if there are 220 members of the 7th grade class then how many students can be expected to prefer the zoo

Answers

Answer 1

66 students can be expected to prefer the zoo in 220 members of the 7th grade class.

What are the median, mode, and mean?

Different techniques are used to calculate the averages of data sets for mean, median, mode, and range. The mean represents the sum of all the numbers. In an ordered list, the middle number is the median. The most frequent number is the mode. The highest number less the smallest number is the range.

The provided table contains the percentage of 7th graders who favor the zoo. Twelve of the 40 7th graders who were sampled prefer the zoo. Out of the 220 pupils in the 7th grade, we can use this proportion to determine how many love the zoo:

12/40 or 0.3 of 7th students say they prefer going to the zoo.

The predicted proportion of seventh graders who prefer the zoo is 0.3 x 220, or 66.

So, 66 is the correct response.

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Complete question is :

--------------------------------------------------------------------

Grade      Zoo   Museum   Sports Complex

--------------------------------------------------------------------

7 Grade      12        18             10

8 Grade      14        19               7

--------------------------------------------------------------------

A random sample of 40 students from each grade level was surveyed regarding their preference for a class field trip.

If there are 220 members of the 7th grade class, then how many students can be expected to prefer the zoo?

394812066

Related Questions

Really need help !!!!!! Give u brainlyist

Answers

Applying the triangle proportionality theorem, the measure of side FD in the image is calculated as: FD = 13.6.

What is the Triangle Proportionality Theorem?

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Use the triangle proportionality theorem to find AB:

AB/BC = AE/ED

Substitute:

AB/12 = 6/9

AB = (12 * 6) / 9

AB = 8

Find CD using the Pythagorean theorem:

CD = √(AC² - AD²)

Substitute:

CD = √(20² - 15²)

CD = 13.2

Since ΔACD ~ ΔDFC, therefore their sides are proportional:

AC/FD= CD/FC

Substitute:

20/FD= 13.2/9

FD= (20 * 9) / 13.2

FD = 13.6

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If there is a positive correlation between number of hours spent studying and exam grades, then the _____ time people spend studying, the _____ their exam grades.
less; higher





b.

more; higher





c.

none of the above.



d.
more; lower

Answers

b. more; higher

A positive correlation means that as one variable (in this case, hours spent studying) increases, the other variable (exam grades) also increases. Therefore, the more time people spend studying, the higher their exam grades will be. So the answer is "more; higher."

Athena was making cupcakes she made 3 dozen cupcakes in 1 1/2 hours Wich of the following represent the same constant rate of change as Athena’s pick 2 answers

Answers

24 cupcakes in 1 hour and 18 cupcakes in 3/4 hour (or 45 minutes) both have same rate of change.

What is rate of change?

The rate of change refers to the speed at which a variable or quantity changes over a given period of time. It is often expressed in terms of units per time, such as meters per second or dollars per year. The rate of change can be positive or negative, depending on whether the variable is increasing or decreasing.

What is constant rate?

A constant rate refers to a fixed or unchanging rate of change over time. In other words, it is a steady and consistent rate that does not fluctuate or vary. This term is commonly used in mathematics and finance to describe situations where a value or quantity changes at a constant rate over a given period of time.

Athena made 3 dozen cupcakes in 1 1/2 hours. To find the constant rate of change, we need to determine the number of cupcakes she made per hour.

1 dozen = 12 cupcakes

So, Athena made 3 dozen cupcakes = 3 x 12 = 36 cupcakes.

Constant rate of change = Cupcakes made / Time taken

Option 1: 24 cupcakes in 1 hour

Option 2: 18 cupcakes in 3/4 hour (or 45 minutes)

Both options represent the same constant rate of change as Athena's, which is 36 cupcakes per hour.

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Match the term to the correct value for the data set.
{12, 16, 3, 18, 5, 5, 9, 11, 15, 8, 10, 21, 17, 19, 23, 14}
Median
8.5
First Quartile
17.5
Third Quartile
13

Answers

Answer:

Step-by-step explanation:

Median: C) 13

First Quartile: A) 8.5

Third Quartile: B) 17.5

Explanation:

To find the median, we need to arrange the numbers in ascending order:

{3, 5, 5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(10 + 11)/2 = 10.5.

To find the first quartile, we need to find the median of the lower half of the data set.

The lower half is {3, 5, 5, 8, 9, 10, 11, 12}.

Since there are an even number of values, we take the average of the middle two numbers:

(8 + 9)/2 = 8.5.

To find the third quartile, we need to find the median of the upper half of the data set.

The upper half is {14, 15, 16, 17, 18, 19, 21, 23}.

Since there are an even number of values, we take the average of the middle two numbers:

(17 + 18)/2 = 17.5.

A lot is in the shape of a trapezoid. The sum of the bases is 280 feet. If the area of the lot is 8,400 square feet, what is the distance across the lot, i.e. the altitude of the figure?

Answers

The distance across the lot, or the altitude of the trapezoid, is 60 feet.

What is the distance?

Let's denote the length of the shorter base by x, and the length of the longer base by y. Then, we can use the formula for the area of a trapezoid:

Area = (x + y) * h / 2,

where h is the altitude (distance across the lot) and Area is given as 8,400 square feet.

We also know that the sum of the bases is 280 feet, so x + y = 280.

Now we can solve for h:

h = 2 x  Area / (x + y)

Substituting the given values, we get:

h = 2 x  8,400 / 280 = 60 feet.

Therefore, the distance across the lot, or the altitude of the trapezoid, is 60 feet.

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trigonometry problems help pls

Answers

Answer:

The value for theta is 16.7 degrees and that of alpha is 73.3 degrees.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.

To find alpha, we can take the inverse tangent of both sides of the equation:

tan α = 10/3

tan⁻¹(tan α) = tan⁻¹(10/3)

α = tan⁻¹(10/3)

Using a calculator, we get:

α ≈ 73.3 degrees (rounded to one decimal place)

Therefore, the value of alpha is approximately 73.3 degrees.

To find theta, we can take the inverse tangent of both sides of the equation:

tan θ = 3/10

tan⁻¹(tan θ) = tan⁻¹(3/10)

θ = tan⁻¹(3/10)

Using a calculator, we get:

θ ≈ 16.7 degrees (rounded to one decimal place)

Therefore, the value of theta is approximately 16.7 degrees.\

Step-by-step explanation:

Question 3(Multiple Choice Worth 1 points)
(05.02 MC)
Solve the system of equations using substitution.
4x + 2y = 6
x = 2y + 4
(1, 1)
(2,-1)
(8,2)
(10,3)

Answers

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

Aaron, Bob and Casper had some marbles. Aaron had ⅙ of the marbles. Bob had 6 marbles more than Aaron. Casper had 18 marbles. How many marbles did they have altogether?​

Answers

Answer:

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.Converting to a mixed number, they had 16 2/3 marbles altogether.

The skid marks for a car involved in an accident measured 216ft. Use the formula s=24d−−−√ to find the speed, s, of the car before the brakes were applied.

Answers

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

The speed (cοmmοnly referred tο as v) οf an οbject is the magnitude οf the change οf its pοsitiοn οver time οr the magnitude οf the change οf its pοsitiοn per unit οf time; it is thus a scalar quantity.

The average speed οf an οbject in an interval οf time is the distance travelled by the οbject divided by the duratiοn οf the interval the instantaneοus speed is the limit οf the average speed as the duratiοn οf the time interval apprοaches zerο. Speed is nοt the same as velοcity.

Here,

The 216-fοοt length οf the car's skid marks is all that is presented tο us. The speed οf the car befοre the brakes were applied can be calculated using the fοrmula s = 24d(1/2), where s is the speed οf the car in miles per hοur (mph) and d is the length οf the skid marks in feet.

When we replace the specified value οf d, we οbtain:

=> s = 24√(216)

=> s = 24(14.6969)

=> s = 352.7256

Thus, the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

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Please help me! Please!

Answers

In the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

What is sample space?

A sample space is a set of potential results from a random experiment.

The letter "S" is used to denote the sample space.

Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results.

There are just two possible results when we toss a coin: either head or tail.

So, S = H, T, where H is the head and T is the tail, will be the sample space.

As a result, we are aware that there will be a total of 2n outcomes available if there are 'n' coins.

So, the coin has 2 outcomes which are H and T.

And the spinner has 8 outcomes which are 1 - 8.

Then, the sample space would be as follows:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

So, the sample space has a total of 16 elements.

Therefore, in the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

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Solve: (x-5)^2 +5=49

Answers

Answer:

Step-by-step explanation:

(x-5)^2 +5=49

(x-5)(x-5)+5=49

x^2-10x+25+5=49

x^2-10x-19 -  quadratic formula

2[tex]\sqrt{11}[/tex]+5 and -2[tex]\sqrt{11}[/tex]+5

Step-by-step explanation:

(x-5)² + 5 =49

(x-5)(x-5) + 5 = 49

(x² - 5x -5x + 25) + 5 = 49

x² - 10x + 25 + 5 = 49

x² - 10x + 30 =49

x² - 10x = 19

x² - 10x - 19 = 0( USING QÜÃDRATÏC FØRMÛLÂ)

2√11 +5 / -2√11 + 5

~~KIM~~

The population of weights of a particular fruit is normally distributed, with a mean of 317 grams and a standard deviation of 29 grams. If 25 fruits are picked at random, then 5% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

Answers

Answer:

The mean of the sample distribution of sample means will be equal to the population mean, which is 317 grams. The standard deviation of the sample distribution (also called the standard error) will be equal to the population standard deviation divided by the square root of the sample size:

standard error = 29 / sqrt(25) = 5.8

To find the weight at which the mean weight of 25 fruits will be greater than 5% of the time, we need to find the z-score that corresponds to the 95th percentile (since 5% of the time we want the mean weight to be greater than some value). Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 95th percentile is approximately 1.645.

Now we can use the formula for z-scores to find the weight at which the mean weight of 25 fruits will be greater than 5% of the time:

z = (x - mu) / se

where x is the weight we want to find, mu is the population mean (317 grams), and se is the standard error (5.8 grams).

Substituting the values we have:

1.645 = (x - 317) / 5.8

Solving for x, we get:

x = 317 + 1.645 * 5.8 = 326.5

Rounding to the nearest gram, we get that the mean weight of 25 fruits will be greater than 326 grams 5% of the time.

Can anyone help me please

Answers

TTHH
HTH
Explanation :

Lorna uses 7.2 cups of flour in 3 different baking recipes she use an equal of flour in each recipe

Answers

Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

If Lorna uses 7.2 cups of flour in 3 different baking recipes, and uses an equal amount of flour in each recipe, we can find the amount of flour she uses in each recipe by dividing the total amount of flour by the number of recipes:

Flour per recipe = Total flour / Number of recipes

Flour per recipe = 7.2 cups / 3 recipes

Flour per recipe = 2.4 cups per recipe

Therefore, Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

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3. Many grocery stores have machines that will give you cash for your change but charge a fee.

a. Coinstar machines charge an average fee of 11.9% of your coins' value. Write an equation that
models the total fee you pay (y) based on the value of your coins (x) if you use a Coinstar machine.


b. A new company, ChangeMaker, has a coin machine that charges a flat fee, plus 5% of your coins'
value. Write an equation to model the fee you pay (y) based on the value of your coins (x).


c. Imagine you have $13.65 in coins that you want to exchange for bills. How much would you pay in
fees at each machine? Round your answer to the nearest cent.


d. When is the ChangeMaker a better deal than the Coinstar? Why?

Answers

The equation Y = x/100 * 11.9 represents the value of the fee on the value of the coins (x) if we use the container machine.

What are equations?

A mathematical assertion that proves the equality of two mathematical expressions is what an equation in algebra means.

For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the 'equal' sign separating them.

So, we know that the machine charges:

11.9%

Then, the equation that will tell the total charge would be:

Let Y represents the total charge and x be the value of coins.

Then, the equation would be:

Y = x/100 * 11.9


Therefore, the equation Y = x/100 * 11.9 represents the value of the fee on the value of the coins (x) if we use the container machine.

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Correct question:

Many grocery stores have machines that will give you cash for your change but charge a fee. Coinstar machines charge an average fee of 11.9% of your coins' value. Write an equation that models the total fee you pay (y) based on the value of your coins (x) if you use a Coinstar machine.

PLEASE HELP I DON'T UNDERSTAND!!!! ASAPPPPPPPPP
TYYYYYYYYYYYYYYYYY

b) A bag contains six yellow jerseys numbered one to six. The bag also contains four purple jerseys numbered one to four. You randomly pick a jersey. It is purple or has a number greater than five.

Answer with Mutually Exclusive OR Not Mutually Exclusive (Inclusive)

Answers

The events are Not Mutually Exclusive (Inclusive)

How to determine if the events are  Mutually Exclusive

The concept of mutually exclusive events is based on the idea that two events cannot occur at the same time. In other words, the occurrence of one event means that the other event cannot happen.

In the case of the jersey example, the events "picking a purple jersey" and "picking a jersey with a number greater than five" are not mutually exclusive because it is possible to pick a jersey that satisfies both conditions (i.e., a purple jersey with a number greater than five).

On the other hand, if the events were mutually exclusive, it would mean that it is impossible for them to happen at the same time. For example, if we modified the scenario to have only yellow jerseys numbered one to five and purple jerseys numbered six to ten, then the events "picking a purple jersey" and "picking a jersey with a number greater than five" would be mutually exclusive, as no jersey can satisfy both conditions.

Therefore, in the original scenario where the bag contains six yellow jerseys numbered one to six and four purple jerseys numbered one to four, the events are not mutually exclusive (inclusive).

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A contractor leans a 19foot ladder against the side of a building making a safe angle of 65° with the ground. Will the contractor be able to reach the repairs that are 17ft up the wall?

Answers

The contractor will not be able to reach them with this ladder alone.

What is Trigonometric ratio?

Trigonometric ratios are mathematical tools used to relate the angles and sides of a right triangle. These ratios are defined as the ratios of the lengths of two sides of a right triangle to a given angle. There are six basic trigonometric ratios, which are sine, cosine, tangent, cosecant, secant, and cotangent.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

To solve this problem, we need to use trigonometry. Let's call the height the ladder reaches up the wall "h".

We know the length of the ladder is 19 feet and the angle it makes with the ground is 65°.

Using trigonometry, we can find the height the ladder reaches up the wall as follows:

sin(65°) = h/19

Multiplying both sides by 19, we get:

h = 19 × sin(65°)

h ≈ 16.37 feet

So the ladder reaches a height of about 16.37 feet up the wall. Since the repairs are 17 feet up the wall, the contractor will not be able to reach them with this ladder alone.

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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval. Give reasons for your answer

Answers

It is not differential at interval [-2,0].

What is the mean value theorem?

The mean value Theorem basically asserts that there is at least one place where the tangent to the arc is parallel to the secant through its ends for any given planar arc between two endpoints. One of the most significant findings from the serious analysis is this one.

Here, we have

Given: f(x) = [tex]\left \{ {{x^2-x, -2\leq x\leq -1} \atop {2x^2-3x-3, -1 < x\leq 0}} \right.[/tex]

We have to find that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.

We need to check the continuity at -1.

LHL: [tex]\lim_{n \to \ -1} x^2-x[/tex]

= (-1)² -(-1)

= 1 + 1 = 2

RHL:  [tex]\lim_{n \to \ -1} x^2-x[/tex]

= 2(-1)² - 3(-1) -3

= 2 + 3 - 3

= 2

f(-1) = 2

f(x) is continuous at x = -1

Now,

f'(x) = [tex]\left \{ {{2x-1, -2\leq x\leq -1} \atop {4x - 3, -1 < x\leq 0}} \right.[/tex]

LHL: [tex]\lim_{n \to \ -1} 2x - 1[/tex]

= 2(-1) - 1

= -3

RHL: [tex]\lim_{n \to \ -1} 4x - 3[/tex]

= 4(-1) - 3

= -7

∴ LHL ≠ RHL

It is not differential at interval [-2,0]

Hence, it is not differential at interval [-2,0].

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The manager of a home economics stores considering the pricing a new model of digital cameras at a current price of $900 the store sells 70 cameras each month. Sales data from other stores indicate that for each 20 decrease in price five more cameras per month would be sold how much should a manager charge for a camera to maximize monthly values what’s the maximum value

Answers

If the manager of a home economics stores considering the pricing a new model of digital cameras. The maximum revenue is $78,000.

How to find the  maximum revenue?

To find the price that will maximize monthly value, we need to determine the price that will give us the highest revenue. Revenue is given by the formula:

Revenue = Price x Quantity

Let's let x be the number of times the price is decreased by $20 from $900. Then the price of the camera would be:

Price = 900 - 20x

And the quantity sold would be:

Quantity = 70 + 5x

So the revenue would be:

Revenue = (900 - 20x)(70 + 5x)

Expanding this expression gives:

Revenue = 63000 + 1300x - 100x^2

To maximize this quadratic function, we need to find the x-value that corresponds to the vertex of the parabola. The x-value of the vertex is given by:

x = -b/2a

where a = -100, b = 1300, and c = 63000. Substituting these values gives:

x = -1300/(2(-100)) = 6.5

Since we can't decrease the price by a fractional amount, we'll round this down to 6, which means we'll decrease the price by $120. So the price of the camera that maximizes monthly revenue is:

Price = 900 - 20(6) = $780

And the quantity sold at this price is:

Quantity = 70 + 5(6) = 100

So the maximum revenue is:

Revenue = 780(100) = $78,000.

Therefore the revenue is $78,000.

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Question 4(Multiple Choice Worth 1 points)
(05.06 MC)
The following inequalities form a system.
yz²x+1
y<--x+2
Which ordered pair is included in the solution to this system?
(-6, 3.5)
(-6, -3)
(-4,3)
(-4,4)

Answers

Answer:

answer is (C).

Step-by-step explanation:

Substituting y = -x + 2 from the second inequality into the first inequality, we get:

z^2x + 1 < (-x + 2)z^2

Rearranging, we get:

z^2(x + 1) < (-x + 2)z^2 - 1

Dividing both sides by z^2, and noting that z^2 > 0, we get:

x + 1 < (-x + 2) - 1/z^2

Simplifying, we get:

2x < -1/z^2

x < -1/(2z^2)

Therefore, for any value of z, the solution set of the system is the set of all ordered pairs (x, y) where x < -1/(2z^2) and y < -x + 2.

Checking each of the answer choices:

   (-6, 3.5): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.

   (-6, -3): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.

   (-4, 3): In the solution set, since -4 is less than -1/(2z^2) for any value of z, and 3 is less than -(-4) + 2 = 6.

   (-4, 4): Not in the solution set, since -4 is not less than -1/(2z^2) for any value of z.

Therefore, the ordered pair included in the solution set is (-4, 3), and the answer is (C).

Help pls i do not understand this

Answers

Answer:

175 = 25 +4tcost of a ticket: $37.50

Step-by-step explanation:

Given a total expense of $175 for 4 tickets and an included parking fee of $25, you want an equation for the cost of a ticket, and the solution to that equation.

Equation

The total cost is the sum of the items that contribute to that total. Here, the 175 total cost is the sum of 25 and the price of 4 tickets. If we let 't' represent the price of a ticket, we can describe this relation by ...

   175 = 25 + 4t . . . . . . equation for the cost of a ticket

Solution

This is a 2-step linear equation. The two steps to the solution are ...

  Step 1: isolate the variable term by subtracting the constant

     175 -25 = 25 -25 +4t

     150 = 4t

  Step 2: find the value of the variable by dividing by its coefficient

     150/4 = 4t/4

     37.50 = t

This tells us the cost of a ticket is $37.50.

__

Additional comment

"Write an equation that can be used ..." covers a lot of territory. It is simplest to interpret it to mean "describe the given relationships using one or more equations." You are expected to know how costs are added based on your life experience: the total you pay is the sum of the costs of the individual items.

We could write the equation as ...

  t + t + t + t + 25 = 175

Some cashiers will add every item separately like this. Others will enter the price once and tell how many times that price is part of the total:

  4t +25 = 175

Multiplication was invented for the purpose of simplifying repeated addition.

An account earns simple annual interest.

$1500 at 4% for 5 years

a. Find the interest earned.

$

b. Find the balance of the account.

Answers

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Solving our equation:

A = 1500(1 + (0.04 × 5)) = 1800

A = $1,800.00

The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 4% per year for 5 years is $1,800.00.

Looking to see how they got to the answer for number 9?

Answers

The vertex of the graph of the given equation y = x² - x - 2 is calculated as: (1/2, -9/4).

How to Find the Vertex of the Graph of an Equation?

To find the vertex of a parabolic function in the form of y = ax² + bx + c, we use the formula x = -b/2a to find the x-coordinate of the vertex.

In this case, the given equation is y = x² - x - 2, so a = 1, b = -1, and c = -2.

Using the formula, we have:

x = -b/2a = -(-1)/(2*1) = 1/2

To find the y-coordinate of the vertex, we substitute this value of x back into the original equation:

y = (1/2)² - (1/2) - 2 = -9/4

Therefore, the vertex of the equation, y = x² - x - 2, is: (1/2, -9/4).

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Escribe una desigualdad que represente c, la cantidad de velas que necesita vender para pagar Knotts. Explique o muestre su razonamiento

Answers

The inequality that represents c, the number of candles she needs to sell to pay for a visit to Knotts costing $100 when each candle is sold for $5, is expressed as: c ≥ 20.

How to Represent C Using an Inequality?

The inequality c * 5 ≥ 100 is derived from the fact that each candle is sold for $5, so the total amount of money she earns from selling c candles is given by 5c. This amount must be greater than or equal to the cost of the visit, which is $100.

By multiplying both sides of the inequality by 1/5, we get c ≥ 20, which means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Therefore, the answer is: c ≥ 20.

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1. The t statistic, the t distribution, and sample size
The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours.
Suppose you have a sample of 35 women who exercise daily, and who have an average duration of labor of 16.9 hours and a sample variance of 39.7 hours. You want to test the hypothesis that women who exercise daily have a different duration of labor than all women.
Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sM
=1.0650 . The t statistic is0.85 .
Now suppose you have a larger sample size n = 89. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size. The new estimated standard error is . The new t statistic is .
Note that the t statistic becomes as n becomes larger.
Use the Distributions tool to look at the t distributions for different sample sizes. To do this, choose the Degrees of Freedom for the first sample size on the slider, and click the radio button with the single orange line. Move the orange vertical line to the right until the number below the orange line is located on the t statistic. The probability of getting that t statistic or one more extreme will appear in the bubble with the orange type. Now repeat the process for the other sample.

What is the probability of getting the t statistic or something more extreme for the sample size of n = 35? p = . What is the probability of getting the t statistic or something more extreme for the sample size of n = 89? p = .
The t distribution is with a smaller n. (Hint: To best see this, click the radio button in the tool with no vertical lines. Slowly move the Degrees of Freedom slider from the smallest value to the largest value, and observe how the shape of the distribution changes.)

Answers

As the sample size increases, the t distribution becomes narrower and closer to a normal distribution.

The t statistic for the larger sample size is larger than the t statistic for the smaller sample size, indicating stronger evidence against the null hypothesis.

What is the value of the test statistic, t?

To calculate the estimated standard error for the larger sample size of n=89:

sM = √(sample variance / sample size)

sM = √(39.7 / 89)

sM= 0.6527

To calculate the t statistic for the larger sample size:

t = (sample mean - population mean) / sM = (16.9 - 16) / 0.6527

t = 1.375

The probability of getting the t statistic or something more extreme for the sample size of n=35 can be found by using the t distribution with degrees of freedom (df) = 34 (n-1). Using the Distributions tool and the given t statistic of 0.85, we find that the probability is approximately 0.2.

The probability of getting the t statistic or something more extreme for the sample size of n=89 can be found by using the t distribution with df=88. Using the Distributions tool and the calculated t statistic of 1.375, we find that the probability is approximately 0.085.

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Hi, can you help me with this question?

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The amount of the Pilipino pesos that we are going to obtain here is 59220.

Explain direct proportionality

Direct proportionality is a mathematical relationship between two variables, where an increase in one variable is accompanied by a corresponding increase in the other variable, and a decrease in one variable is accompanied by a corresponding decrease in the other variable. In other words, if two variables are directly proportional, they change in the same direction at the same rate.

Let the Philippines pesos be P and the US dollars be D

P α D

P = kD

k = P/D

k = 44391.90/1050

k = 42.3

Then;

P = 42.3 * 1400

P = 59220

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A cinderblock is pulled 0.50 meters to the right in 0.2 seconds. What is the block's
average speed to the nearest tenth of a meter per second (m/s)? Your answer should
only contain numbers (no units).

Answers

Answer:

2.5

Step-by-step explanation:

I took the test :)

1 buy 18 packets of cat food in a box. The table shows the different varieties in the box. My cat eats all the packets of tuna. I then take a packet at random from the ones left in the box.
What is the probability that it will be salmon?
Give your answer as a fraction in its simplest form.
Variety. No. of packets
Chicken. 3
Cod. 4
Salmon. 5
Tuna. 6

Answers

The probability of taking salmon packet  is 5/12.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here Total number of packets = 18

Then the cat eat all tune . Number of tune packets = 6.

Then remaining packet= 18-6 = 12

Now number of salmon packet = 5.

Then probability that it will be salmon is,

=> P = Number of salmon packet/ Total number of remaining packet.

=> P = 5/12.

Hence the probability of taking salmon packet in fraction is 5/12.

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A survey is taken at a movie theater in Winterville. The first 225 people who entered the theater were asked about their favorite type of movie. What is true about this situation?

The population is the first 225 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Winterville.
The population is the total number of people who go to the movie theater, and the sample is the first 225 people at the theater.
The population is the number of people in the town of Winterville, and the sample is the number of people who go to the movie theater.

Answers

If a survey is taken at a movie theater in Winterville. The first 225 people who entered the theater were asked about their favorite type of movie. The  true about this situation is: C. The population is the total number of people who go to the movie theater, and the sample is the first 225 people at the theater.

What is true about this situation?

In this situation, the survey was taken of the first 225 people who entered the movie theater. Therefore, the sample is the group of 225 people who were surveyed. The population of interest is the total number of people who go to the movie theater, as these are the individuals who could potentially have a favorite type of movie.

However, it is not practical to survey every person who goes to the movie theater, so a sample of 225 people was taken from the population.

Therefore, option C is the correct answer.

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Bryn takes out a loan of £800. This debt increases by 28% every year. How much money will Bryn owe after 14 years? Give your answer in pounds (£) to the nearest 1p. < Back to task Q Search Watch video Answer >​

Answers

After 14 years, Bryn will owe £2,109.47, when Bryn takes out a loan of £800 and that debt interest increases by 28% every year.

Determine the annual interest rate: 28%

Convert the interest rate from a percentage to a decimal: 28% ÷ 100 = 0.28

Calculate the total interest owed over 14 years: £800 * 0.28 = £224

Calculate the new loan amount after the first year: £800 + £224 = £1024

Repeat steps 3 and 4 for each subsequent year, using the updated loan amount from the previous year instead of the original loan amount:

The amount owed by Bryn after 14 years can be calculated by multiplying the original loan amount by (1 + the annual interest rate) raised to the power of the number of years:

£800 * (1 + 0.28)¹⁴

= £800 * 1.28¹⁴

= £800 * 2.636849

= £2,109.47

So, Bryn will owe £2,109.47 after 14 years; when Bryn takes out a loan of £800 and that debt interest increases by 28% every year.

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