The formula for the area of a triangle is A=12bh. Solve this equation for b.

The equation of red graph is \(F(x) = 2 -x^{2}\).

The general equation of parabola is \(y = a(x-h)^{2} + k\).

Where,

(h, k) are the vertices of the parabola.

According to the given question.

We have two graph.

The blue and red graph both represents the equation of downward parabola.

Since, blue graph represents the equation of downward parabola.

Whose equation is given

\(G(x) = 5 - x^{2}..(i)\)

The general equation of a parabola is \(y = a(x-h)^{2} + k..(ii)\)

Where, (h, k) are the vertices of the parabola.

Compare the equation (i) with (ii)

We get

(h, k) = (0, 5) and a = -1.

Now, the red graph which also represents the downward parabola whose vertices are (0, 2)

Therefore, the equation red graph is given by

\(F(x) = a(x-0)^{2} + 2\)

⇒ \(F(x) = -1(x-0)^{2} + 2\)

⇒ \(F(x) = 2 - x^{2}\)

Hence, the equation of red graph is \(F(x) = 2 -x^{2}\).

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The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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Answer:

  x = 9

Step-by-step explanation:

You want the value of x that satisfies 6/40 = x/60.

This equation can be solved in one step: multiply by the inverse of the coefficient of x.

The coefficient of x is 1/60. Its inverse is 60/1 = 60. Multiplying the equation by 60 gives ...

  60(6/40) = 60(x/60)

  360/40 = x

  9 = x

__

Additional comment

Often, you will be advised to "cross multiply" as the first step in solving a proportion. Doing this would give you ...

  6(60) = 40(x)

Now, you would need to divide by the coefficient of x (or multiply by its inverse).

  6(60)/40 = (40x)/40

  360/40 = x = 9

This accomplishes in two steps what we did above in one step.

Answer:

11 units

Step-by-step explanation:

all we gotta do here is jump a unit and count, until we get to the other point of the coordinate plane.

so (i'm gonna call the left one) point A, and (the right one) point B. pretend you are moving point A over to point B, how many spaces would you go to get to point B? 11. try it yourself!

The total cost is the sum of fixed costs and variable costs. Average is the total cost per unit of production.So,Total cost = Fixed cost + Variable costVariable cost=2q+1q²Fixed cost = $160Putting the given values into the formula;TC(q) = Fixed cost + Variable cost= $160 + 2q + 0.1q²

Given information:Producing q gift baskets has a fixed cost of $160 per month, and variable costs of 2q + .1q²(a) Expression for Total Cost:The total cost is the sum of fixed costs and variable costs.So,Total cost = Fixed cost + Variable costVariable cost = 2q + .1q²Fixed cost = $160Putting the given values into the formula;TC(q) = Fixed cost + Variable cost= $160 + 2q + 0.1q²

(b) Expression for Marginal Cost:The marginal cost is the derivative of the total cost with respect to the quantity of production.q = Quantity of productionTC(q) = 160 + 2q + 0.1q²Differentiating the total cost with respect to q,MC(q) = dTC/dqMC(q) = d/dq (160 + 2q + 0.1q²)MC(q) = d/dq (2q) + d/dq (0.1q²)MC(q) = 2 + 0.2q. Expression for Average Cost: cost Average is the total cost per unit of production.q = Quantity of productionTC(q) = 160 + 2q + 0.1q²AC(q) = TC(q)/qAC(q) = [160 + 2q + 0.1q²] / qSubstitute MC = AC2 + 0.2q = [160 + 2q + 0.1q²] / qMultiplying both sides by q,2q² + 0.2q³ = 160q + 2q² + 0.1q³Simplify the above equation,0.1q³ - 1.8q² - 160q = 0Factorizing the above equation, q(0.1q² - 1.8q - 160) = 0q = 0.00q = 18.0q = - 88.9 (rejected)Therefore, for what quantity is Average Cost equal to Marginal Cost is 18.0.

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Answer:

X=60

Step-by-step explanation:

4/10=24/x

cross multiply

4x=240

x=240/4

x=60

(a) The type of reaction ethanol underwent in Test 5 is oxidation reaction.

(b) The reaction which caused the color change in Test 5 is the reduction of the potassium dichromate ions by ethanol. The reduction of potassium dichromate (VI) to chromium (III) ions causes the orange color to change to olive green color. The green colour is produced by chromium (III) ions.

(a) In Test 6, the type of reaction that happened is esterification reaction.

(b) Concentrated sulfuric acid is a catalyst in the test 6. It helps in the formation of the ester as it increases the rate of the reaction by providing a pathway for the reaction.

(c) The equation for the reaction in Test 6 is: Propanoic acid + ethanol → Ethyl propanoate + water

(d) The smell/odor of the product in Test 6 is pineapple.

Based on these observations, it suggests that an oxidation reaction occurred in which the potassium dichromate (VI) was reduced by ethanol, resulting in the color change from orange to olive green. The smell of apples indicates the presence of a specific compound or ester formed during the reaction.

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The number of sides in a polygon is 9.

Given, a regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius and each of the central angles has a measure of 40°.We know that the sum of all the central angles of a polygon is 360°, so we can find the number of sides of a polygon as follows:Let the number of sides of a polygon be n.Measure of each central angle = 40°Sum of all the central angles = n × 40° = 360°So, n × 40° = 360°n = 360°/40°n = 9So, the polygon has 9 sides (nonagon).

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Answer: there's a 50-50 chance of at least two people having the same birthday.

In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability which are one of their birthdays is approximately 194 days.

The expected number of days of the year which are one of their birthdays in a group of 50 people can be calculated using the formula E(X) = np, where n is the number of trials and p is the probability of success in each trial. In this case, there are 50 people and 365 days in a year, so each person has a probability of 1/365 of having their birthday on a particular day. Therefore, the expected number of people with a birthday on any given day is 50*(1/365) = 0.137. Since there are 365 possible days, we can multiply this by 365 to get the expected number of days with at least one birthday, which is approximately 50.034 days. So, the expected number of days of the year which are one of their birthdays in a group of 50 people is around 50.034.
In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability.
Assuming that each person's birthday is equally likely to fall on any of the 365 days in a year (ignoring leap years), the probability of any particular day being a birthday is 1/365.
Now, the probability of a day not being a birthday for a single person is (364/365). For 50 people, the probability of a day not being any of their birthdays would be (364/365)^50.
To find the expected number of days with at least one birthday, we can calculate the probability of a day having at least one birthday, which is the complement of no birthdays on that day. This probability is:
1 - (364/365)^50
Now, we multiply this probability by the total number of days in a year to find the expected number of days with at least one birthday:
365 * (1 - (364/365)^50) ≈ 194.03
So, in a group of 50 people, the expected number of days of the year which are one of their birthdays is approximately 194 days.

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Hello friend,. I hope it's helps you

enjoy your day

Answer:

\(\dfrac{1}{2}\) day

Step-by-step explanation:

Given that:

Owen who is an alien has only 4/5 of his socks clean.

and he wears 2/5 socks a day.

Out of his total 4/5 clean socks.

It will take him (4/5 ÷ 2/5) days to wash all his socks

i.e

the numbers of days since he washed all his socked is:

= \(\dfrac{4}{5} \div \dfrac{2}{5}\)

= \(\dfrac{4}{5} \times \dfrac{5}{2}\)

= \(\dfrac{1}{2}\)

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

Answer: 4

Based on the given conditions, formulate

Multiply both the numerator and denominator with the same integer

Convert decimal to fraction

Simplify fraction(s)

Answer:

w=15

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

15x

15

the 15 cancels out then you have

15/5 which is 3

An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplification of the given expression can be done as,

\(\dfrac{5x}{x^2-1} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{x^2-1^2} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{(x+1)(x-1)} \times \dfrac{x+1}{x^2}\\\\= \dfrac{5}{(x-1)x}\)

Hence, the simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).

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a) The (9,009, 10,585) range represents the 99% confidence interval for the mean number of steps taken on an average workday for all New York City employees who wear activity trackers. No, we are unable to determine the likelihood of specific values using the confidence interval. Only inferences about the population mean can be drawn from it.

A 99% confidence interval for the mean needs to be calculated.

Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.

Sample Mean(M) = 9,797

Sample Standard Deviation(s) = 2,313.

Sample Size(N) = 61

When σ is unknown, an estimation of σM is made by dividing s by the square root of N:

S = s/√n

S = 2313/√61

S = 2313/7.8102

S = 296.1512

These sample size's degrees of freedom are:

df = n - 1

df = 61 - 1

df = 60

With 61 degrees of freedom and a 99% confidence interval, the t-value is 2.66.

The Margin of Error calculated as:

MOE = t × S

MOE = 2.66 × 296.1512

MOE = 787.7622

The confidence interval's lower and upper bounds are as follows:

Lower Bound = M - MOE

Lower Bound = 9797 - 787.7622

Lower Bound = 9,009.2378

Lower Bound = 9,009(approx)

Upper Bound = M + MOE

Upper Bound = 9797 + 787.7622

Upper Bound = 10,584.7622

Upper Bound = 10,585(approx)

We have a 95% confidence interval between 9,009 and 10,585 steps as the mean number of steps taken on a normal workday for all New York City employees using activity trackers.

b) The value of 8,500 steps is outside the confidence interval, which indicates that it is a high figure for the average number of steps taken by all New Yorkers using activity trackers.

The confidence interval cannot be used to calculate the likelihood of specific values.

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The complete question is:

Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.

a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.

b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.

Answer:

17.6 ft

Step-by-step explanation:

tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

172.5 - 154.9 = 17.6 ft

Answer:

17.6 Ft

Step-by-step explanation:

Geometry B E2020!! :3

Answer:

\(given \\ \frac{ {(y + 1)}^{5} }{(y + 1) ^{3} } \\ as \: they \: have \: same \: base \\ {(y + 1)}^{5 - 3} \\ = (y + 1) ^{2} \\ or \: we \: can \: write \\ = (y + 1)(y + 1) \\ \\ hope \: it \: helps.\)

Answer:

The answer is  \(y^2+2y+1\)

Explanation:

- Properties of Exponent -

\(\frac{a^m}{a^n}=a^{m-n}\)

Our a is y+1

Our m is 5

Our n is 3

\(\frac{(y+1)^5}{(y+1)^3}=(y+1)^{5-3}\\(y+1)^2\)

- Multiply The Polynomial -

As for the Quadratic Polynomial and being squared, we use the following formula:

\((x+y)^2=x^2+2xy+y^2\)

Our x is y

Our y is 1

Thus,

\((y+1)^2=y^2+2(y)(1)+1^2\\(y+1)^2=y^2+2y+1\)

As our simplified, multiplied form is \(y^2+2y+1\)

Answer:

Step-by-step explanation:

See attached image.

Ok, so

Here we have the function:

Remember that:

Before putting the rational function into lowest terms, factor the numerator and denominator. (In our problem the numerator is already factored). If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The solution is the x-value of the hole.

If we factor the denominator:

As you can see, there's not a same factor in the denominator and numerator, so, the function doesn't have holes.

The type of sampling used by the BLS (Bureau of Labor Statistics) for its National Compensation Survey, where employers are divided by size in the second stage of sampling, is known as stratified sampling.

Stratified sampling involves dividing the population into subgroups or strata based on certain characteristics or criteria. In this case, the BLS divides the employers into different size categories. Within each stratum, a sample is then randomly selected to represent that specific subgroup. This approach allows for a more precise estimation of employment costs within each size category. By using stratified sampling, the BLS ensures that the sample is representative of the different employer sizes and allows for more accurate and reliable estimates of employment costs at a national level.

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The answer is yes, y + z ∈ S2.

We need to determine whether the sum of two vectors in S2, y + z, is also in S2.

Let y = (y1, y2, y3) and z = (z1, z2, z3) be two vectors in S2. Then, we know that:

y1y2 + 2y3 = 0 (since y ∈ S2)

z1z2 + 2z3 = 0 (since z ∈ S2)

To show that y + z ∈ S2, we need to show that:

(y + z)1(y + z)2 + 2(y + z)3 = 0

Expanding the left-hand side, we have:

(y1 + z1)(y2 + z2) + 2(y3 + z3) = y1y2 + y1z2 + z1y2 + z1z2 + 2y3 + 2z3

Substituting the expressions for y1y2 + 2y3 and z1z2 + 2z3 from above, we get:

(y1y2 + 2y3) + (z1z2 + 2z3) + y1z2 + z1y2 = 0

Since y1y2 + 2y3 = 0 and z1z2 + 2z3 = 0, we have:

y1z2 + z1y2 = 0

Therefore, we have shown that (y + z)1(y + z)2 + 2(y + z)3 = 0, which implies that y + z ∈ S2.

Hence, the answer is yes, y + z ∈ S2.

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There is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

Given, an ice cream truck aims to keep 30 degrees as the mean temperature inside its delivery truck.

one employee claims that the mean temperature inside its delivery truck is more than 30 degrees. the employee conducts a hypothesis test and rejects the null hypothesis.

The mean temperature inside its delivery truck is 32 degrees.

As, the temperature inside the delivery truck should be 30 degrees and should not be greater than 30 degrees then, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

So, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

Hence, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.

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Answer:

10 minutes

Step-by-step explanation:

I'm not sure if im correct, so im sorry if im wrong.

Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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Answer:

the answer is B

\(y < 2 \: and \: y \geqslant x\)

The lengths of the diagonals of rectangle is 66 units

The properties of a rectangle is given as;

From the information given, we have that;

$WY=14x+10

$XZ=11x+22

Since the diagonals are of the same length, we have;

WY = XZ

14x + 10 = 11x + 22

collect like terms

14x - 11x = 22 - 10

subtract the like terms

3x = 12

Make 'x' the subject of the formula

x = 4

WY = 54 + 10 = 66

XZ = 66

Hence, the values are 66

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Lex will need approximately 18.96 units of tile to surround his pool. The perimeter of the quadrilateral is the sum of these lengths.

To find the number of units of tile Lex will need to surround his pool, we can calculate the perimeter of the quadrilateral ABCD.
Given the coordinates of the vertices on the coordinate plane, we can calculate the lengths of the sides:
AB = \(\sqrt((3-0)^2 + (5-4)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
BC = \(\sqrt((5-3)^2 + (-1-5)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
CD = \(\sqrt((2-5)^2 + (-2+1)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
DA = \(\sqrt((2-0)^2 + (-2-4)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
The perimeter of the quadrilateral is the sum of these lengths:
Perimeter = AB + BC + CD + DA = 3.16 + 6.32 + 3.16 + 6.32 = 18.96 units (rounded to the nearest hundredth)
Therefore, Lex will need approximately 18.96 units of tile to surround his pool.

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Lex will need approximately 20.46 units of tile to surround his pool. To find the number of units of tile needed to surround the pool, we need to calculate the perimeter of the pool.

Given the coordinates of the four vertices of the pool:
    A(0, 4)
    B(3, 5)
    C(5, -1)
    D(2, -2)

We can find the length of segment AB using the distance formula:
    \(AB = \sqrt{(3-0)^2 + (5-4)^2} = \sqrt{9 + 1} = \sqrt{10} = 3.16\)units (rounded to the nearest hundredth).

The length of diagonal BD can also be found using the distance formula:
    \(BD = \sqrt{(2-3)^2 + (-2-5)^2} = \sqrt{1 + 49} = \sqrt{50} = 7.07\) units (rounded to the nearest hundredth).

Since angles A and C are right angles, we know that the opposite sides AB and CD are parallel. Similarly, the opposite sides AD and BC are parallel.

The perimeter of the pool is the sum of the lengths of all four sides:
    Perimeter = AB + BC + CD + AD
                      = 3.16 + BD + 3.16 + BD
                      = 6.32 + 7.07 + 7.07
                      = 20.46 units (rounded to the nearest hundredth).

Therefore, Lex will need approximately 20.46 units of tile to surround his pool.

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