% alcohol solution.

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If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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Answer: 117.2%

Step-by-step explanation:

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

= (1.172 × 100) × 1/100=117.2/100

Write in percentage notation: 117.2%

Answer:

1.172 as a percent is 117.2%

Step-by-step explanation:

To turn a decimal into a percent just move the decimal point(.) 2 spaces back.

To turn a Percent to a decimal move the move the decimal (.) two spaces up.

(If you dont see the decimal in the Percent it is alway behind the the last number) EX: 70% would be .70 as a decimal.

Answer:

The mean number of bags that arrive on time to its intended destination is 1260 with a standard deviation of 21.59.

Step-by-step explanation:

For each bag, there are only two possible outcomes. Either it arrives on time to it's intended destination, or it does not. The probability of a bag arriving on time is independent of other bags. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Luggage checked-in at Airline A arrives on time to its intended destination with a probability of 0.63.

This means that \(p = 0.63\)

In a random sample of 2000 bags

This means that \(n = 2000\)

Mean and standard deviation of the number of bags that arrive on time to its intended destination:

\(E(X) = np = 2000*0.63 = 1260\)

\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.63*0.37} = 21.59\)

The mean number of bags that arrive on time to its intended destination is 1260 with a standard deviation of 21.59.

The hospital can get 4.15 milligrams from these three companies.

A linear equation is one in which the highest power of any variable is not more than 1. A linear equation in 2 variables can be solved by substitution method, if we have two simultaneous equations.

Here, we know that

Company A's supply of medicine = 1.7 mg

also, company A's supply = 2( B's supply - C's supply)

⇒ 1.7 = 2( B - C)

⇒ 1.7 = 2B - 2C .... (1)

Moreover, we are given that

A's supply = C's supply + 0.9

⇒ 1.7 = C + 0.9

⇒ 1.7 - 0.9 = C

⇒ 0.8 = C

Now, substituting the value of C in (1), we get,

1.7 = 2B - 2(0.8)

1.7 = 2B - 1.6

1.7 + 1.6 = 2B

⇒ B = 3.3/2

B = 1.65

Thus, the total supply from all three companies is (1.7 + 1.65 + 0.8) = 4.15 mg

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The amount of the last payment that Elroy will make is $710, which includes the $200 monthly payment and a balance of $510.

The last payment amount is the result of the mathematical operations of subtraction and multiplication.

The first mathematical operation was the subtraction of the down payment from the total cost of the video game system.

Using multiplication, the monthly payments are determined to be $3,400 for 17 months.  This is subtracted from the remaining balance to obtain the last payment amount.

The cost of a custom video game/virtual sound system = $4,210

Down payment = $100

The remaining balance for monthly payment = $4,110 ($4,210 - $100)

Payment period = 18 months (1¹/₂ years)

Monthly payments = $200

Payment for the first 17 months = $3,400 (17 x 200)

Last payment = $710 ($4,110 - $3,400)

Thus, if Elroy makes the minimum monthly payment of $200 till the last payment, then he will pay $710 to settle the account.

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He made a $100 down payment and agreed to pay the entire purchase off in 1 1/2 years The minimum monthly payment is $200 if he makes the minimum monthly payment up until the last payment what will be the amount of his last payment?

The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

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The equation of the graph is,

⇒ y = 6x + 2

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

For each by sitting job. Adam charges a fee for his bus fare plus an hourly rate.

And, The graph shows how he calculates the cost of a babysitting job.

Now, By graph;

Two points on the line are (1, 8) and (2, 14).

Now,

Since, The equation of line passes through the points (1, 8) and (2, 14).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (14 - 8)) / (2 - 1)

m = 6 / 1

m = 6

Thus, The equation of line with slope 6 is,

⇒ y - 8 = 6 (x - 1)

⇒ y - 8 = 6x - 6

⇒ y = 6x + 2

Therefore, The equation of line will be;

⇒ y = 6x + 2

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Answer:

it's 68...............

Answer:

68

Step-by-step explanation:

so 25% of x=17

17*4=68

Answer:

Step-by-step explanation:

Let, width = x

length = x+4

perimeter, 2(x+4+x) = 40

4x+8 = 40

4x = 32

x = 8

so, (x+4) = 8+4 = 12

so, the area would be,

= 12 * 8 = 96 in²

Answer:

6666

Step-by-step explanation:

Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

(a) 45 tens is equal to 450. :- True

(b) 12.3 is equal to 123 ones. :- True

(c) 80 tens is greater than 6 hundreds. :- True

(d) 43,200 is less than 50 thousands. :- True

(e) 60 hundreds = 6,000 :- True

Consider the first statement,

45 tens are equal to 450

So, 45 tens mean 45 times 10 is written as:

45 × 10 = 450

Hence, it's true.

Consider the second statement,

12.3 is equal to 123 ones.

Now, 123 ones is equal to 123 times 1.

123 × 1 = 123

Hence, the statement is true.

Consider the third statement,

80 tens is greater than 6 hundreds.

Now 80 tens = 80 × 10 = 800

Now, 6 hundreds = 6 × 100 = 600

Now, 800 > 600

Hence, the statement is true.

Consider the fourth statement.

43,200 is less than 50 thousands.

Now, 50 thousands = 50 × 1000 = 50,000

We know,

50,000 > 43,200

Therefore, the statement is true.

Consider the fifth statement,

60 hundreds = 6000

Now, 60 hundreds = 60 × 100 = 6000

Therefore, the statement is true.

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