The cost of admission to a popular music concert for 4 children and an adult was
$54. The admission for 8 children and 3 adults in another music concert was $122.
How much was the admission for each child and adult?

Answer:

Step-by-step explanation:

The graph shows that as more time passes, more boxes are being manufactured. Therefore, the number of boxes relies on the number of hours.

Hope this helps :)

SOLUTION

Step 1 : We need to recognize the value of x in 5 places means 5 x

and the value of 1 in 6 times means 6,

so we have that: 5 x + 6 = 1 .

Step 2 : We need the linear equation: 5 x + 6 = 1

collecting like terms, we have that:

5 x = 1 - 6

5 x = - 5

Divide both sides by 5 , we have that:

x = - 1

CONCLUSION : The value of x = -1 ( OPTION B )

To find the weight that represents the 85th percentile of newborn babies given the data. The weight that represents the 85th percentile of newborn babies in the given data is 8.4 pounds.

Follow these steps:
1. Arrange the data in ascending order: 5.5, 6.3, 6.4, 6.5, 6.7, 7.2, 7.7, 7.7, 7.7, 7.7, 7.7, 8.0, 8.1, 8.6, 9.3
2. Determine the total number of data points (n): There are 15 data points in the provided dataset.
3. Calculate the 85th percentile rank (R) using the formula: R = P * (n+1), where P is the desired percentile (0.85 in this case). R = 0.85 * (15+1) = 0.85 * 16 = 13.6
4. Since the calculated rank (13.6) is not a whole number, we will interpolate between the two closest data points. In this case, the 13th and 14th data points. The 13th data point is 8.1, and the 14th data point is 8.6.
5. Interpolate the 85th percentile weight using the following formula: Weight = Weight at lower rank + (R - lower rank) * (Weight at higher rank - Weight at lower rank)
Weight = 8.1 + (13.6 - 13) * (8.6 - 8.1) = 8.1 + 0.6 * 0.5 = 8.1 + 0.3 = 8.4.

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Answer:

$142,857.14

Step-by-step explanation:

As per the question,

Solving for Y

To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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It depends on which edge and by how much you are raising the weight in the minimum spanning tree.

Consider the following example to gain a better understanding of this idea. Let T be the smallest spanning tree of G and let G be a connected, weighted graph. Consider increasing an edge's weight in T by a tiny positive amount.

T continues to be a spanning tree of G if is small enough because it is still connected and contains all of G's vertices. However, T is no longer a minimum spanning tree of G because its weight has increased by. Consider any alternative spanning tree T' of G to understand why. We know that the weight of T is less than or equal to the weight of T' because T was the lowest spanning tree prior to the weight increase.

T' is now a better minimal spanning tree than T since, after the weight increase, the weight of T is greater than the weight of T' plus. T' must be the new minimal spanning tree of G as a result.

In conclusion, altering the weight of an edge in a minimum spanning tree may result in the inclusion of a different set of edges, which may result in a change in the tree's structure. The new minimal spanning tree might, however, nevertheless have the same edges as the previous minimum spanning tree if the weight gain is negligibly tiny.

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Answer:

Cost of each chocolate bar  = $2.65

Cost of each blow pop  = $1.25

Step-by-step explanation:

Let x = Cost of chocolate bar

y= Cost of blow pops

We can make system of equations and find value of x and y

You bought 5 chocolate bars and 8 blow pops for $23.25.\(5x+8y=23.25\)

Your sister bought 2 chocolate bars and 13 blow pops for $21.55. \(2x+13y=21.55\)

Let:

\(5x+8y=23.25--eq(1)\\2x+13y=--eq(2)\)

Multiply eq(1) with 2 and eq(2) with 5 and subtract

\(10x+16y=46.5\\10x+65y=107.75\\- \ \ \ - \ \ \ \ \ \ - \\------\\-49y=-61.25\\y=\frac{-61.25}{-49} \\y=1.25\)

So, value of y = 1.25

Putting value of y in eq(1) to find value of x

\(5x+8y=23.25\\5x+8(1.25)=23.25\\5x+10=23.25\\5x=23.25-10\\5x=13.25\\x=13.25/5\\x=2.65\)

Value of x = 2.65

So, Cost of each chocolate bar = x = $2.65

Cost of each blow pop = y = $1.25

Answer:

I put the equation on math-way and it gave me this:

Answer:

Starting at (0, 1), go up 4 units, then right 3 units. You will end at (3, 5). Plot that point, and then draw a line that goes through the two points.

For the standard normal probability distribution, the area under the probability density function to the left of the mean is 0.5.

This means that half of the distribution lies to the left of the mean, and the other half lies to the right. Since the distribution is symmetric, the area under the curve to the left of the mean is equal to the area under the curve to the right of the mean. Therefore, both areas are 0.5 or 50%.

In a standard normal distribution, the probability density function (PDF) is symmetric about the mean. This means that the area under the curve to the left of the mean is equal to the area under the curve to the right of the mean.

Since the total area under the curve represents the probability of the entire distribution, it sums up to 1. Therefore, when we divide the distribution into two equal parts, each part represents 0.5 or 50% of the total area.

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Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.

Let's denote the number of additional free throws that Michelle needs to make as "x." Since she has made 14 out of her 20 free throws this season, her current shooting percentage is:

Current shooting percentage = (Number of made free throws / Total number of attempted free throws) * 100

                        = (14 / 20) * 100

                        = 70%

To find the number of additional free throws she needs to shoot to achieve a shooting percentage of 90%, we set up the following equation:

(14 + x) / (20 + x) = 90/100

We can now solve this equation to find the value of x:

(14 + x) / (20 + x) = 0.9

Cross-multiplying gives:

0.9 * (20 + x) = 14 + x

18 + 0.9x = 14 + x

0.9x - x = 14 - 18

-0.1x = -4

Dividing both sides by -0.1 gives:

x = 40

Therefore, Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.

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Equation is \(y = \frac{8}{147} (x + \frac{1}{2} )^2 - \frac{3}{7}\)   and the line of symmetry is \(x=-\frac{1}{2}\)

The parabola is split into two congruent halves by a vertical line, which is the line of symmetry for a quadratic function. It also goes by the name of the axis of symmetry.

For a standard form quadratic function:

\(f(x) = ax^2 + bx + c\)

The equation gives the line of symmetry: x = -b/2a

As a result, the vertex of the parabola serves as the intersection of the line of symmetry, which is a vertical line. The point on the graph where the function reaches its minimum or highest value is known as the vertex of the parabola.

Given that the three points are: (-3, 2), (-4, -1), (0, -1)

To find the line of symmetry of a quadratic function, we need to find the x-coordinate of the vertex of the parabola. Since the three given points lie on the graph of the quadratic function, we can use them to find the vertex.

First, let's write the quadratic function in vertex form:

\(y = a(x - h)^2 + k\)  where (h, k) is the vertex of the parabola.

Using the given points, we can set up a system of equations to solve for a, h, and k:

\(2 = a(-3 - h)^2 + k\)

\(-1 = a(-4 - h)^2 + k\)

\(-1 = a(0 - h)^2 + k\)

We can simplify this system by subtracting the third equation from the first two to eliminate k:

\(1 = a(-3 - h)^2 - a(0 - h)^2\)

\(-2 = a(-4 - h)^2 - a(0 - h)^2\)

Simplifying further, we get:

\(1 = 9a - h^2a\)

\(-2 = 16a - h^2a\)

Solving for h, we get h = -1/2. Substituting this into one of the equations, we can solve for a:

\(2 = a(-3 - (-1/2))^2 + k\)

\(2 = a(25/4) + k\)

Subtracting this equation from one of the other equations, we can solve for k:

\(-3 = a(-4 - (-1/2))^2 + k\)

\(-3 = a(147/4) + k\)

Substituting a = 8/147 and h = -1/2 into the vertex form equation, we get:

\(y = \frac{8}{147} (x + \frac{1}{2} )^2 - \frac{3}{7}\)

So the line of symmetry is  \(x=-\frac{1}{2}\)

To select two points on the coordinate plane, we can choose any two points that are not on the line of symmetry. For example, we can choose (1, 1) and (-2, 4). To connect these points with a line, we simply plot them on the coordinate plane and draw a straight line passing through both points.

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The tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate, After 20 minutes, the amount of salt in the tank is still 50 grams.

In order To calculate the amount of salt in the tank after 20 minutes, we basically use the formula:  Salt (in grams) = (Amount of salt in the tank x Time) / Total volume.So, after 20 minutes, the amount of salt in the tank is:  (50 grams x 20 minutes) / 240 liters = 8.33 grams.    

As we can see, both methods produce the same result, confirming that the amount of salt in the tank after 20 minutes is still 50 grams. since the rate of pumping in salt water is equal to the rate of pumping out salt water, so the total amount of salt remains the same.

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A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate. find the number of grams of salt in the tank after 20 minutes

Answer: x=-1/7

Step-by-step explanation:

11-10x-7-4x=6

11-7-10x-4x=6

4-14x=6

-14x=2

x=-1/7

Problem

Solution

The value of r indicates the tendency for the line or the slope if the value of r is negative then the slope would be - and if the value of r is + then the slope would be positive

And as we can see here r =-0.83 and the slope m = -1.21

The first four terms of an arithmetic sequence are 5, 9, 13, 17 and the nth term formula of this sequence is 4n+1.

To find the expression for the (n-1)th term, we need to substitute (n-1) into the nth term formula.

So, the nth term formula is 4n+1.

Substituting (n-1) for n, we get:

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

Therefore, the expression for the (n-1)th term of an arithmetic sequence is 4n-3.

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Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

Answer:

C

Step-by-step explanation:

Don't listen to those *other* answers, clearly the correct one is c

(kidding kidding xD)

The p-value is the statistic that displays the area cutoff by the combined negative and positive values of the t-distribution when running a t-test with equal variances in Excel.

When running a t-test with the assumption of equal variances in Excel, the statistic that displays the area cutoff by the combined negative and positive values of the t-distribution is the p-value.

In Excel, the p-value is calculated using the T.TEST function, which returns the probability associated with a Student's t-test. The function requires the input of two sets of data for the two samples being compared. By comparing the calculated t-value to the t-distribution, the function determines the probability (p-value) of observing such extreme differences between the means of the two samples under the null hypothesis.

The p-value represents the probability of obtaining a t-value as extreme as the one observed, assuming the null hypothesis is true (i.e., there is no significant difference between the means of the two samples). If the p-value is smaller than a chosen significance level (e.g., 0.05), it indicates that the observed difference is statistically significant, and we reject the null hypothesis in favor of an alternative hypothesis.

In summary, the p-value is the statistic that displays the area cutoff by the combined negative and positive values of the t-distribution when running a t-test with equal variances in Excel.

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Answer:

A

Step-by-step explanation:

The answers you have are in (x, y) form

Looking at first answer, -3 is the x and -1/2 is the y. We plug in the -3 as the x in each equation and hope to get -1/2.

So for (-3, -1/2)

y = 1/2(-3) + 1 = -3/2 + 1 = -1/2

Now the other equation

y = 3/2(-3) + 4 = -9/2 + 4 = -1/2

Since we got -1/2 as both. which is also the Y coordinate, this must be the answer. If it wasn't, we could keep going through the answer choices doing the same method.

We are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

To find the confidence interval, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

Where:

CI: Confidence Interval

p: Proportion of students who correctly identified the flavor (sample proportion)

z: Z-score corresponding to the desired confidence level (95% confidence level corresponds to z=1.96)

n: Sample size

Plugging in the values we have:

p = 78/154 = 0.5065

z = 1.96

n = 154

CI = 0.5065 ± 1.96sqrt(0.5065(1-0.5065)/154)

CI = 0.5065 ± 0.0783

CI = (0.4282, 0.5848)

Therefore, we are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

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No, it is not possible to form a right triangle with the sides as 15 cm, 8 cm, and 17 cm .

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) must equal the square of the longest side (the hypotenuse). In this case, 15^2 + 8^2 = 289 + 64 = 353, which is not equal to 17^2 = 289.

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Answer:

x = 2/3

Step-by-step explanation:

5x + 3 - 2x = 5

3x = 5-3

3x = 2

x = 2/3

give brainliest please!

hope this helps :)

It is possible to use a relational operator and math operators in the same expression.

In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.

For example, consider the following expression:

`if (2 * 3) > (4 + 1)`

In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:

`if (6) > (5)`

Then, the relational operator (>) is evaluated, and the expression becomes:

`if True`

The expression is true because 6 is greater than 5.

It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.

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a) It is a vertical dilation of scale factor of 5.

b) It is a translation up of 10 units.

Here we have the line:

S(d) = 5d + 10

That represents the cost for renting the surboard for d days.

Remember that the parent linear function is y =x

A) 5 in this case is the slope, it says how much the cost for the rental increases for each day that passes. The effect on the linear parent function is a dilation of scale factor of 5.

B) 10 is the y-intercept, so this will represent a translation up of 10 units.

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Answer:

x=32

Step-by-step explanation:

that is an isosceles triangle, meaning 2 sides are the same and 2 anlges are the same.

each traingle = 180 degrees

3x+2(x+10)=180

3x+2x+20=180

5x=160

x=32

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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Given:

Mrs. Kato has 6 bags of dried beans and a 2-pound bag of rice in one shopping bag.

In another shopping bag she has a 5-pound bag of flour.

The two shopping bags weigh the same amount.

To find:

The weight of each bag of dried beans.

Solution:

Let x be the weight of each bag of dried beans.

So, weight of 6 bags of dried beans = 6x.

According to the question,

Weight of first bag = (6x + 2) pounds

Weight of second bag = 5 pounds

The two shopping bags weigh the same amount. So,

\(6x+2=5\)

\(6x=5-2\)

\(6x=3\)

Divide both sides by 6.

\(x=\dfrac{3}{6}\)

\(x=0.5\)

Therefore, the weight of each bag of dried beans is 0.5 pounds.

The weight of each bag of dried beans is 0.5 pounds.

Given that,

Based on the above information, the calculation is as follows:

6x + 2 = 5

6x = 5 -2

6x = 3

x = 0.5

Therefore, we can conclude that the weight of each bag of dried beans is 0.5 pounds.

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Answer:

A.32

Step-by-step explanation:

h(x)=x^2-4

h(6)=6^2-4

h(6)=36-4

h(6)=32