Tessa has a coin jar full of dimes and pennies. When she took the coin jar to the bank, she was told that it contained exactly $27.34. Give three different combinations of the number of dimes and pennies that could have been in the coin jar.

Answer:

y=1.34x-3.22

Step-by-step explanation:

y=mx+b

find m/ gradient:

[tex]m = \frac{-3.94 - 2.4}{-4.75 - 0}[/tex]

∴[tex]m=1.34[/tex]

find b/ y-intercept:

sub (2.4,0)

0= 1.34 (2.4) +b

b=0-3.216

b= -3.216

∴ b=-3.22(2.d.p)

linear equation:

∴1.34x-3.22

Answer:

736 - 155 = 581.

581 divided by 12 is 48.416.

that means the minimum number of sets of knives Kaj should buy is 49.

Step-by-step explanation:

True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight true value pays the invoice on may 22.  then true value pay amount is $4900

Invoice dated 08/may/2020. Amounting to $5,800 which includes $800 freight.

Terms:

3/10 ; 2/30 ; n/60

The term 3/10 means that True value can avail of 3% discount if it pays within 10 days from date of issuance. The 10th day would be 18/may/2020

The term 2/30 means that True value can avail of 2% discount if it pays from the 11th day up to the 30th day from the date of issuance.

may 22 is beyond the 10th day but within the 30 days discount period. True Value can avail of the 2% discount.

5,800 - 800 = 5,000  The freight can't be subjected to discount thus it is deducted from the total invoice amount.

5,000 * 2% = 100

5,000 - 100 = 4900 amount True Value has to pay.

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Answer:

0.41

Step-by-step explanation:

Answer:

seven and a half hours

Step-by-step explanation:

aa

For the quadratic equation:

x^2 + 7x = 8x + 12

The two solutions are:

x = 4

x = -3

I'm only solving the first question, as it is how the guidelines say.

Here we have the quadratic equation:

x^2 + 7x = 8x + 12

First, we can rewrite this equation as:

x^2 + 7x - 8x - 12 = 0

x^2 - x - 12 = 0.

Using Quadratic formula we can see that the solutions (or zeros of the quadratic) are:

x = (1 ± √(  (-1)^2 - 4*1*-12))/(2*1)

x = (1 ± 7)/2

Then the two solutions are:

x = (1 + 7)/2 = 4

x = (1 - 7)/2 = -3

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Mang Efren's present age is 30 years.

Let's assume the present age of Mang Efren's son is x years.

Mang Efren is presently 5 times as old as his son.

So, Mang Efren's present age = 5x years

Four years ago,

Mang Efren's son's age = x - 4 years.

Mang Efren's age = 5x - 4 years

According to the question, four years ago, the product of their ages was 52.

From this information, we will create an equation.

(x - 4)(5x - 4) = 52

5x² - 4x - 20x + 16 = 52

5x² - 24x + 16 - 52 = 0

5x² - 24x - 36 = 0

Solving the quadratic equation to obtain the value of x,

5x² - 30x + 6x - 36 = 0

5x(x -6) + 6(x - 6) = 0

(5x - 6)(x - 6) = 0

x = 6

So, Mang Efren's present age is 5 × 6 = 30 years.

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The distance of art store from Ella's house is  2/3 miles or 0.67 miles.

It is a question of time, speed and distance.

It is given in the question that Ella walks to the art store at 2mph, but returns home at 4 mph.

Also, the total time taken by Ella to cover the journey is 1/2 an hour.

We have to find the distance of art store from Ella's house.

Let the distance from Ella's house to art store be d miles.

We know that,

Speed = distance/time

Time = distance/speed

Hence, we can write,

time = d/2  (walking to the art store from from)

Also,

time = d/4  (walking to home from the art store)

Hence,

d/2 + d/4 = 1/2

3d/4 = 1/2

d = 2/3 miles or 0.67 miles.

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Answer: 9/4 and -2/1 (or -2)

Step-by-step explanation: Reciprocals are just the fraction flipped

The number of metal sheets in the stack is 274 metal sheets

Fractions are written as a ratio of two integers. For instance a/b is a fraction.

Given the following parameters

Height of metal sheet = 4.00in

Height of each sheet= 0.0146 in

Number of metal sheet = height of metal sheet/height of each sheet

Substitute

Number of metal sheet  = 4.00/0.0146
Number of metal sheet  = 274 metal sheets

This gives the required number of sheets

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correct value of x will 9 if Maggie corrected her mistake.

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0. The variables x and A in this situation are variables, whereas B is a constant.

Applying the parallel line theorem

alternate angles are always equal -

therefore ,

 4x + 2 = 7x - 25

27 = 3x

x = 9

so , the correct value of x will be 9 if maggie corrected her mistake

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Clay and Jason are 600 feet far apart.

When an object goes above the surface, the altitude is measured as +ve and when an object goes below the surface, the altitude is measured as -ve.

Since Clay is flying a helicopter at an altitude of 400 feet in the air,

The Value of altitude of Clay = +400

Since, Jason is diving 200 feet below the surface,

The Value of altitude of Jason = -200

The the distance between Clay and Jason = (The Value of altitude of Clay) - (The Value of altitude of Jason)

= +400 - (-200)

= 400 + 200

= 600 feet

Therefore, the distance between Clay and Jason is 600 feet.

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In the picture there is a prism with measures. The surface area of prism is 156.

Given that,

In the picture there is a prism with measures.

We have to find the surface area of prism.

The surface area of prism=(2×base area)+(Base perimeter×height)

The base is trapezoid

So, the area of trapezoid is (a+b)/2×h

=(6+12)/2×4

=18/2×4

=9×4

=36

Here base area we got is 36.

Now, we find the perimeter of trapezoid is a+b+c+d

=6+12+5+5

=18+10

=28

Here, base perimeter we got is 28.

Now surface area of prism is

=(2×36)+(28×3)

=72+84

=156

Therefore, the surface area of prism is 156.

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Answer:

-3(-1) + 4 = 3 + 4 = 7

-3(0) + 4 = 0 + 4 = 4

-3(1) + 4 = -3 + 4 = 1

-3(2) + 4 = -6 + 4 = -2

Based on the fact that the two numbers multiply to 2,400 and add up to -16, the numbers are undefined.

Assume that one of the numbers is x and the other number is y, the system of equations to represent this is given that the two numbers add up to -16 and multiplying to 2,400:
x + y = -16

xy = 2,400

Expressing y in terms of x :

xy = 2,400

y = 2,400 / x

Solving for x gives:

x + y = -16

x + (2,400 / x) = -16

x = 0

y = 0

The problem given in the question is wrong because the results of x and y are undefined.

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answer = a

formula; a(1 + r)^x

a = the initial amount - 7.71  [answer cannot be b or d]

! i think it's a as the decay factor is < 1, therefore, 100-.933333

Answer:

b

Step-by-step explanation:

Answer:

alternate angles and corresponding angles.

and vertical opposite angles

Step-by-step explanation:

#G o o g l e

The matchings are:

3x - y = -5 ⇒ table C.

x - 3y = 12 ⇒ table A.

3x - y = -2 ⇒ table D.

2x - 3y = 9 ⇒ table B.

The first equation we have is:

3x - y = -5

Evaluating in x = 0, we have:

3*0 - y = - 5

y = 5

So we have the point (0, 5).

Evaluating in x = -2 we get:

3*-2 - y = -5

6 + y = 5

y = 5 - 6 = -1

So we have the point (-2, -1)

The only table with that point is table C, so we conclude that it is the correct option.

2) The second equation is:

x - 3y = 12

Evaluating in x = 0 we get:

0 - 3y = 12

y = 12/-3 = -4

So we have the point (0, -4)

if x = 3 we have:

3 - 3*y = 12

-3*y = 12 - 3 = 9

y = 9/-3 = -3

So we have the point (3, -3)

The only table with these two points is table A, so that is the correct one.

3) The next equation is:

3x - y = -2

The tables left are B and D.

Now, let's evalaute this equation in x = 3.

3*3 - y = -2

9 - y = -2

9 + 2 = y

11 = y

So we have the point (3, 11)

Notice that on table B,the value associated to x = 3 is y = -1, so we discard table B, and we conclude that this equation relates to table D.

Trivially, the last equation:

2x - 3y = 9

Matches table B.

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The simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .

In the question ,

the expression is given as (3⁴)⁻¹ ,

the rule of law of exponents states that a⁻ⁿ = 1/aⁿ .

Using the above mentioned law of indices , the expression  (3⁴)⁻¹ can be written as ,

(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴

which can be expressed in words as one over three raised to the fourth power .

Therefore , the simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .

The given question is incomplete , the complete question is

The Simplified value of (3⁴)⁻¹ is

(a) one over three raised to the fourth power

(b) one over three raised to the power of negative four

(c) −3 to the power of 4

(d) 3 to the power of 3

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Answer:

1) Conditional

If a month begins with letter M, then it has 31 days.

2) Converse

If a month has 31 days, then it begins with letter M.

3) Inverse

If a month does not begin with the letter M, then it does not have 31 days.

4) Contrapositive

  If a month does not have 31 days, then it does not begin with the letter M.

Step-by-step explanation:

1) Conditional

If a month begins with letter M, then it has 31 days.

2) Converse

If a month has 31 days, then it begins with letter M.

3) Inverse

If a month does not begin with the letter M, then it does not have 31 days.

4) Contrapositive

  If a month does not have 31 days, then it does not begin with the letter M.

Conditional statement states the original statement. If 'p' , then 'q'

Converse statement switch positions in the original if --then statement. If 'q', then 'p'

Inverse statement states the opposite of the original statement. If not 'p', then not 'q'.

Contrapositive if not 'q' , then not 'q'.

Answer:

8800000 or 88x 10^5

Step-by-step explanation:

4x2200000=8800000

Using Venn diagram, if a student is chosen randomly, (a) the probability that he or she is not in any of the language classes is 0.5, (b) the probability that he or she is taking exactly one language class is 0.32, and (c) if 2 students are chosen randomly, the probability that at least 1 is taking a language class is 0.753.

Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)

Let A = students in the Spanish class = 28

B = students in the French class = 26

C = students in the German class = 16

Hence, the probability of each class is:

P(A) = 28/100 = 0.28

P(B) = 26/100 = 0.26

P(C) = 16/100 = 0.16

P(A ∩ B) = 12/100 = 0.12

P(B ∩ C) = 6/100 = 0.06

P(A ∩ C) = 4/100 = 0.04

P(A ∩ B ∩ C) = 2/100 = 0.02

(a) P(not A, B, C) = 1 - P(A ∪ B ∪ C)

P(not A, B, C) = 1 - [P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]

P(not A, B, C) = 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.06 - 0.04 + 0.02)

P(not A, B, C) = 1 - 0.5

P(not A, B, C) = 0.5

(b) P(A, B, C only) = P(A only) + P(B only) + P(c only)

P(A, B, C only) = [P(A) - P(A ∩ B) - P(A ∩ C) + P(A ∩ B ∩ C)] + [P(B) - P(A ∩ B) - P(B ∩ C) + P(A ∩ B ∩ C)] + [P(C) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]

P(A, B, C only) = (0.28 - 0.12 - 0.04 + 0.02) + (0.26 - 0.12 - 0.06 + 0.02) + (0.16 - 0.06 - 0.04 + 0.02)

P(A, B, C only) = 0.14 + 0.10 + 0.08

P(A, B, C only) = 0.32

(c) P = 1 - (50/100 x 49/99)

P = 1 - (49/198)

P = 149/198

P = 0.753

To complete the problem, here are the questions:

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?

(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?

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If the balance were growing according to the exponential function, the balance owed on your credit card after 9 months is equal to $1,502.02.

In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of an argument.

From the information provided, an exponential function that models or represents the rate at which the balance owed on your credit card triples is given by:

f(x) = 500(1 + 0.13)^x

Where:

After 9 months, the balance owed on your credit card would be calculated by substituting the value of x with 9 as follows:

Balance owed,  f(x) = 500(1 + 0.13)^9

Balance owed, f(x) = 500(1.13)^9

Balance owed, f(x) = 500 × 3.0040419380

Balance owed, f(x) = $1,502.02.

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Complete Question:

Growing linearly, the balance owed on your credit card triples from $500 to $1500 in 9 months. If the balance were growing according to the exponential function f(x) = 500(1 + 0.13)^x, where x represents the number of months, what would the balance be after 9 months? Round your answer to the nearest cent.

Answer:

$1502.02

Step-by-step explanation:

f(x)=500(1+0.13)^x

f(9) = 500(1.13)^9

f(9) = 500(3.004041938)

f(9) = 1502.02

Answer: $1502.02

Answer:

As a fraction: 3/50

It cannot be turned into a mixed number

The situation in which the binomial distribution can be approximated to the normal distribution is given by:

(b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.

The formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The binomial distribution can be approximated to the normal distribution if there are at least 10 failures and 10 successes on the experiment, that is:

np ≥ 10, n(1 - p) ≥ 10.

Meaning that a large number of trials is usually required for the approximation.

In the context of this problem, to achieve the large number of trials needed for the approximation, multiple days are needed to take the observations, hence option b is correct.

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The compound interest of $182.60 will not be enough to pay for the award.

So, annual interest will be sufficient to serve the award:

(Refer to the compound chart given below)

Therefore, the compound interest of $182.60 will not be enough to pay for the award.

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Answer: -21x^3 + 28x^2 y