Samantha wants to treat her friends to a movie. Tickets cost $6 each and popcorn and drinks will cost $30. She can spend no more than $150 so how many friends can she take?



a) Write an inequality to represent the situation.



b) Solve the inequality to find the maximum number of friends she can take?

The solution to the equation 2(t - 5) = 48 is t = 29.

To solve the equation 2(t - 5) = 48, we can use the following steps:

Distribute the 2 to the terms inside the parentheses:

2t - 10 = 48

Add 10 to both sides of the equation to isolate the variable term:

2t = 58

Divide both sides of the equation by 2 to solve for t:

t = 29

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Answer:

P=60

Step-by-step explanation:

P=2(l+w)

P=2(14+16)

P=2(30)

P=60

Perimeter of a rectangle with 16in length and 14in width is 60 in.

Perimeter of a rectangle = 2(l+b)

here l = length and b= width

Given : l= 16 in and b= 14 in

perimeter = 2(l+b)

= 2(16+14)

= 2(30)

=60 inches.

The perimeter of rectangle is 60 inches

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We have plotted two points B and C that are 3 units away from point A and also share the same x-coordinate as point A.

To plot two points that are 3 units from point A and also share the same x-coordinate as point A, we can follow the below steps:

Step 1: Identify point A on the coordinate plane.

Step 2: Plot two points (let's say B and C) that are 3 units away from point A on either side of it.

Step 3: Ensure that both points B and C share the same x-coordinate as point A. This means that they lie on a vertical line passing through point A.

For example, let's say that point A is located at (2,5) on the coordinate plane.

To plot two points that are 3 units away from point A and also share the same x-coordinate as point A, we can follow the below steps:

Step 1: Plot point A at (2,5).

Step 2: Plot point B, which is 3 units away from point A and shares the same x-coordinate as point A. Since point A has an x-coordinate of 2, point B will also have an x-coordinate of 2.

To find the y-coordinate of point B, we can add or subtract 3 from the y-coordinate of point A.

Let's subtract 3.

So, point B will be at (2,2).

Step 3: Plot point C, which is also 3 units away from point A and shares the same x-coordinate as point A.

Since point A has an x-coordinate of 2, point C will also have an x-coordinate of 2.

To find the y-coordinate of point C, we can add or subtract 3 from the y-coordinate of point A.

Let's add 3.

So, point C will be at (2,8).

Thus, we have plotted two points B and C that are 3 units away from point A and also share the same x-coordinate as point A.

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If her pay is $8002.14. then 20% of this amount is:

After five-month this amount will be:

Therefore, after 5 month she will have $8002

Answer:

Step-by-step explanation:

Sorry

Answer:

1380

Step-by-step explanation:

Using proportion, then

1 Km² → 60 people , then

23 Km² → 60 × 23 = 1380 people

The value of "x" in the expression "ln(-4x + 5) - 5 = -7" is x = (-1 + 5e²)/4e².

The equation to solve for "x" is represented as : ln(-4x + 5) - 5 = -7,

Rearranging it, we get : ln(-4x + 5) = -7 + 5 = -2,

ln(-4x + 5) = -2,

Applying log-Rule : logᵇₐ = c, ⇒ b = \(a^{c}\),

-4x + 5 = e⁻²,

-4x + 5 = 1/e²,

-4x = 1/e² - 5,

-4x = (1 - 5e²)/4e²,

Simplifying further,
We get,

x = (1 - 5e²)/-4e²,

x = (-1 + 5e²)/4e²

Therefore, the required value of x is (-1 + 5e²)/4e².

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Answer:

n=4

Step-by-step explanation:

\(\sqrt[n]{256} =8^{\frac{1}{3} } *8^{\frac{1}{3} } \\256^{\frac{1}{n} } =(2^{3} )^{\frac{1}{3} } *(2^{3} )^{\frac{1}{3} } \\(2^{8})^{\frac{1}{n} } =2^{3 \times \frac{1}{3} } *2^{3 \times \frac{1}{3} } \\2^{\frac{8}{n} } =2 \times 2\\2^{\frac{8}{n} } =2^{2} \\\frac{8}{n} =2\\n=\frac{8}{2} =4\)

Frequency means how often a number or something appears.

so,

2

4

3

5

The correct statement regarding the attribution requirement of the license is given as follows:

A. It requires the user to give credit to the author.

The attribution requirement of a license means that anyone who uses material under that license must give credit to the original author or creator.

Hence option A is the correct option in the context of this problem.

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Answer:

The base of a power is the factor that is repeatedly multiplied by itself.

The correct formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests is 1950 + 100n.

To find the formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests, we can analyze the given information.

We are given two data points: the cost for 50 guests, which is $6,950, and the cost for 100 guests, which is $11,950. We can observe that the difference between these two costs is $11,950 - $6,950 = $5,000.

Since the cost forms an arithmetic sequence, the difference between consecutive terms will remain constant. In this case, the difference is $5,000.

Now, we need to find the initial term of the sequence. By examining the cost for 50 guests, we notice that the difference between the cost for 50 guests and the initial term is $6,950 - $5,000 = $1,950.

Putting it all together, we have the formula for the general term of the arithmetic sequence: initial term + (difference × (n - 1)).

Plugging in the values, the formula becomes: 1,950 + (5,000 × (n - 1)) = 1,950 + 5,000n - 5,000 = 5,000n - 3,050. Simplifying further, we get the final formula: 5,000n - 3,050.

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The function g(x) is a transformation (flipped upside down and horizontally stretched) of the quadratic parent function, f(x) = x2. g(x) = -0.5x².

Flipping upside down, is found by taking the negative of the original function; that is, the rule for this transformation is −f (x).

Since, g(x) is an upside down function of f(x), g(x) = -f(x).

If we multiply a function by a coefficient, the graph of the function will be stretched.

A function h(x) represents a horizontal compression of f(x) if h(x) = f(cx) and c > 1.

A function h(x) represents a horizontal stretch of f(x) if h(x) = f(cx) and 0 < c < 1.

Since, g(x) is clearly a stretched transformation of f(x), c < 1.

The possible function g(x) = -0.5x².

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Answer:

A

Step-by-step explanation:

just A

successive y values are 5 TIMES the previous y value

In all the others the y value is an ADDITION of the same amount to the previous y value

Answer:

y+2= 3(x-1)

y=3x-3-2

y=3x-5

The y - intercept is at (0,-5)

The only graph that has the y-intercept at -5 is C

Answer is =C

Answer:

GRAPH B!!!

Step-by-step explanation:

hope this helps :)

The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution.

No-shows Probability

0 0.30

1 0.20

2 0.20

3 X

4 0.15

The following

Expected value = (0)(0.30) + (1)(0.20) + (2)(0.20) + (3)(X) + (4)(0.15)

= 0 + 0.20 + 0.40 + 0.15(4) + 3X

= 1.20 + 3X

Since the sum of the probabilities must equal 1, we have

0.30 + 0.20 + 0.20 + X + 0.15 = 1

X = 0.15

Therefore, the expected value of the number of no-shows is

Expected value = 1.20 + 3(0.15) = 1.65

To find the variance, we can use the formula

Variance =\((0 - 1.65)^2(0.30) + (1 - 1.65)^2(0.20) + (2 - 1.65)^2(0.20) + (3 - 1.65)^2(0.15) + (4 - 1.65)^2(0.15)\)= 0.5625

Therefore, the variance is 0.5625, which means the standard deviation is the square root of the variance.

Standard deviation = \(\sqrt{0.5625}\) = 0.75

Hence, the correct option is A 1.65 customers.

Hence, the correct option is E 0 customers.

We have already found the variance to be 0.5625.

Hence, the correct option is C 0.15.

We have already found the expected value to be 1.65.

Hence, the correct option is D 1.424.

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The length of the arc that has a central angle measure of 45 degrees and a circle radius of 12 cm is calculated as: 9.42 cm.

The length of an arc can be calculated by using the formula below:

length of arc = ∅/360 * 2πr, where:

∅ = central angle measure

r = the radius of the circle.

The central angle measure (∅) = 45°

Radius (r) = 12 cm

Plug in the values:

length of arc = 45/360 * 2 * 3.14 * 12

length of arc = 9.42 cm

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An upper bound on the error that can result from approximating cos(x) by 1−(x^2/2!) + (x^4/4!) over the interval [-0.7, 0.7] is 0.00567.

The Taylor series expansion for cos(x) is given by cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + ... . The approximation 1−(x^2/2!) + (x^4/4!) is a truncated version of this series. The error between the actual value of cos(x) and the approximation can be estimated using the Lagrange form of the remainder term, which gives an upper bound on the error.

In this case, the Lagrange remainder term is given by Rn(x) = (f^(n+1)(c)/n+1!) * (x-x0)^(n+1), where f^(n+1)(c) is the (n+1)th derivative of cos(x) evaluated at some point c in the interval [-0.7, 0.7].

The maximum value of Rn(x) over the interval [-0.7, 0.7] occurs when x = ±0.7, and the upper bound on the error is found by evaluating Rn(±0.7).

The resulting upper bound is approximately 0.00567.

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The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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The process to sketch the graph of y =  absolute value x is explained below .

What is Absolute Value ?

The absolute value of a number is the distance of the number from origin of a number line. It is denoted as |a|, which defines the magnitude of any integer "a". Absolute Value is represented by two vertical lines "|a|" , which is called as modulus of a .

we have to sketch the graph of the absolute function given as ; y = |x| ;

put x = -2 , we get ⇒ y = 2 ;

put x = 2 , we get ⇒ y = 2 ;

we see that if we put any value of "x" , positive or negative , the result "y" will always be positive .

Therefore , the graph of the function will be a V shaped graph facing upwards .

The given question is incomplete , the complete question is

How do you graph y =  absolute value x ?

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The sequence of transformation for the triangle are:

i. reflection about the y-axis

ii. 2 units translation downwards

iii. 1 unit translation to the right

Rigid transformation is a process of producing the image of a given figure or shape by either reflection, rotation, dilation or translation method. Thus the orientation and size of the figure changes with respect tot the method applied.

For the given question, some sequence were applied to produce the image of ABC.

The sequence are:

i. reflection about the y-axis

ii. 2 units translation downwards

iii. a unit translation to the right

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Answer:

Step-by-step explanation:

Given : QP║RT and QR║US

To prove: ∠1 ≅ ∠5

                Statements                   Reasons

1).   QP║RT                           1). Given

2). QR║US                           2). Given

3). ∠1 ≅ ∠2                           3). Alternate angles

    ∠2 ≅ ∠5                          

4). ∠1 ≅ ∠5                           4). Transitive property

Reasons for third step,

PQ║RT and QR is a transverse therefore, ∠1 and ∠2 will be alternate angles.

Similarly, QR║US and RT is a transverse therefore, ∠2 and ∠5 will be the alternate angles.

Answer:

Step-by-step explanation:

nth term of a sequence = 2n² - 1

Therefore, terms of the sequence will be,

1, 7, 17, 31, 49, ........... n terms

nth term of a different sequence = 40 - n²

Therefore, terms of the sequence will be,

39, 36, 31, 24, 15, 4, -9, -24 .......... n terms  

Since, there is no negative number in the first sequence,

Therefore, out of 6 positive terms of second sequence only one number (31) is common in both the sequences.

Answer:

12 ^ 1/2 or \(\sqrt{12}\)

Step-by-step explanation:

12^2

We want to do the inverse operation, which is the square root

We can write the square root as

^ 1/2  or as \(\sqrt{ }\)

So the inverse of squaring 12 is

12 ^ 1/2 or \(\sqrt{12}\)

=======================================================

Explanation:

Both of these represent the same idea. Square root notation is probably what you're more familiar with. It turns out that raising any positive number to the 1/2 power is the same as a square root. We can write

\(\sqrt{x} = x^{1/2}\)

The 1/2 power notation may seem more clunky or confusing, but its helpful to extend to things like cube roots, fourth roots, etc.

The more general rule is

\(\sqrt[n]{x} = x^{1/n}\)

which says the nth root of x is the same as x^(1/n).

Answer:

c. Three fourths of the data is greater than 65.

Step-by-step explanation:

If 400 people attend the convention,

the food will last for 3 days.

Two quantities a and b are said to be in inverse proportion if an increase in quantity a, there will be a decrease in quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant.  Sometimes, it is also known as inverse variation.

That is, if ab = k, then a and b are said to vary inversely. In this case, if b1, b2 are the values of b corresponding to the values a1, a2 of a, respectively then a1 b1 = a2 b2 or a1/a2 = b2 /b1

Given,

Food for 300 people will Last for 4 days.

Attending people = 400

Let the food for 400 will last for x days.

According to the question,

300 × 4 = 400 × x

x = 300 × 4 /400

x = 3

Hence, the food will last 3 days,

if 400 people attend the convention.

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A terminating decimal only happens when the fraction has a denominator with factors of 2 and/or 5. No other factors are allowed (other than 1).

Something like 1/12 has the denominator 12 with factors 2*2*3. That '3' means we won't have a terminating decimal. Similarly, the fractions 2/9 and 2/3 won't convert to a terminating decimal either.

3/10 on the other hand does convert to a terminating decimal and 3/10 = 0.3

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that applies to data that is approximately normally distributed. It states that:
Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard deviations of the mean

In the context of your question, where the mean IQ is 100 and the standard deviation is 15, we can use the empirical rule to answer certain questions.
Approximately 68% of individuals would have an IQ between 85 and 115, since this range falls within one standard deviation of the mean.

Approximately 95% of individuals would have an IQ between 70 and 130, since this range falls within two standard deviations of the mean. Approximately 99.7% of individuals would have an IQ between 55 and 145, since this range falls within three standard deviations of the mean.

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Approximately 99.7% of the IQ scores will fall between 55 and 145. The empirical rule, also known as the 68-95-99.7 rule, is a statistical principle that applies to data that follows a normal distribution. It states that:

1. Approximately 68% of the data falls within one standard deviation of the mean.
2. Approximately 95% of the data falls within two standard deviations of the mean.
3. Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the standardized test of intelligence has a mean IQ of 100 and a standard deviation of 15.

1. To determine the range of IQ scores within one standard deviation of the mean, we can use the empirical rule. Since 68% of the data falls within one standard deviation of the mean, we can calculate the range as follows:
  - Lower bound: Mean - Standard deviation = 100 - 15 = 85
  - Upper bound: Mean + Standard deviation = 100 + 15 = 115
  Therefore, approximately 68% of the IQ scores will fall between 85 and 115.

2. To determine the range of IQ scores within two standard deviations of the mean, we can use the empirical rule. Since 95% of the data falls within two standard deviations of the mean, we can calculate the range as follows:
 \(- Lower bound: Mean - (2 \times Standard deviation) = 100 - (2 \times 15) = 70\\- Upper bound: Mean + (2 \times Standard deviation) = 100 + (2 \times 15) = 130\)
  Therefore, approximately 95% of the IQ scores will fall between 70 and 130.

3. To determine the range of IQ scores within three standard deviations of the mean, we can use the empirical rule. Since 99.7% of the data falls within three standard deviations of the mean, we can calculate the range as follows:
 \(- Lower bound: Mean - (3 \times Standard deviation) = 100 - (3 \times 15) = 55\\ -Upper bound: Mean + (3 \times Standard deviation) = 100 + (3 \times 15) = 145\)
  Therefore, approximately 99.7% of the IQ scores will fall between 55 and 145.

These ranges give us an idea of where the majority of IQ scores are likely to fall based on the standard deviation from the mean.

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

The probability value indicates that there is statistical significance in 0.0345 option (a) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

As we know,

Statistical significance is commonly defined as a probability value of 0.05 or even less. P-value can be used in replacement of or in addition to preset levels of confidence when testing the claim.

The value 0.0345 < 0.05

The probability value of 0.0345 indicates that there is statistical significance

Thus, the probability value indicates that there is statistical significance in 0.0345 option (a) is correct.

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