Molly had $10 in her bank account. She used her debit card to purchase eight Monster drinks for $2 each. How much money must she put into her account to bring her balance to $0?​

Answer:

20 months

Step-by-step explanation:

Initial difference = 500$

Monthly difference = 25$

500 / 25 = 20

The original amount borrowed was approximately $34,211.1.

To compute the first sum acquired, we can involve the recipe for the current worth of a customary annuity, which addresses a progression of equivalent installments made toward the finish of every period. The recipe is:

PV = \(PMT * (1 - (1 + r)^{(-n)}) / r\)

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the total number of periods.

In this case, we have monthly payments, so we need to convert the APR to a monthly interest rate by dividing it by 12. We also have a 4-year loan, which means 48 monthly payments.

APR = 9.25%

Monthly interest rate = APR / 12 = 0.0925 / 12 = 0.00771 (rounded to five decimal places)

Total number of payments = 48

Total amount of payments = $4,200.0

Substituting these values into the formula, we get:

PV =\(PMT * (1 - (1 + r)^{(-n)}) / r\)

PV = \($4,200.0 * (1 - (1 + 0.00771)^{(-48)}) / 0.00771\)

PV = $4,200.0 x (1 - 0.5180) / 0.00771

PV = $34,211.1 (rounded to the nearest tenth)

Therefore, the original amount borrowed was approximately $34,211.1.

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The integer solutions of each of the system of inequalities are 0, 1, 2, 3, .....65, 66, 67, 68. There are total 69 integer values that y can take.

In the question, we are given the inequalities:-

y ≥ 0 and 72 - y  ≥ 4

We have to find the integer solutions of each of the system of inequalities.

From 72 - y  ≥ 4, we can write,

72-4 ≥ y

68 ≥ y

Hence, from 68 ≥ y and y ≥ 0, we can write,

68 ≥ y ≥ 0

Hence, y can take 69 integer values from 0 to 68, both included.

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Suppose sin t = 5/7 and cos t < 0. The exact value :
cos t = -√(1 - (5/7²)
tan t =  -(5√6)/12
csc t =7/5
sec t =  -(7√6)/12
cot t =  -12/(5√6)

Since sin t = 5/7 and cos t < 0, we can use the Pythagorean identity cos² t + sin² t = 1 to find cos t:

cos² t + (5/7)²= 1

cos² t = 1 - (5/7)²

cos t = -√(1 - (5/7)²) (since cos t < 0)

Next, we can use the definitions of the trigonometric functions to find the remaining values:

tan t = sin t / cos t = (5/7) / (-√(1 - (5/7)^2)) = -5/√24 = -(5√6)/12

csc t = 1/sin t = 7/5

sec t = 1/cos t = -1/√(1 - (5/7)²) = -7/√24 = -(7√6)/12

cot t = 1/tan t = -12/(5√6)

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After considering all his earnings and savings, we found that Chris started with $120 in his savings.

Let's assume that Chris saved x dollars. According to the equation, he spent half of his savings, so he spent 0.5 * x dollars on video games. After earning an additional $20 cutting grass, his total savings became 0.5 * x + 20 = 60. To solve for x, we can subtract 20 from both sides of the equation, which gives us 0.5 * x = 40.

Then, we can divide both sides of the equation by 0.5 to obtain x = 80. This means that Chris started with $80 in savings, which he then doubled by spending half of his savings and adding $20 earned from cutting grass, resulting in $120 in total savings.

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Answer:

The standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

Step-by-step explanation:

To find the standard deviation for the number of people with the genetic mutation in groups of 900, we can use the properties of the binomial distribution. The binomial distribution describes the number of successes (in this case, people with the genetic mutation) in a fixed number of independent Bernoulli trials (in this case, selecting people), each with the same probability of success.

In our case, we have:

n = 900 (number of trials, i.e., the number of people in each group)

p = 0.05 (probability of success, i.e., the probability of having the genetic mutation)

The mean (μ) and variance (σ²) of a binomial distribution can be calculated using the formulas:

μ = n * p

σ² = n * p * (1 - p)

We are interested in finding the standard deviation (σ), which is the square root of the variance:

σ = sqrt(σ²)

So, in our case:

σ = sqrt(900 * 0.05 * (1 - 0.05))

σ = sqrt(900 * 0.05 * 0.95)

σ ≈ sqrt(42.75)

σ ≈ 6.54

Thus, the standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

To find the standard deviation for the number of people with the genetic mutation in groups of 900, you can use the formula for the standard deviation of a binomial distribution:

σ = √(n * p * (1-p))

Here, n = 900 (number of people randomly selected), p = 0.05 (5% of the population has the genetic mutation).

σ = √(900 * 0.05 * (1 - 0.05))
σ = √(45 * 0.95)
σ ≈ 6.48

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

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The coordinates of point D 0.25 x-axis for the points A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10) are (-2, -2.5) when point D is reflected across the x-axis. This is obtained by negating the y-coordinate of point D and keeping the x-coordinate the same.

To find the coordinates of point D 0.25 x-axis, we need to reflect point D across the x-axis. This will result in the y-coordinate of point D being negated while the x-coordinate remains the same.

The coordinates of point D are (-2, 10), so when we reflect it across the x-axis, we get the new coordinates:

D 0.25 x-axis = (-2, -10/4) = (-2, -2.5)

Therefore, the coordinates of point D0.25∘rx-axis for the given points A, B, C, and D are (-2, -2.5).

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Answer:

38.89%

Step-by-step explanation:

the whole p8e chart is 360° as a perfect circle would be,

so : 360° - ( 66° + 144° ) = 360° - 210° = 140°

140° of the pie chart was cast in favor of candidat C.

(140° ÷ 360°) × 100 = 38.89%

The price at which the total quantity supplied is 250 is $11.58.

In order to find the price at which the total quantity supplied is 250, we need to equate the total quantity supplied by both producers (Supply 1 and Supply 2) and solve for the price.

Supply 1: P = 6 + 0.7Q

Supply 2: P = 16 + 0.6Q

To find the equilibrium price, we set the total quantity supplied equal to 250:

0.7Q + 0.6Q = 250

1.3Q = 250

Q = 250 / 1.3 ≈ 192.31

Now that we have the quantity, we can substitute it back into either supply function to find the price. Let's use Supply 1:

P = 6 + 0.7Q

P = 6 + 0.7 * 192.31

P ≈ 6 + 134.62

P ≈ 140.62

Therefore, the price at which the total quantity supplied is 250 is approximately $11.58.

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Answer:

Step-by-step explanation:

\(8c-4-2c+5\\\\\mathrm{Group\:like\:terms}\\=8c-2c-4+5\\\\\mathrm{Add\:similar\:elements:}\:8c-2c=6c\\=6c-4+5\\\\\mathrm{Add/Subtract\:the\:numbers:}\:-4+5=1\\=6c+1\)

Answer:

Step-by-step explanation:

Divide the tens column dividend by the divisor.

Multiply the divisor by the quotient in the tens place column.

Subtract the product from the divisor.

Bring down the dividend in the ones column and repeat.

okay so look at the image down below

Answer:

17.6

Step-by-step explanation:

The difference in price per passenger for a group of 16 versus a group of 10 is $26.25

An equation is an expression that shows the relationship between two or more number and variables.

From the graph:

The cost for a group of 16 friends is $2500, while for a group of 10 friends is $1300.

Cost per passenger for 16 friend = $2500 / 16 = $156.25

Cost per passenger for 10 friend = $1300 / 10 = $130

The difference in price = $156.25 - $130 = $26.25

The difference in price per passenger for a group of 16 versus a group of 10 is $26.25

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Answer:

D) 26.25

Step-by-step explanation:

Got it right on edge

Answer:

Step-by-step explanation:18

The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Answer:

its d

Step-by-step explanation:

he did one task in 2.25 mins so multiply by 10

Answer:

c<-3

Step-by-step explanation:

move the constant to the right-hand side and change its sing

Then canculate the difference

Then divide both sides for the inequality of 3

the greatest common factor of the given expressions is -5xy.

To find the greatest common factor of the given expressions, we need to factor them first.

\(-15x^2y - 10xy^3 + 5xy^4 = -5xy(3x^2 + 2y^2 - y^3)\\5xy = 5xy(1)\\5x^2y^4 = 5xy^4(x^2)\\5xy^2 = 5xy^2(1)\)

xy = xy(1)

Now, we can find the common factors by taking the minimum exponent of each variable in the factors:

The common factors are:5xy

Therefore, the greatest common factor of the given expressions is -5xy.

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In a data set, the number of items that are in a particular category is called the frequency

Frequency can be defined as the number of items that are in a particular category in a data set.

It is also described as the number of times the value \appears in the data set.

The distribution of a variable is defined by the pattern of frequencies, this means that, the set of all possible values and the frequencies associated with these values

Frequency distributions are also portrayed as frequency in tables or charts,

It is also important to note that relative frequency is the proportion of items  in a particular category in a data set.

Hence, it is the frequency

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A recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s : T(n) = 2T(n-1) + T(n-2) and the initial conditions are : T(1) = 3 and T(2) = 9 .

Let T(n) be the number of ternary strings of length n that do not contain two consecutive 0s.

Consider a ternary string of length n. The last digit can be either 0, 1, or 2. If the last digit is 1 or 2, then we can append either 0, 1, or 2 to any string of length n-1 that does not end in 0 to get a string of length n that does not contain two consecutive 0s. Therefore, the number of such strings of length n is 2T(n-1).

If the last digit is 0, then the second-to-last digit must be 1 or 2, and the rest of the string of length n-2 can be any string of length n-2 that does not end in 0. Therefore, the number of such strings of length n is T(n-2).

Putting these cases together, we get the recurrence relation:

T(n) = 2T(n-1) + T(n-2)

with initial conditions:

T(1) = 3 (0, 1, or 2)

T(2) = 9 (00 is not allowed, but each of the other two digits can be followed by any of the three digits)

Therefore, the number of ternary strings of length n that do not contain two consecutive 0s can be calculated using the recurrence relation T(n) = 2T(n-1) + T(n-2), with initial conditions T(1) = 3 and T(2) = 9.

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Answer:

Given expression:

The first root is valid when:

The second root is valid when:

So the variable x can get values within interval:

In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Answer:

75 feet

Step-by-step explanation:

The perpendicular height from the base of the lighthouse to the top is 160 feet. The angle of depression is the angle that is adjacent to this side. The opposite of this angle is the horizontal distance from the boat to the base of the lighthouse, so we need to use the tangent. tan 25°=x/160, tan 25° is 0.466 so when we multiplty by 160 to find x, we get x=74.56, which rounded up is 75.

Answer:

if its asking you to simplify then the answer is 5p+7q

Step-by-step explanation:

combine like terms;

7p - 2p =5p

6q+q=7q

Answer:

Step-by-step explanation:

7p + 6q - 2p + q

add and subtract like terms

here 7p and - 2p are like terms as they have same base . similarly 6q and q are also like terms .

7p - 2p + 6q + q

5p + 7q

Answer:

Step-by-step explanation:

Remark

All you can really do is remove the brackets. Use FOIL

Solution

First: 3x*8x = 24^2

Outside: 2* 3x = 6x

Inside: -6*8x = - 48x

Last: -6*2 = - 12

Answer

24x^2 + 6x - 48x - 12

24x^2 - 42x - 12

The missing step in this proof is option b, ∠bca ≅ ∠bde.

This can be proven by using the Transitive Property of Congruence, which states that if two shapes are congruent to each other, and a third shape is congruent to one of those two shapes, then it is also congruent to the other.

In other words, if triangle ABC is congruent to triangle DEF, and triangle DEF is congruent to triangle GHI, then triangle ABC is also congruent to triangle GHI. Since we know that ∠bac ≅ ∠bde, and ∠bca ≅ ∠bac (by the Reflexive Property of Congruence), we can conclude that ∠bca ≅ ∠bde.

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If AB=BC and BC=BD the for extencion we know that AB=BD. and if AB=BD then B is the midpiont