I need help on this math question

The density of glycerin at 60°C is approximately 19.9592 g/cm³.

To find the density of glycerin at 60°C, we can use the volume expansion coefficient and the given density at 20°C.

The formula for volume expansion is:

ΔV = β * V₀ * ΔT

where:

ΔV is the change in volume,

β is the volume expansion coefficient,

V₀ is the initial volume, and

ΔT is the change in temperature.

In this case, we want to find the change in density, so we can rewrite the formula as:

Δρ = -β * ρ₀ * ΔT

where:

Δρ is the change in density,

β is the volume expansion coefficient,

ρ₀ is the initial density, and

ΔT is the change in temperature.

Given:

ρ₀ = 20 g/cm³ (density at 20°C)

β = 5.1 x 10⁻⁴ °C⁻¹ (volume expansion coefficient)

ΔT = 60°C - 20°C = 40°C (change in temperature)

Substituting the values into the formula, we have:

Δρ = - (5.1 x 10⁻⁴ °C⁻¹) * (20 g/cm³) * (40°C)

Calculating the expression:

Δρ = - (5.1 x 10⁻⁴) * (20) * (40) g/cm³

≈ - 0.0408 g/cm³

To find the density at 60°C, we add the change in density to the initial density:

ρ = ρ₀ + Δρ

= 20 g/cm³ + (-0.0408 g/cm³)

≈ 19.9592 g/cm³

Therefore, the density of glycerin at 60°C is approximately 19.9592 g/cm³.

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Answer:

B. g(x) = RootIndex 3 StartRoot x minus 3 EndRoot + 4

Step-by-step explanation:

edg 2021 .. its correct

The equation that is graphed along with the parent function is \(g(x)=\sqrt[3]{x-3} +4\)

The parent function is a cube root function, represented as:

\(f(x) = \sqrt[3]{x}\)

First, the parent function is horizontally shifted right by 3 units

The rule of this transformation is:

\((x,y) \to (x - 3,y)\)

So, we have:

\(f'(x) = \sqrt[3]{x - 3}\)

Next, the transformed function is vertically shifted up by 4 units

The rule of this transformation is:

\((x,y) \to (x,y+4)\)

So, we have:

\(g(x)=\sqrt[3]{x-3} +4\)

Hence, the equation is \(g(x)=\sqrt[3]{x-3} +4\)

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Answer:

C.

Step-by-step explanation:

(-90) + (-20) + 100 = -10

Hope I Helped! :)

Answer:

The solution is C. -10

Step-by-step explanation:

Before entering the solution, remember the formula first!

Addition

• (-) + (-) = (-)

• (+) + (+) = (+)

Subtraction

• (+) - (+) = can (-) and (+)

• (+) - (-) = (+)

Multiplication

• (-) x (-) = (+)

• (+) x (-) = (-)

Division

• (-) : (-) = (+)

• (+) : (-) = (-)

Solution:

(-90) + (-20) + 100

= -90 - 20 + 100

= -110 + 100

= -10 (the minus number is greater than the positive, then the result is minus)

Answer:

15

Step-by-step explanation:

15 is your answer

Answer:

Your answer is 15

hope this helps

b)The marginal PDF fx(x) is given by: fx(x) = (\(2\sqrt{(r^2 - x^2))/(\pi r^2}\)), for -r < x <r

c) the marginal PDF fy(y) is given by: fy(y) = (\(2\sqrt{(r^2 - y^2))/(\pi r^2}\)), for -r < y < r

To find the marginal probability density functions (PDFs) fx(x) and fy(y) from the joint PDF fX,Y(x, y), we need to integrate the joint PDF over the appropriate range.

b) To find the marginal PDF fx(x), we integrate fX,Y(x, y) with respect to y while considering the range of x:

fx(x) = ∫fX,Y(x, y) dy

Since the joint PDF is defined over the circle \(x^2 + y^2 < r^2\), the integration limits for y will be -\(\sqrt{r^2 - x^2)}\) to \(\sqrt{r^2 - x^2)}\)

fx(x) = ∫\([-\sqrt{(r^2 - x^2)}\), \(\sqrt{(r^2 - x^2}\))] (1/(πr^2)) dy

Integrating, we get:

fx(x) = (\(1/(\pi r^2)\)) * 2\(\sqrt{(r^2 - x^2}\)

Therefore, the marginal PDF fx(x) is given by:

fx(x) = (2\(\sqrt{(r^2 - x^2}\)/(\(\pi r^2\)), for -r < x < r

c) Similarly, to find the marginal PDF fy(y), we integrate fX,Y(x, y) with respect to x while considering the range of y:

fy(y) = ∫fX,Y(x, y) dx

Since the joint PDF is defined over the circle\(x^2 + y^2 < r^2\), the integration limits for x will be -\(\sqrt{r^2 - y^2}\)) to \(\sqrt{(r^2 - y^2}\)).

fy(y) = ∫[-\(\sqrt{r^2 - y^2}\), √\(\sqrt{r^2 - y^2}\)] (\(1/(\pi r^2\))) dx

Integrating, we get:

fy(y) = (1/\((\pi r^2\))) * 2\(\sqrt{r^2 - y^2}\))

Therefore, the marginal PDF fy(y) is given by:

fy(y) = \(2\sqrt{(r^2 - y^2))/(\pi r^2}\) for -r < y < r

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Answer:

Option D is correct

Step-by-step explanation:

First, let's find side BC by using Pythagoras theorem.

Given:

=> 9² = 7.8² + x²

=> 81 = 60.84 + BC²

=> BC² = 20.16

=> √BC² = √20.16

=> BC = √20.16

=> BC = 4.48998886413 (Using calculator)

=> BC ≈ 4.49 (Estimated)

Therefore, side BC ≈ 4.49 units. Now, let's find the area by using hero's formula.

=> 1/2(Perimeter) = S

=> Perimeter: Hypotenuse + Side 1 + Side 2

=> 7.8 + 9 + 4.49

=> 21.29 = Perimeter

=> 1/2(21.29) = S

=> 10.645 = S

=> √s(s - a)(s - b)(s - c) = Area of triangle

=> √10.645(10.645 - 9)(10.645 - 4.49)(10.645 - 7.8)

=> √10.645(1.645)(6.155)(2.845)

=> √10.645 x 1.645 x 6.155 x 2.845

=> √306.635120999 (Using calculator)

=> √306.64 (Estimated)

=> 17.5111393119 (Using Calculator)

=> 17.51 units² (Estimated)

We can see that option D is the closest option. Therefore, Option D is correct.

If Option D was incorrect, then my second opinion is A.

If both are wrong, I deeply apologize for the inconvenience caused by me. Hoped this helped.

Answer:

answer is d) 18.6

Step-by-step explanation:

area = 1/2ab sin ∅

a= 9

b = 7.8

so it's

1/2 ×7.8 × 9 sin 32

use your calculator to get 18.600 unit squared

*we can also use the heroes formula*...

The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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The level of measurement is required of the independent variable (iv) and dependent variable (dv) to conduct a chi-square analysis is "the chi-squared test for independence."

A chi-square (X²) statistic is a test which compares a model to real observed data. A chi-square statistic requires data that is random, raw, mutually exclusive, obtained from independent variables, & drawn from a large enough sample. Tossing a fair coin, for example, meets these criteria.

Some key features regarding chi-square test are-

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Answer:3/2

Step-by-step explanation: just did the test

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.

16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.

Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12

The corresponding sides are

6/9, 6/9, 8/12

When you simply, we get

2/3, 2/3, 2/3

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

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Answer:

4 = 60     5 =  120     6 = 120     7 = 60

Step-by-step explanation:

Answer:

Hopefully this helps.

The probability of drawing two eights is 16/2,704, which simplifies to 1/169, or approximately 0.59%.

There are a total of 52 cards in each deck, so there are 52 x 52 = 2,704 possible combinations of cards that could be drawn.

To calculate the probability of drawing two eights, we need to determine the number of ways we can draw two eights and then divide that by the total number of possible combinations.

There are four eights in each deck, so there are 4 x 4 = 16 ways to draw two eights (one from each deck).

Therefore, the probability of drawing two eights is 16/2,704, which simplifies to 1/169, or approximately 0.59%.

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Answer:

Step-by-step explanation:
To find the average number of days it takes for the sun to rotate once, we can add the three rotation periods and divide by 3:

Average rotation period = (24.5 + 24.8 + 34.3) / 3

Average rotation period = 83.6 / 3

Average rotation period = 27.87 days (rounded to two decimal places)

Therefore, the average number of days it takes for the sun to rotate once based on the given information is approximately 27.87 days.

The throw of the dice or the drawing of a card is known as random behavior.

Random behavior refers to events that occur by chance, without any predictability or pattern. These events cannot be influenced or controlled, and their outcomes are determined by the laws of probability. In games such as dice and card games, the outcomes are determined by random variables, such as the position of the dice or the shuffle of the deck.

Random behavior can also occur in other contexts, such as weather patterns or the stock market, where events are subject to unpredictable fluctuations. Understanding random behavior is important in many fields, including mathematics, statistics, and economics, as it can help us make informed decisions based on the probability of different outcomes.

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The qualities of the given set are that it is closed and its interior is open.

The given set is the region between two concentric circles centered at the origin with radii of 3 and 4. To determine the qualities of this set, we can consider its boundaries, interior, and exterior. The boundaries of the set are the two circles of radius 3 and 4. These boundaries are included in the set, so the set is closed. The interior of the set consists of all points whose distance from the origin is between 3 and 4. Since the set contains no points on the boundaries, it is open. The exterior of the set consists of all points whose distance from the origin is either less than 3 or greater than 4. Since the complement of the set is the union of two open disks, the exterior of the set is also open. Therefore, the qualities of the given set are that it is closed and its interior is open.

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Answer:

1. i^20 X (2+i^22)

2. i² X (i¹¹-1) X (i²² + i¹¹ + 1) X (i^66 + i³³ + 1)

Step-by-step explanation:

1) 2i^20 + i^42

factor out i^20

i^20 X (2 + i^22)

2) i^101 - i²

i²X(i^99-1)

i²X(i³³-1)X(i^66+i³³+1)

Using a³-b³=(a-b)(a²+ab+b²)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

I almost gave up typing. Quite stressful, but its fine

Answer:

m∠D = 32°

Step-by-step explanation:

From the figure attached,

In ΔABE,

By the property of a triangle,

m∠AEB + m∠ABE + m∠AEB = 180°

14° + 45° + m∠AEB = 180°

m∠AEB = 180° - 59°

m∠AEB = 121°

Since, m∠AEB = m∠CED = 121° [Vertical angles]

Similarly, in triangle CDE,

m∠ECD + m∠CED + m∠EDC = 180°

27 + 121 + m∠CDE = 180

m∠CDE = 180 - 148

m∠D = 32°

Answer:

A correlation coefficient close to zero

Step-by-step explanation:

This makes linear regression unreasonable because the correlation coefficient shows how related the data points are, -1 and 1 being very strong and 0 being uncorrelated. So the line of best fit would not make sense because the data points are random in relation to one another.

Answer:          B. A correlation coefficient close to zero

Step-by-step explanation:

The test statistic for a sample with correlation coefficient r = 0.5 and sample size n = 30 is 3.06.

To test whether a correlation is significant, we need to calculate the test statistic using the correlation coefficient (r) and the sample size (n). The formula for the test statistic is:

t = r * sqrt(n-2) / sqrt(1-r^2)
Here, r is the correlation coefficient (0.5) and n is the sample size (30).
Plugging in the given values of r = 0.5 and n = 30, we get:

t = 0.5 * √((30 - 2) / (1 - 0.5^2))
t = 0.5 * √(28 / 0.75)
t = 0.5 * √(37.33)
t = 0.5 * 6.11
t ≈ 3.06

Thus, the test statistic for this sample is approximately 3.06. To determine whether the correlation is significant, we would need to compare this test statistic to a critical value from a t-distribution with n-2 degrees of freedom at the desired significance level.

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Answer:

7-56n

Step-by-step explanation:

By using the distributive property you multiply the 7 to the 1 which equals 7. Then you distribute the 7 to the -8n which gives you -56n becaus emultiplying a negative and a possitive gives you a negative.

The required solution is -56n+7.

It is required to find the solution.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

Rearrange terms

7(1 - 8n)

=7(-8n+1)

Then distribute by multiplying 7 we get,

-56n+7

Therefore, the required solution is -56n+7.

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Using the vertex of the quadratic function, it is found that:

a) The maximum number of customers in the store is at 12 P.M.

b) 75 customers are in the store at this time.

The number of customers in x hours after 7 AM is given by:

\(y = -x^2 + 10x + 50\)

Which is a quadratic equation with coefficients \(a = -1, b = 10, c = 50\)

Item a:

The maximum value, considering that a < 0, happens at:

\(x_v = -\frac{b}{2a}\)

Hence:

\(x_v = -\frac{10}{2(-1)} = 5\)

5 hours after 7 A.M, hence, the maximum number of customers in the store is at 12 P.M.

Item b:

The value is y(5), hence:

\(y(5) = -(5)^2 + 10(5) + 50 = 75\)

75 customers are in the store at this time.

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Answer:

x = 10

y = 15

Step-by-step explanation:

Angles 8x - 10 and 7x are congruent because they are alternate interior angles of parallel lines cut by a transversal.

8x - 10 = 7x

x = 10

7x = 7(10) = 70

6y + 20 and 7x are supplementary since they are a linear pair.

6y + 20 + 7x = 180

6y + 20 + 70 = 180

6y = 90

y = 15

Answer:

-14 +2

Step-by-step explanation:

because you would do kcc aka keep change change

you would keep -14 change the minus to a addition sign and change the -2 to a positive 2

Answer:

b= -10

Step-by-step explanation:

Divide -10 from both sides to get b alone

hope this helps :)

Answer:

b=-10

Step-by-step explanation:

divide each term by -10 to get your answer

Answer:

1

X+.12*x=190.40

X(1+.12)=190.40

X=190.40/1.12=170

2a

X+x+25=100

2x=75

X=37.5%

Men=.375*270=101

2b

increasing the sample size of an opinion poll will lead to (b) variability of the estimates made from the data collected in the poll.

An opinion poll is a human research survey of the public's opinion from a specific sample. It is frequently referred to as just a survey or a poll, even though strictly speaking an election is a poll. To assess the sentiments and beliefs of the entire population, interviews or surveys with representative samples of citizens are utilised. Students can participate actively in discussions using almost any device with well-designed polls. Each poll must be adjusted separately, and many features that teachers might find helpful demand a subscription package. A greater sample size yields more data on the population and, thus, more accurate population estimates. Better population estimates will also let us know that there is less fluctuation.

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Answer:

seven and eight tenths is greater than three and four tenths

100% of the F2 generation plants are expected to be tall and produce round fruit.

The given information suggests that F1 and F1 represent heterozygous tall and round plants, respectively. When these two genotypes are crossed, we can predict the possible genotype and phenotype combinations of the offspring by using a Punnett square.

The Punnett square for this cross would be:

F1     F1

F2 F1F1 F1F1

F1F1 F1F1

From this square, we can see that all of the F2 generation plants will be homozygous for both tallness and roundness. This is because the F1 generation is heterozygous for both traits, so when they are crossed, the recessive alleles are masked by the dominant alleles.

Therefore, the genotype of all F2 plants will be F1F1, and they will all be tall and round.

In summary, 100% of the F2 generation plants are expected to be tall and produce round fruit.

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Answer:

Your answer is <, Hope it helps.