Which is precisely defined using the undifined terms point and plane

Solution:

The total cost will be the sum of money spent on tickets and on soda and popcorn.

Ticket cost for:

5 year old brother = $4.25.

Grandparents = 2x($6.00)=$12.00

Myself=$7.25.

Total cost of tickets= $4.25+$12.00+$7.25=$23.50

Total money spent= Cost of ticket + cost of soda popcorn= $23.50+$20=$43.50

Total money spent=$43.50.

To find the relative frequency of applicants whose score X is less than 500 on the quantitative GRE, calculate the Z-score for 500 and find the corresponding area under the standard normal curve.

To find the relative frequency of applicants whose score X is less than 500, we need to calculate the Z-score for 500. The formula for calculating the Z-score is: Z = (X - mean) / standard deviation. Plugging in the values, we get Z = (500 - 544) / 103 = -0.427.

Next, we need to find the corresponding area under the standard normal curve for the Z-score of -0.427. Using a calculator or a standard normal table, we find that the area to the left of -0.427 is approximately 0.3356.

Therefore, the relative frequency of applicants whose score is less than 500 is 0.3356, or 33.56%.

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The given in this problem are:

99% confidence level

N = 61

Mean = 2.0 kg

Standard deviation = 4.8

Z value for a 9% confidence interval is 2.576

Confidence Interval = mean ± Z s/ sqrt n

= 2.0 ± 2.576(4.8/sqrt 61)

=2.0 ± 2.576 (0.6145770236779006736364371988794)

= 2.0 ± 1.5832

= 0.4168 < x < 3.5832

The x and y intercept of the given line is required,

The x intercept is [tex](6.2,0)[/tex]

The y intercept is [tex](0,3.1)[/tex]

The given line is [tex]2x+4y=12.4[/tex]

x intercept [tex]y=0[/tex]

[tex]2x+4\times 0=12.4\\\Rightarrow x=\dfrac{12.4}{2}\\\Rightarrow x=6.2[/tex]

The x intercept is [tex](6.2,0)[/tex]

y intercept [tex]x=0[/tex]

[tex]2\times 0+4y=12.4\\\Rightarrow y=\dfrac{12.4}{4}\\\Rightarrow y=3.1[/tex]

The y intercept is [tex](0,3.1)[/tex]

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Another way is to note that there are (104)(104) (“10 choose 4”) ways to select 4 balls from a collection of 10. If 4 of those 10 balls are “special” in some way (in this case, “special” = “red”), then the number of ways to choose 4 special balls is (44)(44). (The factor of (60)(60) is included to convey that, after choosing 4 special balls, we choose none of the 6 non-special balls.) This line of reasoning gives the second expression.

We want to graph the given function for the given domain.

The graph can be seen at the end of the answer.

The given function is:

y = 2*x

The given domain is D: {-2, 0, 2, 4}

To graph this, we need to evaluate the function in the given values of the domain, we will get four points.

y = 2*(-2) = -4

Then we have the point (-2, -4)

y = 2*0 = 0

Then we have the point (0, 0)

y = 2*2 = 4

Then we have the point (2, 4)

y = 2*4 = 8

Then we have the point (4, 8)

Then we need to graph these four points, the graph can be seen below:

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No, our friend is not correct because the absolute value equation has a solution.

Given that,
Friend says that the absolute value equation ∣3x + 8 ∣ − 9 = −5 has no solution because the constant on the right side of the equation is negative.
It is to justify whether our fried is correct or not.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
|3x + 8 | - 9 = -5
| 3x + 8 | = -5 + 9
| 3x + 8 | = 4
3x + 8 = ± 4
x = (-8 ± 4) / 3
Here, it can be seen that the given aboslute value equation has the solution that implies our friend is wrong.

Thus, no, our friend is not correct.

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To classify shapes, one can use the distance formula to calculate the lengths of a shape's sides and the slope formula to determine angles between sides. Analyzing these measurements helps identify if a shape is a rectangle, square, etc., based on side length equality and perpendicular angles.

Classifying Shapes Using Distance and Slope Formulas

To classify shapes using the distance and slope formulas, you'll need to analyze the lengths of sides and the angles between them. The distance formula helps determine the length of sides by calculating the distance between two points. On the other hand, the slope formula is used to find the inclination of sides, which can indicate whether lines are parallel or perpendicular.

Here's an example. Suppose we have a quadrilateral with vertices at (1,1), (1,4), (5,4), and (5,1). We'd calculate the distance between consecutive vertices to determine if the sides are equal. If the distances are the same, our shape might be a square or a rectangle. Next, we calculate the slopes of adjacent sides using the formula (y2-y1)/(x2-x1) (rise over run). If the slopes of adjacent sides are negative reciprocals of each other, the lines are perpendicular, which is a characteristic of rectangles and squares.

Applying the slope formula to our example, the slope from (1,1) to (1,4) would be (4-1)/(1-1), which is undefined, suggesting a vertical line. Between (1,4) and (5,4), the slope is (4-4)/(5-1), which is 0, indicating a horizontal line. Therefore, the expected behavior for a square's or rectangle's sides is observed. By further calculating all side lengths and slopes, we could definitively classify our shape.

Answer:

B. 150 children

Step-by-step explanation:

Let, number of children  = x and number of adults = y.

Since, total number of people attended the fair are 350.

So, x + y = 350.

Moreover, charges per child is $2 and adult is $3.

As, total sales are given to be $900.

So, 2x + 3y = 900

Thus, we get the system of equations,

2x + 3y = 900

x + y = 350

We will now solve the equations,

x + y = 350 ⇒ y = 350 - x

So, 2x + 3y = 900 ⇒ 2x + 3(350 -x) = 900 ⇒ 2x + 1050 - 3x = 900 ⇒ -x = -150 ⇒ x = 150.

Then, y = 350 - x ⇒ y = 350 - 150 ⇒ y = 200.

Hence, number of children and adults that attended the fair are 150 and 200 respectively.

Answer:

a). m∠4 = 143°

b). m∠2 = 37°

c). ∠4 ≅ ∠8

d). ∠3 + ∠5 ≅ 180°

Step-by-step explanation:

a). Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 37°+ m∠4 = 180°

m∠4 = 180 - 37

        = 143°

b). Since m∠6 ≅ m∠2  [Corresponding angles]

and m∠6 ≅ m∠7 [Vertically opposite angles]

Therefore, m∠2 ≅ m∠6 ≅ m∠7 ≅ 37°

c). ∠4 ≅ ∠8 [Corresponding angles]

d). ∠3 + ∠5 ≅ 180° [Interior angles of parallel lines m, l and a transverse].

Distance from point (-1,1) to line l: [tex]\( \frac{60}{\sqrt{74}} \)[/tex] units.

To find the distance from point P to line l, we can use the formula for the distance between a point and a line in the coordinate plane.

The formula to find the distance from a point (x1, y1) to a line Ax + By + C = 0 is given by:

[tex]\[ \text{Distance} = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}} \][/tex]

Where A, B, and C are the coefficients of the equation of the line, and (x1, y1) are the coordinates of the point.

First, let's find the equation of the line passing through the points (11, -1) and (-3, -11).

The slope of the line, m, can be calculated using the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

[tex]\[ m = \frac{-11 - (-1)}{-3 - 11} = \frac{-11 + 1}{-3 - 11} = \frac{-10}{-14} = \frac{5}{7} \][/tex]

Now, we have the slope of the line. We can use the point-slope form of the equation of a line:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Using one of the given points, let's say (11, -1):

[tex]\[ y - (-1) = \frac{5}{7}(x - 11) \][/tex]

[tex]\[ y + 1 = \frac{5}{7}(x - 11) \][/tex]

Now, let's convert this equation into the standard form Ax + By + C = 0:

[tex]\[ \frac{5}{7}x - y - \frac{5}{7} \cdot 11 + 1 = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{55}{7} + 1 = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{55}{7} + \frac{7}{7} = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{48}{7} = 0 \][/tex]

Now, we have the equation of line l:[tex]\(\frac{5}{7}x - y - \frac{48}{7} = 0\)[/tex]

Now, we can plug in the coordinates of point P (-1, 1) into the formula for the distance:

[tex]\[ \text{Distance} = \frac{| \frac{5}{7}(-1) - 1 - \frac{48}{7} |}{\sqrt{(\frac{5}{7})^2 + (-1)^2}} \][/tex]

[tex]\[ = \frac{| -\frac{5}{7} - 1 - \frac{48}{7} |}{\sqrt{\frac{25}{49} + 1}} \][/tex]

[tex]\[ = \frac{| -\frac{5}{7} - \frac{7}{7} - \frac{48}{7} |}{\sqrt{\frac{25 + 49}{49}}} \][/tex]

[tex]\[ = \frac{| -\frac{60}{7} |}{\sqrt{\frac{74}{49}}} \][/tex]

[tex]\[ = \frac{\frac{60}{7}}{\frac{\sqrt{74}}{7}} \][/tex]

[tex]\[ = \frac{60}{\sqrt{74}} \][/tex]

So, the distance from point P to line l is [tex]\(\frac{60}{\sqrt{74}}\)[/tex] units.

Answer:

75 miles/hour

Step-by-step explanation:

Given information: d=337.5 miles and t=4.5 hours.

The given formula is

[tex]r=\frac{d}{t}[/tex]

where d is the distance in miles, r is the rate, and t is the time in hours.

We need to find the rate for d=337.5 miles and t=4.5 hours.

Substitute d=337.5 and t=4.5 in the above formula.

[tex]r=\frac{337.5}{4.5}[/tex]

[tex]r=75[/tex]

The value of r is 75, therefore we need to travel at the rate of 75 miles per hours to cover 337.5 miles in 4.5 hours.

Answer:

[tex]7\cdot g-3 = 42[/tex]

Step-by-step explanation:

As the first three guest are three and each aditional guest costs $ 7 dollars. The formula is presented as follows:

[tex]7\cdot (g-3) = 42[/tex]

Or:

[tex]7\cdot g = 63[/tex]

Or:

[tex]g = 9[/tex]

The wrong equation is:

[tex]7\cdot g-3 = 42[/tex]

The value of k in the expression is 12.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify the given expression, we first need to expand the second term using the distributive property:

(x + 8)(x - 4) = x² - 4x + 8x - 32 = x² + 4x - 32

Now we can substitute this expression into the original expression:

x² + 16x + 64 - (x² + 4x - 32)

Simplifying further, we can combine like terms:

12x + 96

Now we can see that the expression can be rewritten as:

12(x + 8)

So the value of k is 12.

Thus,

The value of k is 12.

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Justin and his wife should focus on ( b) managing liquidity, as their savings are not sufficient to cover emergencies or unexpected expenses.

Based on the information provided, the area Justin and his wife should work on is b. managing liquidity. Justin's family has a set income from both his and his wife's jobs, and they have basic insurance coverage and are contributing to retirement. However, the fact that they have a relatively low balance in savings compared to their monthly outflow suggests that they may face challenges if unexpected expenses arise or if there is a disruption in their income. It’s important for them to focus on building a larger emergency fund to cover at least three to six months of living expenses to ensure they have sufficient cash on hand to handle unforeseen situations without jeopardizing their financial stability.

Answer:

Step-by-step explanation:

We have the length of AC which is opposite angle B; we also have the length of the hypotenuse.  We will use trig here to solve for angle B.  The sin ratio is the one that fits.

sin(B) = side opposite / hypotenuse:

[tex]sin(B)= \frac{ 4.8}{ 5.1}[/tex] so

sin(B) = .9411764706

Now we will use the 2nd button on our calculators.  This will give us the missing angle value.  Press 2nd then sin and you will see on your screen:

[tex]sin^{-1 ([/tex]

Enter that decimal after the open parenthesis and hit "enter" to get

B = 70.25 or 70°