The junior and senior classes at Central High School were asked to choose a destination for a field trip. The results are shown in the given two-way frequency table.


Central High School Field Trip Destination

Amusement Park Museum Broadway Show Total

Juniors 57 21 42 120

Seniors 64 44 58 166

Total 121 65 100 286


What percentage of surveyed students chose the amusement park?


A.

38.55%

B.

47.50%

C.

19.93%

D.

42.31%

Answer:

B Barney stops less than a foot from the car.

Step-by-step explanation:

From the information given:

The initial speed of barney \(v_o\) = 25 mph

Coefficient of friction \(\mu\) = 0.7

Recall that

1 mph = 0.447 m/s

Then

\(v_o\) = 25 × 0.447 m/s

\(v_o\) = 11.175 m/s

The force of friction acting on the barney is expressed as:

\(F = \mu N \\ \\ F = \mu mg\)

\(ma = \mu mg\)

\(a = \mu g\)

a = 0.7 × 9.8 m/s

a = 6.86 m/s²

Since the force acts in an opposite direction to the motion of Barney, Thus the acceleration must also be negative.

a = -6.86 m/s²

Now;

Suppose Barney stops after traveling a  distance (s), so that the final speed is zero.

Then;

Using the kinematic equation;

\(v^2 - v_o^2 = 2as\)

\(0 - (11.17)^2 = 2 \times (-6.86) s\)

\(-124.76 = -13.72 s\)

\(s = \dfrac{124.76}{13.72}\)

s = 9.09 m

Recall that;

1 m = 3.28 ft

So;

s = 9.09 m = 9.09 × 3.28 ft

s = 29.81 ft

∴

The distance traveled by the Barney is 29.81 ft which implies that Barney stops less than a foot from the car.

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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Answer:

Option C.

Step-by-step explanation:

It is given that,

\(P(A)=\dfrac{1}{4}\)

\(P(B)=\dfrac{13}{20}\)

It is given that events A and B are mutually exclusive. It means they have no common elements.

\(P(A\cap B)=0\)

We know that,

\(P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

On substituting the values, we get

\(P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0\)

\(P(A\cup B)=\dfrac{5+13}{20}\)

\(P(A\cup B)=\dfrac{18}{20}\)

\(P(A\cup B)=\dfrac{9}{10}\)

Therefore, the correct option is C.

The P (A or B) should be \(\frac{9}{10}\)

Given that,

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

\(= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}\)

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

The fundraiser did not raise more money this year compared to last year.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying by 100.

The percentage change is also calculated using the same method.

In percentage change we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

To determine if the fundraiser raised more money this year, we need to compare the amount raised this year to the amount raised last year.

Let's assume that the amount raised last year was $100.

If the fundraiser raised 120% of last year's goal.

Then the amount raised this year.

= 120% x $100

= 120/100 x 100

= $120

Now,

Let's assume that the goal for this year was $200.

If the fundraiser raised 25% of this year's goal.

Then the amount raised this year.

= 25% x $200

= 25/100 x 200

= $50

We can see that,

The fundraiser did not raise more money this year.

Thus,

The fundraiser did not raise more money this year compared to last year.

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The fuel consumption per liter of Lilly's car is  12.5 kilometers per liter .

Average mileage The average mileage of a vehicle is the ratio of the distance traveled by the vehicle and the total amount of fuel used for that distance.

You can specify:

where (d) is the distance traveled and (n) is the fuel consumption.

Lily's car consumes 8 liters per 100km. This is your car's mileage or efficiency.

average mileage = 100/8 = 12.5 kilometers per liter

Therefore, the fuel efficiency in kilometers per liter of a Lily car with a fuel efficiency of 8 liters per 100 kilometers is 12.5 kilometers per liter.

Complete Question - Lily’s car has a fuel efficiency of 8 liters per 100 kilometers. What is the fuel efficiency of Lily’s car in kilometers per liter ?

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this is the answer

(x+x+10)*2=4x+20

(a) After 1 minute, the airplane will reach an altitude of approximately 9,564.9 feet.

(b) It will take the plane approximately 36.4 seconds to climb to an altitude of 10,000 feet.

(a) To find the plane's altitude after 1 minute, we need to calculate the vertical distance traveled during that time. The vertical distance can be determined using the formula:

Vertical Distance = Speed × Time × sin(Angle)

Given that the speed is 275 feet per second, the time is 1 minute (or 60 seconds), and the angle of ascent is 18°, we can substitute these values into the formula:

Vertical Distance = 275 ft/s × 60 s × sin(18°) ≈ 9,564.9 feet

Therefore, after 1 minute, the airplane will reach an altitude of approximately 9,564.9 feet.

(b) To determine the time it takes for the plane to climb to an altitude of 10,000 feet, we need to rearrange the formula:

Time = Vertical Distance / (Speed × sin(Angle))

Substituting the given values into the formula:

Time = 10,000 ft / (275 ft/s × sin(18°)) ≈ 36.4 seconds

Thus, it will take the plane approximately 36.4 seconds to climb to an altitude of 10,000 feet.

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Answer:it is 32

Step-by-step explanation:

48-16=32

The smallest number among the given options is 0.07.

To determine the smallest number, we compare the given options. Among the numbers 0.5, 0.17, 0.07, 1.7, and 0.071, the smallest number is 0.07. This can be determined by examining the decimal places. The number 0.07 has the fewest decimal places and is the smallest value.

When comparing decimal numbers, the digits after the decimal point are crucial.

In this case, we observe that 0.07 has the smallest digit in the hundredths place, while the other numbers have larger digits in that place. Therefore, 0.07 is the smallest number among the given options.

It is important to note that the order of magnitude (the number before the decimal point) does not affect the comparison when determining the smallest number among decimal values.

In summary, by comparing the decimal places, we find that 0.07 is the smallest number among the given options.

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Answer:

x=4, y=4

Step-by-step explanation:

X=(4+8y)/9

-6×(4+8y)/9 +6y=0

-2×(4+8y)/3+ 6y=0

-2×(4+8y) + 18y =0

-8-16y+18y=0

2y=8

y=4

-6x+6×4=0

-6x=-24

x=4

Answer:

y = (-4)

Step-by-step explanation:

Given equation is,

-2y = 4y + 24

By subtracting 4y from both the sides of the equation,

-2y - 4y = (4y + 24) - 4y

-6y = 24

By dividing the equation by (-6),

\(\frac{-6y}{-6}=\frac{24}{-6}\)

y = (-4)

Answer:

1x29

Step-by-step explanation:

The prime factorization of 29 is simply 29 as it is prime number.

Prime factorization is the process of expressing a composite number as a product of its prime factors.

It involves breaking down a number into its constituent prime numbers, which are the building blocks of all other positive integers.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Since 29 is a prime number, it cannot be further factored into smaller prime factors.

Therefore, the prime factorization is 29.

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The solution to the equation is n = -2.

To solve the equation 30 = -5(6n + 6) step-by-step, follow these procedures:

Step 1: Distribute the -5 on the right side:

30 = -5 * 6n - 5 * 6

Step 2: Simplify the right side:

30 = -30n - 30

Step 3: Move constant term to one side:

30 + 30 = -30n

Step 4: Combine like terms:

60 = -30n

Step 5: Divide both sides by -30 to isolate 'n':

n = 60 / -30

Step 6: Simplify the right side:

n = -2

The solution to the equation is n = -2.

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The sum of all two-digit numbers such that the tens digit is one less than the units digit is 495.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

Let's represent the tens digit "x" and the units digit "y".

According to the question, x = y - 1.

The two-digit number can be written as 10x + y. Substituting x = y - 1, we get:

10x + y = 10(y - 1) + y

10x + y = 11y - 10

To find all the two-digit numbers where the tens digit is one less than the units digit, we need to find all values of y that make the expression 10x + y = 11y - 10 a two-digit number. This means that 10x + y must be greater than or equal to 10 and less than or equal to 99.

Simplifying the equation, we get:

10x - 10 = 10y - y

10x + 9 = 11y

y = (10x + 9)/11

Since y is a digit, x must take on integer values that make y an integer between 0 and 9. Solving for x, we get:

x = (11y - 9)/10

Plugging in the possible integer values for y between 0 and 9, we get the following values for x:

x = 0, y = 1

x = 1, y = 2

x = 2, y = 3

x = 3, y = 4

x = 4, y = 5

x = 5, y = 6

x = 6, y = 7

x = 7, y = 8

x = 8, y = 9

For each pair of x and y values, we can find the corresponding two-digit number by multiplying x by 10 and adding y. The sum of all these two-digit numbers is:

10(0) + 1 + 10(1) + 2 + 10(2) + 3 + 10(3) + 4 + 10(4) + 5 + 10(5) + 6 + 10(6) + 7 + 10(7) + 8 + 10(8) + 9

Simplifying the expression, we get:

10(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

= 10(45) + 45

= 495

Therefore, the sum of all two-digit numbers such that the tens digit is one less than the units digit is 495.

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Answer:

P = 48°

Step-by-step explanation:

Its an isosceles triangle so angle M and angle N are the same since they are the opposite angles to the sides that have the same measurement. so it would

180 - (66)2 = angle P

Sorry if you dont understand what i mean

If the histogram shows a bell-shaped curve and the normality test (if performed) supports the normality assumption, it appears safe to assume that the normality condition is satisfied for the wood pieces prepared for the lab session, considering them as an SRS of all similar pieces of Douglas fir.

To determine if the normality condition is satisfied, you can follow these steps:

1. Organize the data: Collect the measurements for the characteristics of the wood pieces in your sample (such as density, strength, etc.) and organize them in a list or a table.

2. Create a frequency distribution: Calculate the frequencies of the different measurements and arrange them in a frequency distribution table.

3. Plot a histogram: Using the frequency distribution, create a histogram to visually represent the data. The x-axis represents the measurements and the y-axis represents the frequency.

4. Evaluate the shape of the histogram: Examine the shape of the histogram to determine if it resembles a normal distribution. A normal distribution is characterized by a bell-shaped curve, which is symmetrical around the mean value.

5. Conduct a normality test (optional): If you want to statistically confirm the normality of the data, you can perform a normality test, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.

For the wood pieces manufactured for the lab session, using them as an SRS of all comparable pieces of Douglas fir, it is acceptable to infer that the normality criterion is satisfied if the histogram displays a bell-shaped curve and the normality test (if performed) confirms the normality assumption.

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The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.

The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.

Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.

The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.

Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .

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\(vertex \: from \: y \: = - 4(x - 2) {}^{2} + 3\)

Therefore , the solution of the given problem of expression comes out to be  =C3 by using this formula, the spreadsheet is instructed to show the value in column C3.

Mathematical processes like multiplying, dividing, addition, and subtracting are essential. Combining them would result in the following phrase: An equation, some information, and a mathematical function Values, variables, and functions, such as additions, subtractions, multiplications, and divisions, are the building blocks of a statement of truth. Words and sentences can be contrasted and compared.

Here,

Simply type the following formula into the formula bar to show the value of cell 3 in a chosen cell:

=C3

By using this formula, the spreadsheet is instructed to show the value in column C3.

You can change "C3" to the complex number of the cell whose value you want to show.

Make sure the formula is written in the proper cell and that the cell reference is accurate.

The formula would then calculate and display a value from the designated cell in the chosen cell after you hit the Enter key.

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Answer:

Option (3)

Step-by-step explanation:

There are two parallel line m and n.

A transverse 'p' is intersection these parallel lines.

Pair of corresponding angles between these parallel lines are,

Angle 3 and angle 7

Angle 2 and angle 6.

Similarly, angle 4 and angle 9 are also a pair of corresponding angles.

Therefore, from the given options, Option (3) is the correct option.

In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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Answer:

C

.........................

Answer:

a

Step-by-step explanation:

Answer:

4 3/10

Step-by-step explanation:

Answer:

4 3/10

Step-by-step explanation:

The optimal number of pots and plates Josh should make is given from

the graph of the inequalities.

Response:

a. 2·p + a ≤ 50

p ≤ 24

a ≤ 40

b. The coordinates of the vertices of the feasible region are; (24, 2), (40, 5), (0, 40), (24, 0), (0, 0)

c. 40 pots and 5 plates

Given:

Number of days Josh has to make pots and plates to sell = 8 days

Weight of each pot = 2 pounds

Weight of each plate = 1 pound

Weight Josh cannot carry = More than 50 pounds

Number plates he can make each da = At most 5 plates

Number of pots he can make each day = At most 5 pots

The profit Josh makes for each plate sold = $12

Profit from each pot sold = $25

a. Let p represent the number of pots Josh makes and let a represent the

number plates. The linear inequalities are;

2·p + a ≤ 50

p ≤ 8 × 3 = 24

p ≤ 24

a ≤ 5 × 8 = 40

a ≤ 40

b. When p = 24, we have;

2 × 24 + a = 50

a = 2

When a = 40, 2·p + 40 = 50, gives;

p = 5

The vertex points are;

The coordinates of the vertices of the feasible region are;

(24, 2), (40, 5), (0, 40), (24, 0), (0, 0)

c. The profit function is; P = 25·p + 12·a

The profit at the vertices are;

\(\begin{tabular}{|c|c|c|}p&a&Profit\\0&0&0\\0&40&12 \times 40 = 480\\24&0&25 \times 24 = 600\\24&2&12 \times 2 + 25 \times 40 = 624\\40&5&12 \times 5 + 25 \times 40 = 660\end{array}\right]\)

To maximize his potential profit, therefore;

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To approach this type of problem, you have to make a couple of reasonable assumptions - first, that each worker works at the same pace, and second, that the effort to build each wall is the same.

Next, figure out how much effort is required to build one wall. The effort is measured in “working days”. So, how many days does one worker need to build one wall, or how many workers would be required to build one wall in one day? We can calculate this by dividing the 25 worker days used to build five walls by the number of walls (5). So we need five worker days per wall.

(5 workers) x (5 days) = 25 worker-days;

25 worker days/5 walls = 5 worker days per wall.

With 100 workers, it will take five days to build 100 walls. Each worker will build one wall in 5 days. So it will also take 5 days for all 100 workers to build all 100 walls.

100 x 5 = 500 worker days;

500 worker-days / 100 workers = 5 days (answer)

Answer: x=10 and y=25

Step-by-step explanation:

ok, so since we know straight angles=180 degrees, so since one part=100, the other smaller angle=80. This means that 11x-30=80 and 5y-25=100. 11*10=110, and 110-30=80, so x=10. 5*25=125, and 125-25=100, so y=25. And lol. me too. When I used to do these problems, I was stuck for a very, very long time. Just try to use logic most of the time.

Answer:

y = 25 and x = 10

Step-by-step explanation:

the angles on top and on bottom are equal so...

5y - 25 = 100

5y - 25 + 25 = 100 + 25

5y = 125

5y/5 = 125/5

y = 25

Every line is 180 degrees so we know that if the top and bottom angles are 100 then the other angles need to equal 80

11x - 30 = 80

11x - 30 + 30  = 80 + 30

11x = 110

11x/11 = 110/11

x = 10

Can you please copy and paste it here?
-
I cannot read it clearly.