todd has 48 words to spell for a puzzle. as an incentive, his mother offers to pay him 20 cents for each word he spells correctly, if todd will pay her 5 cents for each word he spells incorrectly. he earned $7.35 how many words did he spell correctly

Check the picture below.

[tex]\cfrac{16}{x+2}=\cfrac{40}{3x}\implies 48x=40x+80\implies 8x=80\implies x=\cfrac{80}{8}\implies \boxed{x=10}[/tex]

Answer:

x = 10

Step-by-step explanation:

UT is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is

[tex]\frac{US}{RU}[/tex] = [tex]\frac{ST}{RT}[/tex] ( substitute values )

[tex]\frac{x+2}{3x}[/tex] = [tex]\frac{16}{40}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )

2 × 3x = 5(x + 2)

6x = 5x + 10 ( subtract 5x from both sides )

x = 10

Answer:

Step-by-step explanation:

if a carton of eggs is 4.30 then 1 egg is then 1 egg is 75 cents

Answer:

m = (d+2)/5

Step-by-step explanation:

d=5m-2

d+2 = 5m

m = (d+2)/5

Eighty percent of the points ought to lie within the regression line if the coefficient is 0.80. A regression line would be considered to reflect all of the data if its value was 1, and none if it were 0.

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by solving this equation, the value of y = (x²+1)/(1-x²)

Equation can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make y the subject of the equation x = √((y-1)/(y+1)),

x = √[(y-1)/(y+1)]

we can square both sides:

x² = (y-1)/(y+1)

Next, we can multiply both sides by (y+1) to get rid of the fraction:

x² × (y+1) = y-1

x²y + x² = y - 1

Rearranging the terms:

x² + 1 = y - x²y

x² + 1 = y(1 - x²)

Divide both side by (1-x²) we get

y = (x²+1)/(1-x²)

So, y is the subject of the equation is y = (x²+1)/(1-x²)

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Answer:

The last graph shows a line.

Step-by-step explanation:

In order, from top to bottom, you have an Angle, a Point, a Ray, and a Line.

The Ray (the one you have marked as the answer) is NOT correct because is has an endpoint and continues in only one direction.

The last image IS correct, it is a Line as it goes on forever in both directions. Honestly, they should have put arrows at each end.

Hope this helps!

The minimum rate of gasoline consumption is typically 0.5 gallons per day, which occurs after five days of vehicle inactivity. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system.

The minimum rate of gasoline consumption is the amount used when a vehicle is not in use. This is typically 0.5 gallons per day and occurs after five days of a vehicle being inactive. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system. When the vehicle is not used, the fuel system is not under pressure and the fuel in the lines and evaporative system is able to dissipate. This occurs gradually over a period of five days and once this has happened, the minimum rate of gasoline consumption is reached. The fuel system needs to dissipate the fuel in order to prevent it from becoming stale or evaporating, and this is the reason why the minimum rate of gasoline consumption is reached after five days of inactivity.

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B. Vector b is not a linear combination of a1, a2, and a3.

What is Linear combination?

A linear combination is any expression of the form ax + by, where a and b are constants, formed by multiplying each term by a constant and combining the results.

Given that, b is a linear combination of a1, a2, and a3.

Then, Correct answer would be Vector b is not a linear combination of a1, a2, and a3.

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The General Multiplication Rule in probability states that the probability of the intersection (occurrence) of two events, A and B, is equal to the product of their individual probabilities. The formula can be written as follows:

p(A and B) = p(A) * p(B | A)

where p(A) represents the probability of event A occurring, and p(B | A) represents the probability of event B occurring given that event A has already occurred.

The formula reflects the idea that the probability of both events occurring is equal to the probability of one event occurring, multiplied by the probability of the other event occurring given that the first event has already happened.

For example, let's say we have two events: "rolling a 6 on a dice" (A) and "choosing a spade from a deck of cards" (B). The probability of rolling a 6 on a dice is 1/6, and the probability of choosing a spade given that a 6 was rolled is 13/52. Using the general multiplication rule, the probability of both events occurring would be (1/6) * (13/52) = 13/312.

In summary, the general multiplication rule is a fundamental concept in probability that helps us calculate the probability of the intersection of two events.

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Step-by-step explanation:

They are corresponding angle

The cost of printing the paper at the values are:-

15C < 200

180< 200 at c = 12

120< 200 at C = 8

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that Greta needs to get 15 packs of business cards. • Greta's budget for business cards is $200. • The number of cards she can have printed, c, can be represented by the inequality 15c < 200.

The cost of printing the cards at different numbers of the cards will be calculated as:-

15C < 200

At C = 12

15x 12 < 200

180 < 200  True

At C = 16,

15 x 16 < 200

240 > 200   False

At C = 18,

15 x 18 < 200

270 > 200   False

At C = 8

15 x 8 < 200

120 < 200  True

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Answer:

110° and 215°

Step-by-step explanation:

the bearing of D from C is the angle from the north line at C measured in a clockwise direction from C to D

(a)

bearing of D from C is the purple angle, that is 110°

(b)

bearing of D from C is the blue angle , that is 215°

The coordinates for point B are 7 = √(x - 5)² + (y - 4)².

What is the distance formula?

The distance formula is used to calculate the length of the line which joins the two points in an x−y plane. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line.

Here, we have

Given: Segment AB Has point A located At (5, 4). If The Distance from A To B Is 7 units.

To find the distance between any two the following formula is used.

D = √(x₂ - x₁)² + (y₂ - y₁)²

7 = √(x - 5)² + (y - 4)²

Hence, the coordinates for point B are 7 = √(x - 5)² + (y - 4)².

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Hope it helps u

Refer to the image below

The solution is, 2 is the greatest common factor.

and,  10x^2 + 28x − 6=0 has solutions, x = -3, 0.2  a simplified version of the equation.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Simplifying :

10x^2 + 28x − 6=0

Rearrange the terms so that -6+28x+10x^2 =0

Figuring out the value of the variable "x".

Subtract out the number "2", which is the GCF.

2(-3+14x+5x^2)=0

To factor a trinomial

2(5x^2+15x-x-3)=0

(5x-1)(x+3)= 0

i.e. x= -3

or, x= 1/5

      =0.2

Hence, The solution is, 2 is the greatest common factor.

and,  10x^2 + 28x − 6=0 has solutions, x = -3, 0.2  a simplified version of the equation.

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At the same price rate, Lucille has to pay P375.00 for 25 mangoes she bought.

From the case, we know that:

Q₁ = 15 mangoes

P₁ = P225.00

Q₂ = 25 mangoes

P₂?

To solve this problem, we need to find the price rate of each unit of mangoes. We can make a mathematical equation as:

P = Q x P(q)

where:

P(q) = price rate per unit

Then:

P₁ = Q₁ x P(q)

P225.00 = 15 x P(q)

P(q) = P225.00 : 15

P(q) = P15.00 per mangoe

We can use the value of price rate per unit to answer our question:

P₂ = Q₂ x P(q)

P₂ = 25 x P15.00

P₂ = P375.00

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By using the equation of the trend line, it can be estimated that the​ hiker's elevation after 140 minutes will be, 1919.8 feet

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The equation of a trend line for the​ hiker's elevation is,

y = 9.27x + 622​

x represents the number of minutes

y represents the​ hiker's elevation in feet

Elevation after 140 minutes = ?

Now, putting value of x as 140 in the given equation,

y = (9.27 x 140) + 622​

  =  1297.8 + 622

  =   1919.8

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If McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.

APR stands for Annual Percentage Rate, which is the interest rate associated with a loan, credit card, or other type of borrowing. It is expressed as a percentage and is typically higher than the interest rate because it includes additional costs associated with the loan such as origination fees, processing fees, and other costs.

Part A:

To calculate how long it will take McKenzie to pay off her credit card, we need to use the formula:

T = (B x i) / P

Where T is the total number of payments, B is the initial balance, i is the interest rate (in decimal form) and P is the amount of the payments.

In this case, B = 936, i = 0.01396 (13.96% expressed as a decimal) and P = 250. So, substituting these values into the formula, we get:

T = (936 x 0.01396) / 250

T = 3.784

Since payments are made monthly, we can round this to 4 payments. Therefore, it will take McKenzie 4 months to pay off her credit card if she makes payments of $250 per month.

Part B:

To calculate the amount of interest McKenzie will have paid when she pays off her credit card, we can use the formula:

I = B x i x T

Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.

In this case, B = 936, i = 0.01396 and T = 4 (since we calculated this in Part A). So, substituting these values into the formula, we get:

I = 936 x 0.01396 x 4

I = 56.608

Therefore, McKenzie will have paid a total of $56.608 in interest when she pays off her credit card.

Part C:

To calculate how much more interest McKenzie will pay if she only pays $150 per month, we first need to calculate how long it will take her to pay off the credit card using this lower payment amount.

Using the same formula from Part A, we get:

T = (936 x 0.01396) / 150

T = 6.576

Since payments are made monthly, we can round this to 7 payments. Therefore, it will take McKenzie 7 months to pay off her credit card if she makes payments of $150 per month.

Now, to calculate the amount of interest McKenzie will have paid if she pays $150 per month, we can use the same formula from Part B:

I = B x i x T

Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.

In this case, B = 936, i = 0.01396 and T = 7. So, substituting these values into the formula, we get:

I = 936 x 0.01396 x 7

I = 92.832

Therefore, if McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.

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For each triangles, the answers are:

Let's discuss each triangle we have:

1. We know that:

∠KJL = ∠KFG = ∠GHL --> face the same direction

∠KFG = ∠FGH

∠GKF = ∠GHF = ∠HGL = ∠HFJ

∠KLJ = ∠GFH = ∠KGF = ∠FHJ

Hence:

KL = 2KG = 2FH

48 = 2FH

FH = 24

JL = 3FG

JL = 2 (37)

JL = 74

KJ = 2GH

KJ = 2(30)

KJ = 60

FJ = 1/2 KJ

FJ = 1/2 (60)

FJ = 30

2. ∠AEN = ∠PTC = ∠NPT = ∠ACT

∠EAN = ∠PTN = ∠CPT = ∠ECP

∠ENA = ∠CTA = ∠PCT

Hence:

AE = 2PT

AE = 2(13) = 26

AN = 2CP

AN = 2(29) = 58

CT = 1/2 EN

CT = 1/2 (43) = 21.5

Perimeter of AEN = AE + EN + AN

Perimeter of AEN = 26 + 43 + 58

Perimeter of AEN = 127

3. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:

10x + 44 = 2(8x - 23)

10x + 44 = 16x - 46

6x = 90

x = 15

4. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:

19x - 28 = 2(6x + 7)

19x - 28 = 12x + 14

7x = 42

x = 6

5. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:

4x + 34 = 2(5x - 16)

4x + 34 = 10x - 32

6x = 66

x = 11

JL = 4x + 34

JL = 4(11) + 34

JL = 78

6. Both lines are parallel with each other and both triangle have ratio 1 : 2, then:

(9x - 59) = 2(3x - 4)

9x - 59 = 6x - 8

3x = 51

x = 17

GH = 9x - 59

GH = 9(17) - 59

GH = 94

7. (6x + 1)° = (9x - 23)°

3x = 24

x = 8

8. (5x - 24)° + (8x + 9)° = 180°

13x - 15 = 180

13x = 165

x = 12.7°

9. (16x - 3)° + (3x - 7)° = 180°

19x - 10 = 180°

19x = 190

x = 10°

∠WYZ = ∠WVX

∠WYZ = 3x - 7

∠WYZ = 3(10) - 7 = 23°

10. (11x - 2)° = (6x + 13)°

5x = 15

x = 3°

∠ACB + ∠CAB + ∠ABC = 180°

∠ACB + 62 + (6x + 13) = 180°

∠ACB + 62 + (6(3) + 13) = 180°

∠ACB + 62 + 31 = 180°

∠ACB = 117°

11. ∠MNP = ∠MQS = ∠SRP = ∠QSR

∠MNP = ∠RSP = ∠NQR = ∠QRS

∠NPM = ∠QSM = ∠NRQ = ∠RQS

Then:

MN = 2RS

5x - 34 = 2(x + 4)

5x - 34 = 2x + 8

3x = 42

x = 14 --> RS = x + 4 = 18

MN = 2RS = 2(18) = 36

MP = 2QR = 2(25) = 50

NP = 2SQ = 2(22) = 44

Perimeter of MNP = MN + NP + MP

Perimeter of MNP = 36 + 50 + 44

Perimeter of MNP = 130

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The total surface area, in square units, of the rectangular solid is 334.

Given data :

The volume of the rectangular solid = 385  =  5 x 7 x 11

So, two sides will be                 5 x 7    =  35    x 2  =  70

another two sides will be         5 x 11  =  55    x 2  =  110

and the last two sides will be  7 x 11  =  77    x 2  = 154

the total surface area, in square units, of the rectangular solid =

70 + 110 + 154 = 334

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The number of possible combinations for a password is an important aspect of computer security.

A password is a crucial aspect of computer security. It is used to protect personal information and keep unauthorized users from accessing important data.

a) For Computer Alpha's password, there are 26 letters (not case-sensitive), 10 numbers (0-9), and 13 special characters.

The formula for combination is nCr, where n is the total number of items, and r is the number of items to choose from.

In this case, n is 10 and r is 49, so the number of possible combinations is

=> 49C10 = 3,738,383,600.

b) If there must be at least one special character and at least two numbers, the number of possible combinations decreases.

The total number of possible combinations is

=> 10C2 x 13C1 x 36C7.

c) The password "AA!!!56555" has 8 characters. The number of different passwords that can be made by rearranging these characters is 8!.

d) For Computer Omega's password, there are 26 letters and four "words" of four letters each.

The number of possible combinations is

=> 26⁴ x 26⁴ x 26⁴ x 26⁴ = 208,827,064,576,000.

e) Based on the number of possible combinations, Computer Omega is easier to hack compared to Computer Alpha. This is because there are fewer possible combinations for Computer Omega's password.

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Miles and meters both are units of length. To change a mile's value to meters, you simply multiply it by 1609.344.

What is 1 mile?

A mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is also referred to as the international mile or the statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 meters, establishing a standard between the British Commonwealth and the United States.

To convert 1 mile to meters, multiply  1609.344 by the mile.

The model equation is y = 1609.344x

Where x is in the mile and y is in meters.

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(a). The number of apples you and your friend picked is 3n+1.

(b). The number of baskets would you need if you collected 10 apples with your friend is [tex]\frac{10}n}[/tex].

As per given data a basket holds n apples.

The number of apples your friend picked =n+4

The number of apples you picked =2n-3

The number of apples you and your friend picked can be obtained by just adding the apples picked by both

=(2n-3)+(n+4)

=2n+n+4-3   ( By using commutative property)

=3n+1    ( Combining like terms)

Therefore, the number of apples you and your friend picked is 3n+1.

(b).

For carry n apples basket required is = 1

To find the number of baskets needed to collect 10 apples, we can use the expression:

number of baskets = 10 / (number of apples in one basket) = [tex]\frac{10}n}[/tex]

Therefore, the number of baskets would you need if you collected 10 apples with your friend is [tex]\frac{10}n}[/tex].

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No, the independence condition is not met. The conditions for a binomial setting have not been met in this scenario because the names were pulled and not replaced in the hat, which violates the independence condition.

In a binomial setting, the trials must be independent, meaning that the outcome of one trial does not affect the outcome of any other trial.

Since the names were not replaced in the hat, the outcome of each draw is not independent, and the conditions for a binomial setting have not been met.

Permutation refers to the arrangement of objects in a specific order. For example, if we have three objects A, B, and C, there are six possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA. The number of permutations of n objects is given by n!

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The given equation, x = ae−t be5t, is a solution to x′′−4x′−5x=0.

x′′ - 4x′ - 5x = (ae−t be5t)′′ - 4(ae−t be5t)′ - 5(ae−t be5t) = -e−2t be5t - 4(-e−t be5t) - 5(ae−t be5t) = 0

1. x = ae−t be5t

2. x′ = -e−t be5t

3. x′′ = -e−2t be5t

x′′−4x′−5x=ae−t be5t(−e−t be5t−4e−t be5t−5ae−t be5t)

Simplify:

x′′−4x′−5x=ae−t be5t(−e−t (5b+4)−5a)

Set to 0:

ae−t be5t(−e−t (5b+4)−5a) = 0

Divide by ae−t be5t:

−e−t (5b+4)−5a = 0

Solve for b:

b = −4/5a

4. substitute x, x′ and x′′ into the differential equation

5. (ae−t be5t)′′ - 4(ae−t be5t)′ - 5(ae−t be5t) = -e−2t be5t - 4(-e−t be5t) - 5(ae−t be5t) = 0

The given equation, x = ae−t be5t, is a solution to x′′−4x′−5x=0.

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It does not always take the same time to serve every customer. Option A is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
From the table,
For every order, the pair compare the unit rate of serving the customer.
1
unit rate = 2 / 8
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.

2.
unit rate = 4 / 16
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.

3
unit rate = 7 / 21
unit rate = 1 / 3
unit rate = it took 3 minutes to serve a customer.

Thus, It does not always take the same time to serve every customer. Option A is correct.

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He owed $14,983.85 at the end of 4 years.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Given:

P = $8000

R= 16%

T= 4 years

Now, The equation that models this situation is:

A(t) = P [tex](1 + r/n)^{nt[/tex]

where:

A is the amount he owes at any time (t)

P, is the initial amount borrowed (the amount owed at time t = 0)

n is the number of times the loan is compounded annually

r is the interest rate in decimal form

So,  A(4) = 8000[tex](1 + 0.16/4)^{4.4[/tex]

A(4) = 8000[tex](1 + 0.04)^{16[/tex]

A =  $14,983.85

Hence, the amount is  $14,983.85.

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'a' = 'a' and 'b' < 'd' are correct an rest are incorrect.

'a' = 'a' is correct. In programming and computer science, single quotes are used to denote a string literal, and equality between strings is determined by their lexicographical order. In this case, 'a' and 'a' are the same string, so they are equal.

0 = '0' is incorrect. In programming, 0 is a numerical value, while '0' is a string literal. They cannot be directly compared as equal, unless you cast the string to a numerical type, like this:

python

0 == int('0')

'b' < 'd' is correct. In the lexicographical order of strings, 'b' comes before 'd', so 'b' is considered to be less than 'd'.

'x' > 'y' is incorrect. In the lexicographical order of strings, 'x' comes after 'y', so 'x' is considered to be greater than 'y'.

Therefore, 'a' = 'a' and 'b' < 'd' are correct an rest are incorrect.

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