Find an equation of the line that passes through the points (-3, 4) and (0, 7)

Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

\(P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\\)
This is 25% (for each one, equally)

b) The experimental probability is given by:

\(P(A)= \frac{32}{150} =0.2133\)

\(P(B)= \frac{38}{150} =0.2533\)

\(P(C)= \frac{35}{150} =0.2333\)
\(P(D)= \frac{45}{150} =0.3000\)

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

Answer:

Original equation: 6x=216

Divide by 6: x=36

Let me know if this helps!

Answer:

If 216 = 6x then x = 216/6

216/6 = 36

x = 36

Step-by-step explanation:

Answer:

(-4,-9)

Step-by-step explanation:

multiply (a,b)

Answer:

Step-by-step explanation:

well if you know the term than you know the pattern

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.

From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.

This is an arithmetic sequence and will be expressed as:

= a + (n - 1)d

a = first term = 33

d = common difference = 6

n = 8

This will be:

= a + (n - 1)d

= 33 + (8 - 1)6

= 33 + (7 × 6)

= 33 + 42

= 75

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Answer:

D. all real numbers

Step-by-step explanation:

i think this is the answer sorry if you get it wrong.

Answer: 849309

Step-by-step explanation:

Answer:

\( \frac{1}{3} x + \frac{1}{2} \)

This is the answer after simplifying

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

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Answer:

1. Probability of drinking tea and finishing the lecture early = 0.2 * 0.2 = 0.04 or 4%

2. Probability of finishing the lecture early = 50% (0.3 + 0.2).

3. Probability of drinking coffee = 0.21 or 21% (0.7 * 0.3)

Step-by-step explanation:

a) Data and Calculations:

            Probability   Early Ending    Expected Probability

Coffee     0.7               0.3                     0.21

Tea          0.2               0.2                    0.04

Water      0.1                

b) The probability of drinking coffee, tea, or water is the chance that the lecturer drinks either coffee or tea or water.  The combined probability of the three actions is always 1.  The expected probability is the weighing of the probabilities with another event, ending the lecture early.  This is obtained by multiplying their respective probabilities.

Answer:

15.98 dollars

Step-by-step explanation:

its really easy

we need to subtract the total amount that she has spent from the total amount that she had in her purse

the total amount in Megan's purse=$45.12

total amount that Megan spent=$7.89+$21.25 =$29.14

now,

the exact amount that Megan has left = $45.12-$29.14=$15.98

Step-by-step explanation:

3^2x = 11

we take the logarithm (to the base of 3) of both sides.

log3(3^2x) = log3(11)

2x = log3(11) = log(11)/log(3)

x = log(11)/log(3) / 2 = log(11)/(2×log(3)) =

= 1.091329169... ≈ 1.09

Answer:

3^2x = 11

we take the logarithm (to the base of 3) of both sides.

log3(3^2x) = log3(11)

2x = log3(11) = log(11)/log(3)

x = log(11)/log(3) / 2 = log(11)/(2×log(3)) =

= 1.091329169... ≈ 1.09

Step-by-step explanation:

Answer:

the one complete circuit of the track is 600 meters

Step-by-step explanation:

divide the 2.4 kilometers by 4 which gives you your answer.

2.4 kilometers = 2,400 meters

2,400/4 = 600

Answer:

600 m

Step-by-step explanation:

4 times around track = 2.4 km

2 times around track = 1.2 km

1 time around track = 0.6 km

0.6 km = 600 m

The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

\(0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70\)

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

\(s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }\)

Where \(X_{mean}\) is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate \((X - X_{mean})^2\)for each data point and sum up the values:

\((0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36\)

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

\(\sqrt{1.31} = 1.15\)

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

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The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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The probability of randomly selecting socks that are not blue is 1/6.

A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.

To get it, we will calculate number of favorable outcomes of socks that are not blue and divide by number of possible outcomes.

Out of 3 colors (purple, blue, orange), there are 2 colors (purple, orange) that are not blue. As we are selecting socks, there is only 1 option for the piece of clothing, so, number of favorable outcomes is 2.

The total number of possible outcomes is:

= 4 * 3

= 12.

Probability of selecting socks that are not blue is:

= Number of favorable outcomes / Total number of possible outcomes

= 2 / 12

= 1/6.

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Answer: 18.18%

Step-by-step explanation:

First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:

\($$SA = 2lw + 2lh + 2wh$$\)

where \(\(l\)\) is the length, \(\(l\)\) is the width, and \(\(h\)\) is the height. For the original piece of wood, \(\(l = 10\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\).

After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, \(\(l = 5\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\). The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.

The percent increase in the total surface area is given by the formula:

\($$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$\)

Let's calculate these values.

The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.

\(\begin{aligned}\frac{5}{8}-\frac{1}{3}&=\frac{15-8}{24}\\&=\bf\frac{7}{24}\end{aligned}\)

The expression, in the end, is 10 x 3 = 30

i.e

Length = 10

Width = 3

The number of tiles = 10 x 3 = 30

We have,

We see that,

The number of tiles:

18, 24, 30,

This is an arithmetic sequence.

So,

The next term:

= 30 + 6

= 36

Now,

The length is a sequence in ascending order of the factor of the arithmetic sequence.

So,

30 is a factor of 2, 3, 5, 6, and 10.

This means,

The expression, in the end, is 10 x 3 = 30

So,

Length = 10

Width = 3

The number of tiles = 10 x 3 = 30

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Answer:

$8,888

Step-by-step explanation:

if he makes $35,876, then to find out the amount he has left, you jsut need to take away the expenses which would be $26,988. When you do the math, he has $8,888 left.

Answer:

7/8

Step-by-step explanation:

Answer:

1/4 x 7/2

First, let's convert each fraction into percentages.

1/4= 25%

7/2= 350%

Now just multiply them together.

25x350= 8750

Convert it back into a fraction.

8750% = 175/2 = 871/2 as a fraction.

Hope this helps!

Answer:

19/99

yes this is the answer