About 300,000 Mexican Free-tailed Bats occupy the caves at Carlsbad Caverns during the summer months. Each bat can eat about 800 insects in one hour. What other information is needed to find the number of insects a bat can eat each day?

Answer:

56

Step-by-step explanation:

68-12=56

Answer:

56

Step-by-step explanation:

56

all the x number smaller than 1

Explanation

the symbol

represents an inequality, it means smaller than , this is Strict inequalities without the “or equal to” component are indicated with an open dot on the number line and a parenthesis using interval notation.so in thsi case 1 is not part of the solution set

so, as 1 is not part of the solution this is a open interval

all the x number smaller than 1

I hope this helps you

Answer: 3/10 of an hour

Step-by-step explanation:

Over the past 10 years, you have paid off $1,80,000 - $1,12,681 = $67,319 of the original loan.

This amount represents the reduction in the loan balance over the years. It is essential to consider that your monthly payments were not entirely directed towards the loan principal; a portion went towards paying interest charges. As a result, the loan balance was gradually reduced over time.

The interest on the loan accumulated each month, which affected the allocation of your payments. Initially, a significant portion of your payments likely went towards interest, with a smaller fraction reducing the principal balance. However, as time progressed, the interest portion decreased, and more of your payments started chipping away at the loan's principal.

It is crucial to recognize the impact of interest on loans, especially over extended periods. The difference between the current value of your house and the remaining loan balance illustrates the progress you have made in building equity over the years. As you continue making payments, the loan balance will further diminish, and your equity will continue to grow.

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Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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If you go twice as fast, your stopping distance will increase by four times (option C).

This relationship is based on the laws of physics and the principles of motion.

When an object is in motion, its stopping distance is influenced by its initial speed, reaction time, and braking capabilities. The stopping distance consists of two components: the thinking distance (the distance traveled during the reaction time) and the braking distance (the distance needed to bring the object to a complete stop).

According to the laws of physics, the braking distance is directly proportional to the square of the initial speed. This means that if you double your speed, the braking distance will increase by a factor of four. In other words, going twice as fast will require four times the distance to come to a stop.

It is important to note that this relationship assumes other factors, such as road conditions and braking efficiency, remain constant. However, in real-world scenarios, these factors may vary and can affect the stopping distance to some extent.

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Answer:

11/20

Step-by-step explanation:

Answer:

6.4008

Step-by-step explanation:

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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The area of a farm is the amount of space the farm can occupy.

The farmer will be able to pick 70 apples, in total

From the complete question (see attachment), we have:

\(Length = 5\)

\(Width = 14\)

So, the area of the farm is:

\(Area =Length \times Width\)

This gives

\(Area = 5 \times 14\)

\(Area = 70\)

In this scenario, the area of the farm is the number of trees on the farm.

So, we have:

\(Tree=70\)

Since there are 70 trees, and 1 apple is to be plucked from each;

The total number of apples is:

\(n = Trees \times 1\)

\(n = 70 \times 1\)

\(n = 70\)

Hence, the farmer will pluck 70 apples.

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Answer:

22 m

Step-by-step explanation:

The computation of the how much far does the boat travel is as follows:

sin 43 degrees = 15 ÷ d

d = 15 ÷sin 43 degrees

= 15 ÷ 0.6820

= 21.99

= 22 m

Hence, the how much far does the boat travel is 22 m

We simply applied the above formula so that the correct value could come

The same is to be considered

A = 119.4in^2

hope it's helpful ❤❤❤❤

THANK YOU.

Answer:

B, 7/24

Step-by-step explanation:

(x=theta)

sec(x) = 1/cos(x) so 1/cos(x) = 25/24

\((\frac{1}{cosx})^-1 = (\frac{25}{24} )^-1\\\\cos(x) = 24/25\)

Then use the cos^-1 function on your calculator to find out theta.

Then tan your found value of theta.

You should find that tan (theta) = 7/24

Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

The amount of the annual withdrawals will be $16,574.24.The amount is the sum of the principal and the simple interest gain.

The complete repayment of money at the end of the time period for which it was borrowed is referred to as the amount.

The given data in the problem is;

P ia the annual payment

PV is the present value = $150,261

r is the rate of intreast = 9.1% = 0.091

n is the time period= 20

The formula for the annual payment is found as;

\(\rm P= \frac{r \times PV}{1-(1+r)^{-n}} \\\\ \rm P= \frac{0.091 \times 150261}{1-(1+0.091)^{-20}} \\\\ \rm P=16,754.2437\)

Hence the amount of the annual withdrawals will be $16,574.24.

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Based on the given dataset, we cannot say whether the sample size is a problem or not. Therefore, it cannot be determined whether the sample size is a problem or not for the dataset for number 11.

Parametric statistical methods refer to the techniques that deal with populations with known parameters. These methods are used when a population's characteristics are known, such as the population mean and standard deviation.

For instance, the student's t-test, ANOVA, and the correlation coefficient are some of the most commonly used parametric tests.Parametric statistical methods usually prefer a sample size of ~30. However, in some situations, even small samples may be sufficient, depending on the size of the effect being measured.

The larger the effect size, the smaller the sample size required, and vice versa. For instance, if there is a large difference between the two groups being compared, a small sample size may be sufficient.

Consequently, whether the sample size is a problem or not for the dataset for number 11 cannot be determined based on this information because the sample size is unknown.

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Answer: -36-54n

Step-by-step explanation:

 -9(8+6n-4)

=-72-54n+36

=-72+36-54n

=-36-54n

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

-54n-36

Step-by-step explanation:

-9x8= -72

-9x6n=-54

-9x-4= -54n

-72-54n+36

-72+36=-36

-54n-36

a. The volume of a rectangular package is given by V = LWH, where L is the length, W is the width, and H is the height. From the problem statement, we have:

L = W + 10

H = W - 12

Substituting these expressions into the formula for volume, we get:

V = (W + 10)(W)(W - 12)

V = W^3 - 2W^2 - 120W

So the polynomial function that calculates the volume of a package with width, w, is:

V(w) = w^3 - 2w^2 - 120w

b. To find the dimensions that will give us the maximum allowable volume, we need to find the maximum value of the volume function V(w), subject to the constraint that the volume cannot exceed 4800 cubic inches. We can use the method of calculus to find the maximum value.

First, we need to find the derivative of V(w):

V'(w) = 3w^2 - 4w - 120

Setting V'(w) equal to zero and solving for w, we get:

3w^2 - 4w - 120 = 0

(w - 6)(3w + 20) = 0

The only positive solution is w = 6 inches (since the width cannot be negative). To verify that this is a maximum, we need to check the sign of the second derivative of V(w):

V''(w) = 6w - 4

When w = 6, V''(w) = 32, which is positive. Therefore, the function V(w) has a local minimum at w = 6, which is also the global maximum (since V(w) approaches infinity as w goes to infinity).

So the dimensions that will give us the maximum allowable volume of 4800 cubic inches are:

Width = 6 inches

Length = 16 inches (since L = W + 10 = 16)

Height = -6 inches (since H = W - 12 = -6, we interpret this as a package with the top and bottom sides flipped, so that the height is positive)

Therefore, the maximum volume of the package that meets the size requirement is:

V = LWH = (16)(6)(6) = 576 cubic inches.

Hope this helped!

Monthly revenue:

As the monthly revenue is given by a quadratic equation, the number of units that must be sold each month maximize the revenue and the maximum revenue are the coordinates of the vertex for the parabola that correspond to the given function.

x is the number of units

y is the maximum revenue

To find the x coordinate of the vertex, use the next formula:

Use the x-coordinate in the function to find the y-coordinate (R(600)):

Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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Answer:

\(y=\frac{7}{3}-\frac{2}{3}x\)

Step-by-step explanation:

To solve for y, we will have to get y by itself on one side of the equation, with all of the other variables and values on the other side.

2x + 3y = 7

Subtract 2x to both sides of the equation.

3y = 7 - 2x

Divide both sides by 3.

\(y=\frac{7}{3}-\frac{2}{3}x\)

And now we have solved for y.

I hope you find my answer helpful.

hi

reminder :

area of square :  side * side

area of circle  :   π * radius²

here :  side of square is  30 meters

so area of square :  30*30 = 900 m²  

One side of the square is  a diameter of the circle  :  a diameter is  twice the radius.

so diameter = 30 so radius  =  30/2 = 15

now if radius is  15 so area of circle :   π*15² =  706.5 m²

so area of the figure is  :   900 + 706.5 =  1 606.5 m²

..

Answer:

42

Step-by-step explanation:

The lengths of the diagonals are:

GE = 8√5 units

DE = 4√5 Units

Area = 80 sq. units

We have been given an image of a kite on coordinate plane.

To find the length of GE we will use distance formula:

Distance = √[x₂ - x₁)² + (y₂ - y₁)²]

Substituting coordinates of point G and E in above formula we will get,  

GE = √[16 - 0)² + (8 - 0)²]

GE = √(256 + 64)

GE = √320

GE = 8√5 units

Similarly we will find the length of diagonal DF using distance formula.

DF = √[14 - 10)² + (2 - 10)²]

DE = √(16 + 64)

DE = √80

DE = 4√5 Units

Area of kite is given by the formula:

Area = (p * q)/2

where p and q are diagonals of kite.

Thus:

Area = ( 8√5 *  4√5)/2

Area = 80 sq. units

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Answer:

A

Step-by-step explanation:

So timing a fraction with a fraction smaller by 1 means its a proper fraction.

And it can't get bigger than it already is because it's timing a less than 1 itself.

So it's A, it will be smaller

The fact that Maria has decided to still put in more effort to get no grade lower than C shows that c. she is able to set and evaluate her goals.

Maria was able to set goals on the grades that she would like to earn throughtout her high school.

She was also able to evaluate her progress when she saw that she hadn't reached her overall goal. This then led to her taking even more lessons.

In conclusion, option C is correct.

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Translations, reflections, and rotations produce a figure that is congruent to the original figure.

When we perform translations, reflections, and rotations on a figure, the resulting figure maintains the same size, shape, and orientation as the original figure. In other words, the transformed figure is congruent to the original figure.

Here's a brief explanation of each transformation:

1. Translations: A translation involves sliding a figure in a particular direction without changing its orientation or shape. Every point of the figure moves the same distance and direction. The resulting figure is congruent to the original because all corresponding sides and angles remain the same length and measure.

2. Reflections: A reflection involves flipping a figure over a line, called the line of reflection. Each point of the figure is mirrored across the line, creating a symmetrical image. The resulting figure is congruent to the original because the distance between corresponding points remains the same, and the angles formed between intersecting lines are preserved.

3. Rotations: A rotation involves turning a figure around a fixed point, known as the center of rotation. The figure is rotated by a specific angle in a clockwise or counter clockwise direction. The resulting figure is congruent to the original because all corresponding angles and side lengths remain unchanged.

In each of these transformations, the congruency of the resulting figure to the original figure is a fundamental property. Congruent figures have the same shape and size, even though they may be positioned differently in space. This property allows us to apply the concept of congruence in geometry to establish relationships, prove theorems, and solve geometric problems.

Therefore, when we perform translations, reflections, and rotations on a figure, we produce a transformed figure that is congruent to the original figure.

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a. Paired t-test – Dependent samples. Relevant parameter: mean sales. (b) Independent samples t-test – Independent samples. Relevant parameter: rating score. (c) Chi-squared test – Independent samples. Relevant parameter:   positive/negative ratings

a. For scenario a, where Hughes records the mean sales before and after the menu change, a paired t-test would be an appropriate statistical method. The samples in this scenario are dependent because they come from the same group of customers (i.e., sales before and after the menu change). The relevant parameter in this case would be the mean sales. To determine whether the difference in mean sales before and after the change is statistically significant, a paired t-test would be used for inference.

b. In scenario b, where Hughes randomly samples 100 people and asks them to rate both menus, an independent samples t-test would be suitable for analyzing the problem. The samples in this scenario are independent because each person rates both menus separately. The relevant parameter would be the rating score. To determine if there is a significant difference in ratings between the two menus, an independent samples t-test can be used for inference.

c. In scenario c, where Hughes randomly samples 100 people and separates them into two groups, asking for positive/negative ratings for the old and new menus, a chi-squared test would be appropriate for analyzing the problem. The samples in this scenario are independent because each person belongs to either group 1 or group 2 and rates only one menu. The relevant parameter would be the proportion of positive and negative ratings for each menu. A chi-squared test can be used to assess whether there is a significant association between the menu (old or new) and the positive/negative ratings.


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Answer:

x = 7

Step-by-step explanation:

160+3x=195-2x

Add 2x to each side

160+3x+2x=195-2x+2x

160 +5x = 195

Subtract 160 from each side

160+5x-160 = 195-160

5x = 35

Divide by 5

5x/5 = 35/5

x = 7