Determine whether the ordered pair is a solution to the system.
x + 4y > 10
3x - 2y < 12
a. (-2, 4) b. (3,1)​

Answer:

the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).

Step-by-step explanation:

We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.

a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.

z-score = (54 - 53) / 4 = 0.25

Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.

Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).

b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.

First, we find the z-scores for each height requirement:

z-score for 42 inches = (42 - 53) / 4 = -2.75

z-score for 48 inches = (48 - 53) / 4 = -1.25

Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.

Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).

c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.

z-score = (42 - 53) / 4 = -2.75

Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.

Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).

d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.

First, we find the z-scores for each height requirement:

z-score for 42 inches = (42 - 53) / 4 = -2.75

z-score for 54 inches = (54 - 53) / 4 = 0.25

Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.

Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).

The probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu is: 0.087.

This is a binomial distribution problem, where n = 55 and the probability of success (i.e. a person subscribing to Hulu) is p = 0.41.

The probability mass function of a binomial distribution is:

P(X = x) = (nCx) * p^x * (1-p)^(n-x)

where nCx is the binomial coefficient (i.e. the number of ways to choose x items from n items).

So, in this case, we want to find P(X = 20):

P(X = 20) = (55C20) * 0.41^20 * (1-0.41)^(55-20)

P(X = 20) ≈ 0.087

Therefore, the probability that in a random sample of 55 18 to 29-year-olds, 20 will say they currently have a subscription to Hulu is approximately 0.087or 8.7%.

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The equation for the trigonometric graph is y = 2sin4x

A trigonometric graph is the graph of a trigonometric function.

Since we desire to find the equation of the graph, we then want to use the equation for the general sine graph.

y = AsinBx where

Now, A = (maximum - minimum)/2

From the graph,

So, we now substitute the variables into the equation, thus

A = (maximum - minimum)/2

= [2 - (-2)]/2

= (2 + 2)/2

= 4/2

= 2

Also B = 2π/T

Now from the graph, T = π/2

So,  we substitute for B in the equation for B, thus

B = 2π/T

= 2π/(π/2)

= 2π × 2/π

= 4

We then substitute A and B into y, thus

y = AsinBx

= 2sin4x

So, y = 2sin4x

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Answer:

3

Step-by-step explanation:

Amount used:

8 - 7.25 = 0.75

He used 0.75 cup

Each day he had 0.25 cup.

0.75/0.25 = 3

Answer: 3

The answer is (B) 1.5 percent.

You can find the growth accounting equation by using:

Growth rate of output equals Technology growth rate plus a* Capital growth rate plus (1-a*Labor growth rate)

Inputting the values provided yields:

5% equals 3% plus (0.8 * Capital Growth Rate) plus (0.2 * 4%).

When we simplify the equation, we obtain:

Capital growth rate equals (5% - 3% - 0.2%) / 0.8, or 1.5%

As a result, the capital growth rate is predicted to be 1.5%.

(B) 1.5 percent is the right answer.

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Answer:

[tex]A=\frac{4}{6} *600 = 400\\B=\frac{2}{6} *600 = 200[/tex]

The interquartile range for the amounts of money spent by some male students on their holidays is £ 160.

To find the interquartile range (IQR) on a box plot, the IQR is the difference between the upper and lower quartiles. The upper quartile (Q3) is the median of the upper half of the data, and the lower quartile (Q1) is the median of the lower half of the data.

The interquartile range for the amount spent by male students on their holidays is :

= Q3 - Q 1

= 800 - 640

= £ 160

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To calculate the standard error σM for a sample, we can use the formula [tex]σM = s / \sqrt{n}[/tex], where s: sample standard deviation and n: sample size.

The formula for calculating the standard error, M, which indicates the standard deviation of the sampling distribution of the mean, is as follows:

[tex]σM = σ / \sqrt{n}[/tex]

where σ: population standard deviation and n: sample size.

If we don't know the population standard deviation, we estimate it using the sample standard deviation s. We use formula:

[tex]σM = s / \sqrt{n}[/tex]

We can apply the method above with the sample size n and the sample standard deviation s if we are given a sample and asked to determine the standard error M for this sample.

By adding up each value in the sample and dividing by the sample size, we can determine the sample mean x, from which we may compute the sample standard deviation. The sample variance is then determined by adding up the squared deviations between each value and the sample mean, then dividing the result by the sample size less one. Lastly, we calculate the sample standard deviation by taking the square root of the sample variance.

Once we have calculated the sample standard deviation s and the sample size n, we can plug these values into the formula for σM:

[tex]σM = s / \sqrt{n}[/tex]

and calculate standard error.

In conclusion, the formula M = s / [tex]\sqrt{n}[/tex]n, where s: sample standard deviation and n: sample size, can be used to compute the standard error M for a sample.

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Answer:

Step-by-step explanation:

a. 25% of 5000 tickets = 0.25 x 5000 = 1250 tickets

Total sales of $45 tickets = 1250 x $45 = $56,250

b. 15% of 5000 tickets = 0.15 x 5000 = 750 tickets

Total sales of $35 tickets = 750 x $35 = $26,250

c. General admission tickets = Total tickets - Reserved tickets

= 5000 - 1250 - 750

= 3000 tickets

d. Total sales for general admission tickets = Number of general admission tickets x Price per ticket

= 3000 x $20

= $60,000

e. Total sales = Sales of $45 tickets + Sales of $35 tickets + Sales of general admission tickets

= $56,250 + $26,250 + $60,000

= $142,500

The volume and sum of the composite shape is 13L² and 13V³ respectively

A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other. Also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles

The composite is made up of 13 squares in total

The area of 1 square is given as A = S²

The volume of the composite is 13L³ units

Hence there are 13 squares. the sum of the areas and volume of the square is 13 S²

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Answer:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

Step-by-step explanation:

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)

x→∞ x→∞

= 4√(lim(x-6))

x→∞

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞

x→∞

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

Answer:

Step-by-step explanation:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞x→∞.

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

m = (-12 - 5) / (3 - (-5))

m = (-17) / (3 + 5)

m = (-17) / 8

Therefore, the slope between the points (-5, 5) and (3, -12) is -17/8.

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Si 25 dólares representan el 15% de una cuenta, podemos usar una regla de tres simple para determinar cuánto hay en total en la cuenta:

15% -----> $25

100% ----> ($25 x 100)/15

100% ----> $166.67

Por lo tanto, hay $166.67 en total en la cuenta.

After making the minimum payment of $125, the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

If the minimum monthly payment of $125 is made, we can calculate the new balance, unpaid balance, and interest charge as follows:

The interest rate per month is (18% per year) / 12 = 1.5% per month.

First, we calculate the interest charge for the month on the unpaid balance:

Interest charge = (1.5% per month) x ($5000 unpaid balance)

Interest charge = $75

Next, we subtract the minimum payment from the unpaid balance to get the new unpaid balance:

Unpaid balance = $5000 - $125

Unpaid balance= $4875

Then, we add the interest charge to the new unpaid balance to get the new balance:

New balance = $4875 + $75

New balance = $4950

Finally, we can calculate the purchasing power as the credit limit minus the new balance:

Purchasing power = $5000 - $4950

Purchasing power = $50

Therefore the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

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An equation of a line parallel to that passes y = 4/3x + 4 through the point (3, -7) include the following: A. y + 7 = 4/3(x - 3).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since y = 4x/3 + 4, the slope is equal to 4/3.

At data point (3, -7) and a slope of 4/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-7) = 4/3(x - 3)  

y + 7 = 4/3(x - 3)  

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Answer:

Graph A

Step-by-step explanation:

As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;

This is because the scale of the y-axis in graph B has smaller increments;

This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.

Answer: graph A.

appear to increase less.

Step-by-step explanation:

To stretch the graph horizontally by a factor of 3, we need to multiply the x-coefficient by 1/3. Similarly, to stretch the graph vertically by a factor of 7, we need to multiply the y-coefficient by 1/7. Therefore:

Horizontally stretched graph: 5(1/3x)² + 8(1/3x) + 4y² - 4y = 70

Simplifying:

(5/9)x² + (8/3)x + 4y² - 4y = 70

Vertically stretched graph: 5x² + 8x + 4(1/7y)² - 4(1/7)y = 70

Simplifying:

5x² + 8x + (4/49)y² - (4/7)y = 70

Using Pythagoras theorem, we can find the length of the missing side to be 10 units.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also referred to as the Pythagorean theorem.

The Pythagorean Theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of its other two sides.

In the given triangle, the base is given as:

b = 6 units.

height, h = 8 units.

Let the missing side be = x.

Now as per the Pythagoras theorem,

x² = 8² + 6²

⇒ x² = 64 + 36

⇒ x² = 100

⇒ x = 10.

Therefore, the length of the missing side of the triangle here is 10 units.

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Answer:

8

Step-by-step explanation:

line WL is a straight line intersecting line GZ at J so angles LJW is 180o

therefore

LJG + GJH + HJW = 180

9x + 90 + 18 = 180

9x = 180 - 90 - 18

9x = 72

x = 72/9 = 8

Answer:

Mary Ellen is MOST LIKELY going to use shears to cut the linen.

The values of x and y such that the table represents a function are given as follows:

x = 8, y = 7.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

The input-output pairs for the function in this problem are given as follows:

Hence the x-value can only by 8 or 12, and we choose y = 8, while the y-value is free, hence we choose y = 7.

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Answer:

the scale factor = 3

Step-by-step explanation:

the question is basically saying: how did (12,-4) jump to (36,-12)

we can make d represent the scale factor used to get (12,-4) to (36,-12)

so,

12d = 36

-4d = -12

all there's left to do is to simply solve for d, which is 3

The price οf the jacket was $115.

Let's start by defining sοme variables tο represent the unknοwn quantities:

Let x be the price οf the shirt

Let y be the price οf the jacket

Frοm the prοblem statement, we knοw that:

y = 2x + 17 (the cοst οf the jacket was $17 mοre than twice the price οf the shirt)

x + y = 164 (the tοtal cοst οf the shirt and jacket was $164)

We can use these twο equatiοns tο sοlve fοr the values οf x and y. One way tο dο this is tο substitute the expressiοn fοr y frοm the first equatiοn intο the secοnd equatiοn, and then sοlve fοr x:

x + (2x + 17) = 164

3x + 17 = 164

3x = 147

x = 49

Nοw that we knοw the price οf the shirt is $49, we can use the first equatiοn tο sοlve fοr the price οf the jacket:

y = 2x + 17

y = 2(49) + 17

y = 115

Therefοre, the price οf the jacket was $115.

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The area of the smaller triangle is 12 square units

If the scale factor between two similar triangles is 2/3

It means that every length of the smaller triangle is 2/3 the length of the corresponding side of the larger triangle.

So, the ratio of their areas is the square of the scale factor

This is represented as

(area of smaller triangle) / (area of larger triangle) = (2/3)^2 = 4/9

We are given that the area of the larger triangle is 27

So, we have

Area of smaller triangle/27 = 4/9

Multiplying both sides by 27, we get:

Area of smaller triangle = (4/9) * 27

Evaluate

Area of smaller triangle = 12

Hence, the area of the smaller triangle is 12.

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Answer:

length of the pan is 10 inches

Step-by-step explanation:

Volume = length x width x height

V = lwh

l = (V) / (wh) = (150 in³) / (7.5 in)(2 in) = 10 in

Answer:

4Step-by-step explanation:

Therefore , the solution of the given problem of data plot comes out to be value (r) is roughly 0.975.

The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear. The pinkish haze with the letter P stands in for the number 2.3.

Here,

We must compute several numbers in order to determine the Pearson correlation coefficient r for the information provided in the table.

Before anything else, we figure out the average and standard deviation of the amount of TV airings (x) and car sales (y):

mean(x) = (40 + 30 + 20 + 50 + 10) / 5 = 30

mean(y) = (30 + 20 + 10 + 40 + 20) / 5 = 24

These mean numbers allow us to determine the standard deviation:

=> SX = √ (( (40-30)² + (30-30)² + (20-30)² + (50-30)² + (10-30)²) / 4)

≈> 15.81

=> SY = √(( (30-24)²+ (20-24)² + (10-24)² + (40-24)² + (20-24)²) / 4)

≈> 8.16

Next, we determine x and y's covariance:

=> cov(x,y) =

=> [(40-30)(30-24) + (30-30)(20-24) + (20-30)(10-24) + (50-30)(40-24) + (10-30)(20-24)] / 4

≈>  125

Last but not least, we can figure out the Pearson association coefficient:

0.975 r = cov(x,y) / (s x * s y)

As a result, the table's data's Pearson correlation value (r) is roughly 0.975. This shows a significant positive correlation between the volume of car purchases and the frequency of the TV ad.

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