5/8 divided 2 1/2 simply

Answer:

d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The average rate of change tell you in this context the volume of water in the base as the volume changes from 2.5 cups to 4.25 cups.

The average rate of change is a mathematical concept used to describe how a change in one quantity affects another quantity.

To calculate the average rate of change, we need to know the height of water in the vase at two different volumes. Let's call the height of water at a volume of 2.5 cups "h1" and the height of water at a volume of 3.25 cups "h2". Then, the average rate of change over the interval from 2.5 cups to 3.25 cups is calculated as:

=> (h2 - h1) / (3.25 - 2.5) = (h2 - h1) / 0.75

This average rate of change tells us how much the height of water changes, on average, for every one cup increase in the volume of water in the vase.

In other words, the average rate of change provides us with a measure of the "slope" of the relationship between the height of water and the volume of water in the vase over the interval from 2.5 cups to 3.25 cups.

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Answer:

Step-by-step explanation:

inside angle = 180

180 = x - 4 + 2x + 10 + (180 - 153)

180 + 4 - 10 - 27 = 3x

147 = 3x

x = 147 / 3

x = 49

The height of the tree is 6.4m

the difference is that in one case the shadow of the tree is 60 - 20 = 40 m, and in the other case it is 60 + 20 = 80 m long.

anyway, for a certain angle of the sunlight we know the shadow of the pole is 60 m long, which creates with the 4.8 m height a right-angled triangle, with the line of sight from the top of the pole to the ground end of the shadow being the Hypotenuse or radius for or trigonometric triangle in a circle.

the shadow length (60 m) is sine of the sunshine angle multiplied by the radius.

the height (4.8 m) is cosine of that sunshine angle multiplied also by that radius.

Pythagoras gets us the radius for the pole triangle :

radius² = 60² + 4.8² = 3600 + 23.04 = 3623.04

radius = sqrt(3623.04) = 60.19169378... m

sin(angle) × radius = 60

sin(angle) = 60/radius = 0.996815279...

angle = 85.42607874...°

the sunshine creates with the tree also a right-angled triangle with the same sunshine angle (the sun is so far away, that the tiny, tiny difference is irrelevant, we can simply assume the angles are equal).

but the shadow is of different length (sin(angle)×radius), which means also the radius for the tree triangle has to be different. and that defines the height of the tree (cos(angle)×radius).

but now we know the angle, and we can reverse calculate the side lengths.

but the question is (as mentioned at the beginning) : is the tree shadow 40 m or 80 m long.

we have therefore 2 solutions for the height of the tree.

1. the shadow is 40 m long.

sin(angle) × radius = 40

radius = 40/sin(angle) = 40.12779585... m

tree height = cos(angle)×radius = 3.2 m

2. the shadow is 80 m long.

sin(angle) × radius = 80

radius = 80/sin(angle) = 80.25559171... m

tree height = cos(angle)×radius = 6.4 m

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Answer: He spent $7.25 dollars.

Step-by-step explanation:

Inequality shows a relationship between two numbers or two expressions.

The inequality that would represent the possible values for the number of candies purchased c and the number of pretzels purchased p is

3.50c + 3.25p ≤ 30

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

Cost of candy = $3.50

Cost of a pretzel = $3.25

Total amount to spend = $30

Let the number of candies = c

Let the number of pretzels = p

The inequality to spend on possible numbers of candies and pretzels:

3.50c + 3.25p ≤ 30

Thus,

The inequality that would represent the possible values for the number of candies purchased c and the number of pretzels purchased p is

3.50c + 3.25p ≤ 30

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a. The probability that the drills are all completed by 11:40 am is very close to 0.
b. The probability that the drills are not completed by 12:10 pm is also very close to 0.

a. To find the probability that the drills are all completed by 11:40 am, we need to calculate the total time required to complete the drills. Since there are 35 drills and each drill takes an average of 6 minutes, the total time required is 35 * 6 = 210 minutes.

Now, we need to calculate the z-score for the desired completion time of 11:40 am (which is 700 minutes). The z-score is calculated as (desired time - average time) / standard deviation. In this case, it is (700 - 210) / 35 = 14.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 14. However, the z-score is extremely high, indicating that it is highly unlikely for all the drills to be completed by 11:40 am. Therefore, the probability is very close to 0.

b. To find the probability that drills are not completed by 12:10 pm (which is 730 minutes), we can calculate the z-score using the same formula as before. The z-score is (730 - 210) / 35 = 16.

Again, the z-score is very high, indicating that it is highly unlikely for the drills not to be completed by 12:10 pm. Therefore, the probability is very close to 0.

In summary:
a. The probability that the drills are all completed by 11:40 am is very close to 0.
b. The probability that the drills are not completed by 12:10 pm is also very close to 0.

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The unit price per quart is given as follows:

$4.61.

The unit price is obtained using the proportions in the context of the problem.

Each gallon has four quarts, hence the number of quarts in two gallons is given as follows:

2 x 4 = 8 quarts.

The total price was of $36.88, hence the price per quart is given as follows:

36.88/8 = $4.61.

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Answer:

1 yes

2 yes

3 yes

4 no

5 no

Step-by-step explanation:

Decimals cannot be integers

:D

Answer:

y = 45 - 3x

Step-by-step explanation:

Given that:

Bathtub drains at a constant rate :

Amount of water in tub after 3 minutes = 36 gallons

Amount of water in tub after 7 minutes later (3 + 7) ;(after 10 minutes) = 15 gallons

Using the slope - intercept relation:

y = mx + c

y = gallons in tub after x minutes

m = slope (rate at which water drains per minute)

C = intercept

Hence,

Amount of water in tub after 3 minutes = 36 gallons ; x = 3,; y = 36

Since water is draining gradient m is negative

36 = c - 3m - - - (1)

Amount of water in tub after 7 minutes later (3 + 7) ;(after 10 minutes) = 15 gallons

15 = c - 10m - - - (2)

Subtract (2) from (1)

21 = - 3m + 10m

21 = 7m

m = 3

From (1)

36 = c - 3(3)

36 = c - 9

36+ 9 = c

45 = c

Hence, the equation becomes ;

y = 45 - 3x

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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Answer:

a) p÷m=k

Step-by-step explanation:

P=mk

so you are going to divide both side by m to make k the subject of the formula

P/m=mk/m

therefore m will cancel m in k side

ans will be P/m=k

B) ans W-hg=k

hg is gonna come the other side and change sign(-)

W=k+hg

W-hg=K

Answer:

a = 11

b = 6

Step-by-step explanation:

\( \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - b \sqrt{3} \\ \\ \frac{(5 + 2 \sqrt{3} )}{(7 + 4 \sqrt{3}) } \times \frac{(7 - 4 \sqrt{3})}{(7 - 4 \sqrt{3})} = a - b \sqrt{3} \\ \\ \frac{(5 + 2 \sqrt{3)} (7 - 4 \sqrt{3} )}{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } a - b \sqrt{3} \\ \\ \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{49 - 48} = a - b \sqrt{3} \\ \\ \frac{11 - 6 \sqrt{3}}{1} = a - b \sqrt{3} \\ \\ 11 - 6 \sqrt{3} = a - b \sqrt{3} \\ \\ equating \: like \: terms \: on \: both \: \\ sides, \: we \: find : \\ \\ a = 11 \\ \\ b = 6\)

The age of the artifact is 3523.77 years.

What is radioactive decay?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Here,

The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)

 All radioactive decay processes follow the first-order reaction.

The equation for the half-life for first-order reaction follows:

t(1/2) = 0.693/k....(1)

where,

k = rate constant of a first-order reaction

Given value:

t(1/2) = 5715 years

Put the value of t in equation (1), and we get

k = 0.693/5715

k = 1.21×10⁻⁴yr

The integrated rate law expression for first-order reaction follows:

t = 2.303/k×㏒(a/(a-x))

where,

t = time period

a = initial concentration of the reactant = 58.2 counts per minute

(a-x) = Concentration of reactant left after time t = 38.0 counts per minute

k = rate constant of a first-order reaction

Put the values in the equation and we get

t = 2.303/1.21×10⁻⁴㏒58.2/38

t = 3523.77 years.

Hence, the age of the artifact is 3523.77 years.

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Answer:

y = -4x + 1

Step-by-step explanation:

We find the equation of a line passing through two given points using the generalized slope-intercept which is

y = mx + b

m is the slope(gradient) of the line and b is the y-intercept i.e. the y-value where it crosses the y-axis. This is nothing but the value of y when x  0

Start by finding the slope first

Slope, m = (y2-y1)/(x2-x1)  

Taking(x1, y1) as (-1, 5) and (x2, y2) as (2, -7)

we get

y2 - y1 = -7 -5 = -12

x2 - x1 = 2 - (-1) = 1 2 + 1 = 3

m = -12/3 = -4

Equation would be
y = -4x + b

To find b, choose a known value for x and its corresponding y value and solve for b

Let's take (-1, 5)

Subbing this into the equation gives

5 = (-4)(-1) + b

5 = 4 + b

or b = 1

So the equation of the line in slope-intercept form is

y = -4x + 1

Answer:

Your answer would be 9.

Step-by-step explanation:

12*12=144

15*15*15=3375

The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The factors of 3375 are: 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 675, 1125, 3375

So the greatest common factor would be 9 since is the largest number that is the same for both of the numbers.

Answer:

answer 26

ok now help me

It indicates that the test is highly accurate in correctly identifying individuals with hepatitis C (high sensitivity) and accurately ruling out individuals without the disease (high specificity).

Sensitivity and specificity are two important measures of a diagnostic test's performance. Sensitivity refers to the test's ability to correctly identify individuals who have the condition, while specificity refers to its ability to correctly identify individuals who do not have the condition.

In the case of the ELISA test for hepatitis C, a sensitivity of 95% means that the test will correctly identify 95% of individuals who actually have hepatitis C as positive. This indicates a high probability of detecting the disease when it is present.

On the other hand, a specificity of 90% means that the test will correctly identify 90% of individuals who do not have hepatitis C as negative. This suggests that there is a 10% chance of a false positive result, where individuals without the disease are mistakenly identified as positive.

Overall, the high sensitivity and specificity of the ELISA test for hepatitis C make it a valuable tool in the diagnosis and screening of individuals for this infectious disease. However, it is important to consider that no test is 100% accurate, and false results can still occur. Therefore, additional confirmatory tests may be required in certain cases to ensure accurate diagnosis and appropriate medical intervention.

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Answer: \(76.1222\)

Step-by-step explanation:

\(Simplify\) \(the\) \(expression\)\(.\)

\(14.53.48 + 12.12.42 + 13.53.48 + 13.28.6 + 20.17.3 + 19.43.8 + 28\)

The degree is the largest exponent on the variable.

\(0\)

Solve the rational equation by combining expressions and isolating the variable.

No solution

Answer:  9 1/10      91/10

Step-by-step explanation:

Answer:

9 1/10 and 91/10

Step-by-step explanation:

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Answer:

There are 3 numbers that are not whole numbers.

3/4, 3.7, and sqrt 3 are not whole numbers

Answer:

3

Step-by-step explanation:

There are only 3 that aren't whole numbers. The whole numbers are: 32, 1,265, 3000, and 1. The numbers that aren't whole are: 3/4, 3.7, and √3

Answer:

(5y-8)^2

Step-by-step explanation:

Answer:

Monopoly is a market situation in which a single firm produces a good or service that has no close substitutes, and the company is the only seller.

The following are some of the qualities of monopoly:

Characteristics of Monopoly: The following are some of the features of monopoly:

Single Seller: The most important feature of a monopoly is that it has only one seller.

No close substitutes: Another important feature of monopoly is that the commodity has no close substitutes.

No entry: A monopoly industry cannot have any new competitors in the market.

Price Discrimination: Price discrimination is the process of charging various prices for the same product or service to different customers or groups of customers.

Real-World Examples:

The following are some examples of price discrimination in the real world:

Student Discount: Colleges and universities provide students with discounted tickets, subscriptions, or software licenses based on their student status.

Senior Citizen Discount: Senior citizens are offered discounts on a variety of goods and services, including transportation, health care, and entertainment.

Matinee Discount: Some movie theaters offer discounted tickets for daytime screenings.

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Answer:

2√(5)

Step-by-step explanation:

Since it's stated that thegiven is right triangle :

The square length of hypotenus (the side lenght that sees 90 degrees) is equal to sum of square length of side lengths

2^2 + 4^2 = x^2

4 + 16 = x^2

20 = x^2 and x = 2√(5)

Answer:

The breadth of rectangular carpet is 1.8 m.

Step-by-step explanation:

We have,

We know that,

= Area of rectangle = Length × Breadth

= 23.4 = 13 × Breadth

= 23.4/13 = Breadth

= 234/130 = Breadth

= 1.8 m = Breadth

For given expression, solution will be y=(t-1)/(1+t).

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is t^2dy/dt-t=1+y+ty

After differentiation : As (d/dx) (x^n ) = nx^{n-1}

2t-t=1+y+ty

t-1=y(1+t)

y=(t-1)/(1+t)

for y(1)=2

2+2t=1-t

3t=-1

t=-1/3

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The pints of  water left in the aquarium is  2.5 pints

Using the conversion rule sho below:

1 cup  = 0.5 pint

If Sassan finds that 2 pints 1 cup of water have evaporated from the class aquarium, the total pint that evaporated is expressed as:

Total pint =  2  pints + 0.5 pint

Total pint =  2.5 pints

Hence the pints of  water left in the aquarium is  2.5 pints

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The relative frequency of the class interval 65-75 is .20.

The word 'relative' is used to indicate that an event is being considered in relation or in proportion to something else.

Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences.

Given that: 50 participants scored between 65 and 75 on a test.

Hence,

The relative frequency of the class interval 65-75 = 75 - 65 = 20

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Answer:

y=-2x+4

Step-by-step explanation:

You want to get y by itself, so you would subtract 2x from both sides giving you, \(y=-2x+4\). -2x is the slope (m), and 4 is the y-intercept (b).