Some values for two linear equations are shown in the tables. What is the solution to the system of equations?​

Answer:

b

Step-by-step explanation:

make sure the y axis doesnt repeat

Complete question is;

Katie just opened a checking account at the bank. Within the first month, she deposited three checks for $21.68, $42.09, and $65.44. She withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.

Write Katie’s withdrawals as negative rational numbers and her deposits as positive rational numbers.

Answer:

Deposits are; +21.68, +42.09, and +65.44.

Withdrawals are; -4.64, -23.11, and -9.78

Step-by-step explanation:

We are told that the deposits are;

$21.68, $42.09, and $65.44.

Now, she withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.

We are told to write Katie’s withdrawals as negative rational numbers and her deposits as positive rational numbers.

A rational number is a number that can be expressed as the ratio of two integers. In this question, by inspection, all the given values for deposits and withdrawals can be expressed as the ratio of 2 integers.

Thus;

Deposits are; +21.68, +42.09, and +65.44.

Withdrawals are; -4.64, -23.11, and -9.78

The solution to the given simultaneous equations are:

x = -3 and y = -12

The three primary methods for solving simultaneous equations are:

1) Substitution

2) Elimination

3) Graphical

We are given the simultaneous Equation:

y = 4x    ------(1)

y = -6x - 30    ------(2)

Substitute eq 1 into eq 2 to get:

4x = -6x - 30

Add 6x to both sides to get:

10x = -30

Divide both sides by 10 to get:

x = -3

Put -3 for x in eq 1 to get:

y = 4(-3)

y = -12

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Using the simple interest formula, the interest will the customer earn in 30 years is $1350, the account balance be after 30 years is $3850 and the customer earn $1350 interest.

In the given given that;

A new bank customer with $2,500 wants to open a money market account.

The bank is offering a simple interest rate of 1.8%.

So the Principal Amout(P)=$2500

Interest Rate(R)=1.8%

(a) So we have to find the interest will the customer earn in 30 years.

So the time (T)=30 years

So the formula of Simple Interest;

I=PRT/100

I=2500*1.8*30/100

I=1350

So the interest will the customer earn in 30 years is $1350.

(b) Now we have to find the account balance be after 30 years.

The account balance = Principal Amount+Interest Amount

The account balance = 2500+1350

The account balance = $3850

(c) Now we have to find the customer will earn $_ in interest.

The customer earn $1350 interest.

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Based on the information given, the null hypothesis states that the newscast reaches 41% of the viewing audience, while the alternate hypothesis states that it does not reach 41% of the audience. So, the correct answer is d. Fail to reject the null hypothesis.

To determine the decision, we need to perform a hypothesis test using the given significance level α = 0.01. This significance level represents the maximum acceptable probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

In the survey of 100 viewers, 36% indicated that they watch the late evening news on the local CBS station. To test the hypothesis, we can use a one-sample proportion test. We compare this sample proportion to the claimed 41% to see if there is a significant difference.

Using a statistical calculator or software, we calculate the p-value associated with the observed sample proportion. If this p-value is less than α (0.01), we reject the null hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

Based on the decision criteria, if the p-value is less than 0.01, we would reject the null hypothesis and conclude that the newscast does not reach 41% of the audience. However, if the p-value is greater than or equal to 0.01, we would fail to reject the null hypothesis. To summarize, the correct decision, given α = 0.01, would be d. Fail to reject the null hypothesis.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The maximum error of the midpoint approximation is 0.55.

To estimate the maximum error, we can consider the worst-case scenario by assuming that the second derivative is at its maximum value throughout the interval [11, 31]. In this case, we can use the largest possible value for M.

To find the maximum error of the midpoint approximation, we need to determine the width of the interval and divide it by 2.

Width of the interval = upper bound - lower bound = 10.5 - 9.4 = 1.1

Maximum error (E) = (Width of the interval) / 2 = 1.1 / 2 = 0.55

Therefore, the maximum error of the midpoint approximation is 0.55.

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Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

If the formatting should be \(\frac{\frac{5}{6} }{p} =\frac{\frac{2}{3} }{\frac{1}{2} }\), then this should be correct.

Answer:

p = \(\frac{5}{8}\)

Step-by-step explanation:

\(\frac{\frac{5}{6} }{p} =\frac{\frac{2}{3} }{\frac{1}{2} }\)                 [Given]

\(\frac{5}{6} *\frac{1}{p} =\frac{\frac{2}{3} }{\frac{1}{2} }\)            [Keep, change, and flip on the left side]

\(\frac{5}{6} *\frac{1}{p} =\frac{2}{3}*2}\)       [Keep, change, and flip on the right side]

\(\frac{5}{6} *\frac{1}{p} =\frac{4}{3}}\)            [Simplify the right side]

\(\frac{5}{6p}=\frac{4}{3}}\)                [Simplify the left side]

6p * 4 = 5 * 3    [Cross multiply]

24p = 15            [Simplify]

p = \(\frac{15}{24}\)                 [Divide both sides by 24]

p = \(\frac{15/3}{24/3}\)              [Simplify the fraction]

   p = \(\frac{5}{8}\)              [Answer]

If Jill was shopping for cars. She noticed the price of a mercedes c class is 8,000 higher than a year ago. If it cost 32,500 last year, Then 24.6  is the % increase in the price of the car

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

In last year the cost of the car is thirty two thousand five hundred. 32500

The price of a mercedes c class is 8,000 higher than a year ago

We need to find the percentage of increase in the price of the car.

32500×x=8000

Divide both sides by 32500

x=8000/32500

x=0.246

As we know percent is hundredths part of a quantity.

So multiply x value with hundred

0.246×100

24.6%

Hence 24.6  is the % increase in the price of the car.

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Answer:

D) There were 176,400 samples of the orchestra music taken every second

Step-by-step explanation:

Just did the test

Answer:

Hello,

Step-by-step explanation:

\(weighted\ average=barycentre=\dfrac{(-6)*3+2*1}{3+1}=\dfrac{-18+2}{4}= \dfrac{-16}{4} =-4\\\)

The weighted average is -4 if the coordinate −6 has a weight of 3, and the coordinate 2 has a weight of 1.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that;

Coordinate −6 has a weight of 3, and coordinate 2 has a weight of 1.

As we know, the formula for weighted average is given by:

Weighted average = (aW + bw)/(W + w)

Here a = -6

b = 2

W = 3

w = 1

Plug the above values in the formula:

Weighted average = (-6(3) + 2(1))/(3 + 1)

Weighted average = [-18 + 2]/4

Weighted average = -16/4

Weighted average = -4

Thus, the weighted average is -4 if the coordinate −6 has a weight of 3, and the coordinate 2 has a weight of 1.

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5×15= 75 the 4 days is irrelevant

Answer:

The answer would be: 75

Step-by-step explanation:

15×5=75

we ignore the 4 because it's irrelevant.

I hope this helps :)

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Answer:

C= 25.12 cm

Step-by-step explanation:

The exact value of the function cosecant of the angle is equal to - √353 / 8.

In this exercise we find the coordinates of a point in rectangular form, of which the exact value of a trigonometric function has to be found, to be precise, the value of the cosecant function:

csc θ = 1 / sin θ = √(x² + y²) / y         (1)

If we know that x = 17 and y = - 8, then the exact value of the function cosecant is:

csc θ = √[17² + (- 8)²] / (- 8)

csc θ = - √353 / 8

The exact value of the function cosecant of the angle is equal to - √353 / 8.

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The fraction of the original passengers remaining on the bus is 11/21.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.

.At the 1st stop 1/3 of the passengers exit.

At the 2nd stop, 3/7 of the remaining passengers exit the bus.

Therefore, The fraction of the original passengers who remain on the bus is,

= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].

= [ 1 - (1/3) - (3/21)].

= [ (2/3) - (3/21)].

= [(14 - 3)/21].

= 11/21.

So, 11/21 remains on the bus.

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Answer:

B. 3 to 2

Step-by-step explanation:

I calculated it logically

The ratio of the frequency of G to C is 1.5. So, option b is correct.

Frequency of a wave is defined as the number of oscillations completed by the wave in one second.

Here,

The frequency of note G, f(G) = 392 Hz

The frequency of note C, f(C) = 262 Hz

The ratio of the frequency of G to C, r = frequency of G/frequency of C

r = f(G)/f(C)

r = 392/262

r = 1.496 approximately r = 1.5

Hence,

The ratio of the frequency of G to C is 1.5

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Answer:

Scalene and Acute

Step-by-step explanation:

We know that,

A scalene triangle is a triangle whose none of the sides are equal in measure.

A triangle is acute if all of it's angle measure below 90 degree.

Here,

The sides of the given triangle are 12.1,11,10 and 12.1≠11≠10, due to which the triangle is scalene.

All the angles of the given triangle are 51,59,70 and 51,59,70<90, Hence, the given triangle is acute

Answer:

40572

Step-by-step explanation:

Answer:

It is a solution

Step-by-step explanation:

Given

\(y + 4 > 3x-1\)

Required

Is \((-1,4)\) a solution

\((-1,4)\) implies that:

\(x=-1\ \ \y = -4\)

Substitute in:

\(y + 4 > 3x-1\)

\(-4 + 4 > 3 * -1 -1\)

\(-4 + 4 > -3 -1\)

\(0 > -4\)

The above inequality is true.

Hence, \((-1,4)\) is a solution y + 4 > 3x-1

Answer: Suppose there exists a positive rational number r such that r^2 < 2. Then we have 2 - r^2 > 0. Let h = (2 - r^2)/4. Then h > 0 because r^2 < 2.

Consider the number rh = r + h. We have:

(rh)^2 = (r + h)^2 = r^2 + 2rh + h^2 = r^2 + 2(2 - r^2)/2 + (2 - r^2)/16

= r^2 + 2 + (2 - r^2)/16

< 2 + 2 + (2 - 2)/16 = 2.

Thus, for any positive rational number r such that r^2 < 2, there exists a larger positive rational number rh = r + h such that (rh)^2 < 2.

Step-by-step explanation:

Answer:

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

Find the difference of the initial and used amounts:

Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

Please refer to the attachment for the answer and explanation. Hope it helps!!:))

It should be noted that the cheetahs average rate for the entire trip is 55mph

The average rate for the trip is equal to the total distance traveled divided by the total time traveled.

Average Rate = 70+ 40/2= 110/2 = 55mph

Yes the average rate of the cheetah is 55 mph

The following equations represent the distance traveled on each leg of the trip.

First leg of trip: td=r1 t1= 70*t

Second leg of trip: td=r2 t2= 40*t

Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.

Total distance = r1 t1+ r2 t2

Average rate = Total distance / total time

=  r1 t1+ r2 t2/ t1+ t2

=70t+ 40t/ 2t

=110t/2t

= 55mph

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Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph. Using the equation for average rate above determine the cheetahs average rate for the entire trip

Answer:

8

Step-by-step explanation:

diameter is the radius times 2

Answer:

p > 34

He wrote more than 34 pages before today.

Step-by-step explanation:

Eduardo wrote 16 more pages, increasing his total number of pages above 50.

p = pages he wrote before today

p + 16 > 50

p > 50 - 16

p > 34

He wrote more than 34 pages before today.

Answer:

I believe it would be C

Step-by-step explanation: