A single marble tile measures 25 cm by 20 cm. How many tiles will be required to cover a floor with dimensions 2 meters by 3 meters?
A. 320 tiles
B. 240 tiles
C. 180 tiles
D. 120 tiles

(Please do step by step and the answer)

A Single Marble Tile Measures 25 Cm By 20 Cm. How Many Tiles Will Be Required To Cover A Floor With Dimensions

Answers

Answer 1

The number of tiles that will be required to cover a floor with dimensions 2 meters by 3 meters is given as follows:

D. 120 tiles.

How to obtain the area of a rectangle?

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width

The area of the floor is given as follows:

2 x 3 = 6 m².

The area in m² of each tile is given as follows:

0.25 x 0.2 = 0.05.

Hence the number of tiles that will be required to cover the floor is given as follows:

6/0.05 = 120 tiles.

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Related Questions

In Circle C, the diameter AB bisects the chord EF.
If m

Answers

In the circle the mesaure of ∠ACF is  7

What do you mean by Diameter ?

The distance from the centre of a circle to any point on the boundary is called the radius. The radius is half of the diameter; 2r=d 2 r = d . The line segment that joins two points on the circle is a chord.

If diameter of a circle bisects a chord ,then it must be perpendicular to the chord.

∴ m∠ACF = 90°  

(8x + 34)° = 90°

8x = 90 - 34

x = 56/8

x = 7

Hence,mesaure of ∠ACF = 7

Complete question : In Circle C, the diameter AB bisects the chord EF.

If m∠ACF = (8x+34)°, enter in the correct value of x.

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Find the measures of angle a and B. Round to the nearest degree.

Answers

The measure of angle A and angle B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.

What is trigonometric ratios?

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan B = 6/11 {opposite/adjacent}

B= tan⁻¹(6/11) {cross multiplication}

B = 28.6105.

tan A = 11/6 {opposite/adjacent}

A= tan⁻¹(11/6) {cross multiplication}

A = 61.3895.

Therefore, the measure of angles A and B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.

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HELLLPPP Quick
What is the mean of this data set?
12, 17, 16, 10, 20
35
25
15​

Answers

Answer:

15

Step-by-step explanation:

The numbers in the given data = 12, 17, 16, 10, 20

Total number = 5

12 + 17 + 16 + 10 + 20 = 75

Mean = 75/5

Mean 15

es meet at right angles.) 6 m 2 m 3 m 5 m grass cement 2 m 4 m square meters​

Answers

The area of the cement part is 24 m².

What is area?

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Area of the part with cement = Area of the backyard-Area of the grassA = LW-lw....................... Equation 1

Where:

A = Area of the part with cementL = Length of the backyardW = Width of the backyardl = Length of the cementw = Width of the cement

From the question,

Given:

L = 5 mW = 6 ml = 3 mw = 2 m

Substitute these values into equation 1

A = (5×6)-(2×3)A = 30-6A = 24 m²

Hence, the area is 24 m².

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Graph y ≥ -x2 - 1.



Click on the graph until the correct graph appears.

Answers

Answer:

To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).

To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.

So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).

I hope this helps!

The diameter of a circle is 10cm find the circumference to the nearest tenth

Answer c= Cm

Answers

Answer:

31.4 cm

Step-by-step explanation:

Circumference of circle = D x π

D = 10 cm

π = 3.14

Let's solve

10 x 3.14 = 31.4 cm

So, the circumference of the circle is 31.4 cm

The function f(x) = -4(3)-4+3 represents the value of a savings account in dollars, x months after the individual opened
the account.
In how many months will be account have a balance of $0?
O 0.26 months
O 2.46 months
O 3.74 months
O 4.26 months
NEED HELP ASP

Answers

Answer: A

Explanation:

TIME SENSITIVE! please help !

Consider the word PENCIL. If all the letters are used, and the first letter can’t be N or L, how many ways can the letters be arranged?

A) 720

B) 480

C) 360

D) 96

Answers

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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The​ life, in​ years, of a certain type of electrical switch has an exponential distribution with an average life betaequals3. If 300 of these switches are installed in different​ systems, what is the probability that at most 70 fail during the first​ year?

Answers

The probability that at most 70 switches fail during the first year is low, at around 1.3%.

The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.

The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.

To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.

This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.

Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:

P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)

This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.

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Which expression can be used to find the surface area of the following rectangular prism? Choose 1 answer: (Choice A) A 15+15+10+10+6+615+15+10+10+6+615, plus, 15, plus, 10, plus, 10, plus, 6, plus, 6 (Choice B) B 10+10+6+610+10+6+610, plus, 10, plus, 6, plus, 6 (Choice C) C 15+15+10+10+615+15+10+10+615, plus, 15, plus, 10, plus, 10, plus, 6 (Choice D) D 10+610+6

Answers

The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

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The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

assume the mapping t w p2 ! p2 defined by t a0 c a1t c a2t 2 d 2 a0 c .3 a1 c 4 a2/t c .5 a0 6 a2/t 2 is linear. find the matrix representation of t relative to the basis b d f1; t; t 2 g.

Answers

So, the matrix representation of T relative to the basis B = {f1, t, t²} is:
| 2.5  3  0 |
|  0   4  0 |
|  0   0  6 |

To find the matrix representation of the linear transformation T relative to the basis B = {f1, t, t²}, we need to apply T to each element of the basis and then express the result as a linear combination of the basis elements.
Let's apply T to each element of the basis B:
1. T(f1) = T(1) = 2(1) + 0.5(1) = 2.5
2. T(t) = T(c) = 3(c) + 4(c²) = 3f1 + 4t
3. T(t²) = T(c²) = 6(c²) = 6t²
Now, we can express the results as linear combinations of the basis elements:
1. T(f1) = 2.5f1 + 0t + 0t²
2. T(t) = 3f1 + 4t + 0t²
3. T(t²) = 0f1 + 0t + 6t²
Finally, we can form the matrix representation of T relative to the basis B by using the coefficients of the linear combinations as the columns of the matrix:
T matrix = | 2.5  3  0 |
                  |  0   4  0 |
                  |  0   0  6 |

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The matrix representation of t with respect to the basis b = [tex]{f1, t, t^2}[/tex] is:

[1/2   -4/3      1 ]

[1       8/3      0 ]

[0     -5/2   3/2 ].

To find the matrix representation of the linear transformation t with respect to the given basis, we need to apply t to each of the basis vectors and represent the result as a linear combination of the basis vectors.

The coefficients of these linear combinations will form the columns of the matrix representation.

First, we apply t to each of the basis vectors:

[tex]t(1) = a0 + a1t + a2t^2 = a0 + a1f1 + a2t - (a1/2)f1 - (3a2/2)t^2[/tex]

[tex]t(t) = a0 + (4/3)a1t + (5/6)a2/t = a0 + (4/3)t + (5/6)t^2 - (4/3)f1 - (5/2)t^2[/tex]

[tex]t(t^2) = a0 + (3/2)a2/t^3 = a0 + (3/2)t^2 - (3/2)f1[/tex]

Next, we represent these results as linear combinations of the basis vectors:

[tex]t(1) = (a0 - a1/2)f1 + (a1 + a2)t - (3a2/2)t^2[/tex]

[tex]= 1f1 + 0t + 0t^2 + (-1/2)f1 + 1t + 0t^2 + 0f1 - (3/2)t^2[/tex]

[tex]= (1/2)f1 + 1t - (3/2)t^2[/tex]

[tex]t(t) = (-4/3)f1 + (a0 + 4/3)t + (5/6)t^2[/tex]

[tex]= 0f1 + 1t + 0t^2 + (-4/3)f1 + (4/3)t + (5/6)t^2 + 0f1 + 0t - (5/2)t^2[/tex]

[tex]= (-4/3)f1 + (8/3)t - (5/2)t^2[/tex]

[tex]t(t^2) = f1 + (a0 - 3/2)t^2[/tex]

[tex]= 0f1 + 0t + 1t^2 + 1f1 + 0t + 0t^2 + 0f1 + (1/2)t^2[/tex]

[tex]= 1f1 + 0t + (3/2)t^2[/tex]

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Noah is visiting his aunt in Texas. He wants to buy a belt buckle whose price is $25. He knows that the sales tax in Texas is 6.25%.
How much will the tax be on the belt buckle?

Answers

The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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(15 POINTS) HELP ASAP TY!!

How are solving systems of two linear equations or inequalities and solving systems of two quadratic equations or inequalities alike? How are they different?

Answers

Solving systems of two linear equations or inequalities and solving systems of two quadratic equations or inequalities are both ways of finding the intersection points between two curves in the plane.

The main difference between the two methods is that linear equations and inequalities are much simpler and easier to solve than quadratic equations and inequalities. In fact, linear systems can be solved using straightforward algebraic methods, such as substitution, elimination, or graphing, while quadratic systems require more advanced techniques, such as factoring, completing the square, or using the quadratic formula.

Another important difference is that linear systems always have either one solution, no solution, or infinitely many solutions, while quadratic systems can have one, two, or no real solutions depending on the discriminant of the equations.

The shapes of the curves represented by linear and quadratic equations are also different. Linear equations and inequalities always produce straight lines, while quadratic equations and inequalities can produce parabolas or other more complex shapes.

Divide. Write the missing
numbers.
62) 5,472
1
9
16
R
62 5 4 7 2
"
R
9
1 6
(Type whole numbers.)

Answers

we get the quotient as 161 and remainder as 11.So the missing numbers are:R = 11

9, 1, 6

What is long division method ?

First divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.

To divide 5,472 by a two-digit number, we can use long division method as follows:

34) 5 4 7 2( 34

   -    4 0

     ______

       1 4 7

  -    1 3 6

      _______

            1 1

Therefore, we get the quotient as 161 and remainder as 11.

So the missing numbers are:

R = 11

9, 1, 6

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question 1 options: as a quality control inspector: you have previously believed a claim that 3.2% of items made on your production line are defective. to see if you should still believe this claim: you decide to do a two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective. in percentage form, and rounded to four digits past the decimal point: what is the approximate p-value of your test? answer: the approximate p-value of this test is % state your answer in percentage form. a percentage symbol is already provided. round your answer to four digits past the decimal point. include all four digits past the decimal point, even if some digits are zeros. include only your number for the answer. do not include any other information (such as another percentage symbol, or equal symbol, words, spaces, etc).

Answers

The approximate p-value is 5.1250%.

P-value is the probability of obtaining a test statistic as or more extreme than what was actually observed, given that the null hypothesis is true.

Two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective.

The approximate p-value for this two-sided significance test, with a significance level of 2%, is 5.1250%.

This is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This was calculated using a binomial test, which takes into account the sample size and the expected rate of defects.

This p-value indicates whether or not the observed rate of defects is significantly different from the expected rate.

In this case, the p-value is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This can be calculated using a binomial test.

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math help i beg anything will do just pleas help

Answers

Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

anova with replication is also known as? repeated measures between-group design mixed design one-way anova

Answers

this is "Repeated measures ANOVA, which is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions.

What is a repeated measures ANOVA ?

A repeated measures ANOVA is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions. This design is sometimes referred to as a "within-subjects design" because each participant is measured within the same group.

Here are the steps for conducting a repeated measures ANOVA:

State the null and alternative hypotheses.Check the assumptions of the test, which include normality, sphericity, and homogeneity of variance.Calculate the within-subjects sum of squares (SSW), the between-subjects sum of squares (SSB), and the total sum of squares (SST).Calculate the degrees of freedom (df) for each of these sums of squares.Calculate the mean square (MS) for each source of variance by dividing the sum of squares by the degrees of freedom.Calculate the F ratio by dividing the between-subjects MS by the within-subjects MS.Determine the critical value for the F ratio using a table or software.Compare the calculated F ratio to the critical value. If the calculated F ratio is greater than the critical value, reject the null hypothesis and conclude that there is a significant effect of the independent variable on the dependent variable.If the null hypothesis is rejected, follow up with post hoc tests to determine which conditions differ significantly from each other.

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Can someone help me asap? It’s due tomorrow.

Answers

Answer:

I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.

help please its due in a few minuets

Answers

Answer:

use desmos graphing calculator it helps alot

Step-by-step explanation:

x^{2}-x-6=0 has two zeros/solutions

x^{2}-x-6=0 has 1 zero/solution

x^{2}-x-6=0 has no zero/solution

Our school raises $150 for six charities. Each charity gets 1/6 of the amount raised. How much did each charity get

Answers

The amount that each charity gets is $25.

The charity raise simply define as we raise funds in the form of small amounts of money from a huge crowd of people within a specific period of time.

For example, if 100 people donate $50 each to your crowdfunding campaign in two weeks, you will be able to raise $5000.

To find the amount that each charity got, we have to divide the total charity amount raised in the proportion given, i.e., 1/6.

Each charity gets 1/6 of the total amount raised, which is $150.

So, we need to divide $150 by 6:

$150 ÷ 6 = $25

Therefore, each charity received $25.

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Juan can run 38 yards in 5 seconds. If he keeps the same pace, how many yards can he run in 30 seconds? Responses

Answers

Answer: 228 yards

Step-by-step explanation:

Answer:

228

Step-by-step explanation:

a student willing to participate in a debate competition is required to fill out a registration form. answers to the follow questions on the form are what type of data?

Answers

A student willing to participate in a debate competition is required to fill out a registration form.

Form filling in two types of data i.e.,

Quantitative dataCategorical data

Quantitative data :

Quantitative data is data that can be counted or measured in numerical values. The two main types of quantitative data are discrete data and continuous data. Height in feet, age in years, and weight in pounds are examples of quantitative data. Qualitative data is descriptive data that is not expressed numerically.

Categorical data:

Categorical data is a collection of information that is divided into groups. i.e., if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical.

a. What is your date of birth?

Quantitative.

b. Have you participated in any debate competition previously?

Categorical.

c. If yes, how many debate competitions have you participated so far?

Quantitative.

d. Have you won any of the competitions?

Categorical.

e. If yes, how many have you won?

Quantitative.

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The given question is incomplete, complete question is:

A student willing to participate in a debate competition required to fill a registration form. State

whether each of the following information about the participant provides categorical or quantitative

data.

a. What is your date of birth?

b. Have you participated in any debate competition previously?

c. If yes, how many debate competitions have you participated so far?

d. Have you won any of the competitions?

e. If yes, how many have you won?

Please write answer in two parts. A. Main answer (correctly paraphrased, addressing all aspect of the question) B. Explanation (Step-by-step explanation)

A paper distributor offers discounts to individuals who buy in quantity. They offer a 10 percent discount for orders of 50 -100 boxes of paper, a 20 percent discount for orders of 100 - 200, and a 30 percent discount for orders of 200 boxes or more. If Lee placed an order of 140 boxes (each box is $2.50), what would his discount and final price be?

Answers

His discount and final price be $280 for his order of 140 boxes.

What is Discount ?

A discount is a drop in a product's or service's price.

It is frequently provided as a perk to customers to entice them to buy. Discounts are often stated as a percentage or dollar amount off the list price.

Depending on the sort of discount and the situation, discounts can be computed in a variety of ways.

For instance, a product that costs $100 would have a discounted price of $80 with a 20% discount applied. Similar to this, a product that costs $50 would have a discounted price of $40 if it received a $10 reduction.

In marketing and sales, discounts are frequently used to draw customers and boost sales volume.

What percentage is it?

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test.

In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."

This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Exampe of Percentage :-

10% = 10/100 ( = 1/10 (or) 0.1)

25% = 25/100 ( = 1/4 (or) 0.25)

According to question

Lee qualifies for a 20% discount because his order of 140 boxes falls within the range of 100-200 boxes.

Since each box originally cost $2.50, the full price of 140 boxes, after any discounts, is:

140 * $2.50 = $350

The 20% Lee discount is determined as follows:

20% * $350 = $70

Lee's discount is therefore $70, and his adjusted price is as follows:

$350 - $70 = $280

Therefore, Lee will ultimately pay $280 for his order of 140 cartons.

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The population of your town is about 30,000. This is about 1/10 the population of your friend’s town about what is the population of your friend’s town?

Answers

The population of your friend's town is 300,000 if the population of your town is about 30,000.

To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.

If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.

So, the population of your friend's town is

30,000 x 10 = 300,000

Therefore, your friend's town has a population of about 300,000.

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need help! please give example if can

Answers

The two statements are;

The area of sector 1 is  20n² + 15n square meters

The total distance around the garden is 20n + 2 meters

Option A  and C

How to determine the value

The formula for the area of a rectangle is expressed as;

A = lw

Such that the parameters are;

A is the area of the rectangle l is the length of the rectanglew is the width of the rectangle

For the first sector, we have that;

Length = 4n + 3

Width = 6n - 2 - 5n = n - 2

Substitute the values

Area of sector 1 = (4n + 3)(5n)

expand the expression

Area of sector 1 = 20n² + 15n square meters

Area for the sector 2

Area = (3n - 3)(n -2)

expand the bracket

Area = 3n² - 6n - 3n + 6 = 3n² - 9n + 6

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Help me pls........................

Answers

All the possible angle measures are given as follows:

25º and 35º.

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.

On the first quadrant, we have that:

The cosine is greater than the sine for angles that are less than 45º.The cosine is equals to the sine for an angle of 45º.The cosine is less than the sine for angles that are greater than 45º.

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Help solve this! ASAP

Answers

Answer:

  2

Step-by-step explanation:

You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].

Average rate of change

The average rate of change of f(x) on the interval [a, b] is computed as ...

  m = (f(b) -f(a))/(b -a)

For the given function f(x), this is ...

  m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2

The average rate of change of f(x) on the interval [-7, 3] is 2.

__

Additional comment

The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:

  -2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.

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Jane set up a lemonade stand to sell lemonade. The total cost of making the lemonade was $1. 50. She sold each cup of lemonade for $0. 25,

Enter an equation that can be used to find the number of cups of lemonade, x, Jane sold if her earnings were $9. 75 after paying out the cost of the lemonade.

Answers

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

To solve this problem

Let x be the number of cups of lemonade Jane sold.

The total earnings she made from selling x cups of lemonade is:

Total earnings = price per cup * number of cups sold

Total earnings = $0.25 * x

The total cost of making x cups of lemonade is:

Total cost = cost per cup * number of cups sold

Total cost = $1.50 * x

Jane's profit is equal to her total earnings minus her total cost:

Profit = Total earnings - Total cost

Profit = $0.25x - $1.50x

Profit = -$1.25x

We know that Jane's earnings were $9.75, so we can set up the equation:

$9.75 = -$1.25x

To solve for x, we can divide both sides by -$1.25:

-$9.75 / -$1.25 = x

x = 7.8

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

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suppose the life time of a component ti in hours is uniformly distributed on [100, 200]. components are replaced as soon as one fails and assume that this process has been going on long enough to reach equilibrium. (a) what is the probability that the current component has been in operation for at least 50 hours? (b) what is the probability that the current component will last for at least 50 more hours?

Answers

a. The probability that the current component has been in operation for at least 50 hours is 0.5

b. The probability that the current component will last for at least 50 more hours is also 0.5.

(a) The probability that the current component has been in operation for at least 50 hours is given by the cumulative distribution function (CDF) of the uniform distribution on [100, 200] evaluated at 50.

The CDF of a uniform distribution on [a, b] is given by:

F(x) = (x - a) / (b - a) for a <= x <= b

F(x) = 0 for x < a

F(x) = 1 for x > b

Therefore, in this case, the CDF is:

F(x) = (x - 100) / 100 for 100 <= x <= 200

F(x) = 0 for x < 100

F(x) = 1 for x > 200

So the probability that the current component has been in operation for at least 50 hours is:

P(ti >= 50) = 1 - F(50) = 1 - ((50 - 100) / 100) = 0.5

(b) The probability that the current component will last for at least 50 more hours is also given by the CDF of the uniform distribution on [100, 200], but evaluated at 150 instead of 50.

That is,

P(ti >= 150) = F(150) = (150 - 100) / 100 = 0.5.

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If you spin the spinner 36 times, what is the best prediction possible for the number of times it will not land on yellow?

Answers

The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

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