In AABC, m_A = 45°, m_B= 89º and AC = 15. To the nearest tenth what is the measure of BA? ANSWER RN PLz!!

O A. 10
O B. 11.34
O C. 10.8
O D. 11


The given statement, "We can use the normal distribution to approximate the sampling distribution of the average (\(\bar X\)) for a small sample (n<30) even if our sample has clear outliers." is false.

Several random samples of a predetermined size are taken from the same population to generate a sampling distribution, which is a sort of probability distribution. You can better understand how a sample statistic fluctuates from sample to sample by using these distributions.

The given statement is false because when the sample size is small (n < 30) and the data have clear outliers, the normal distribution may not be a suitable approximation for the sampling distribution of the average (\(\bar X\)). In such cases, the presence of outliers can significantly affect the distribution, causing it to deviate from a normal distribution.

For small samples with outliers, it is generally recommended to use alternative methods or non-parametric tests that do not assume a specific distribution. These methods take into account the non-normal nature of the data and provide more robust and reliable results.

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Answer:

-1.47, 1.14 to 2 decimal places.

Step-by-step explanation:

3x^2 + x - 5 = 0

3(x^2 + 1/3x) - 5 = 0

Completing the square on the expression in the parentheses:

3[(x + 1/6)^2 - 1/36) - 5 = 0

3(x + 1/6)^2 - 1/12 - 5 = 0

(x + 1/6)^2 = 61/12 / 3

(x + 1/6)^2 = 61/36

(x + 1/6) = +/-√61 / 6

x = -1/6 +/- √61 / 6

x = 1.135, -1.468

Answer: x = 70

Step-by-step explanation:

Sum of angles in a triangle is 180

55 + 45 + y  = 180

110 + y = 180

(110 - 110) + y = (180 - 110)

y = 70

Vertical angles are congruent so y = x

x = 70

the actuarial expression for the account balance after the final deposit is made as:\(FV = $5000 \times [(1.03^{(n-10)}+1)(1.02)^{(204)}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{(104)}-1]/(0.02)\)The account balance after the final deposit is made is \($62,297.36.\)

The account balance after the final deposit is made, the formula for the future value of an annuity due with a growth rate.

Actuarial expression for the account balance after the final deposit is made:

A be the annual deposit amount, n be the number of deposits, i be the nominal annual interest rate, m be the number of compounding periods per year, and g be the annual growth rate of the deposits.

The formula for the future value of an annuity due with a growth rate is:

\(FV = A \times [(1+g)\times (1+i/m)^{((n-1) \times m)+1}] / (i/m)\)

Louis' situation, we have:

\(A = $5000\) for the first 10 years, and then \(A = $5000 \times 1.03^{(n-10)}\) for the remaining 20 years.

n = 30 years

i = 8% nominal annual interest rate, compounded quarterly, so i = 2% per quarter

m = 4 quarters per year

g = 3% annual growth rate for each deposit after the 10th year

The account balance after the final deposit is made:

The above actuarial expression and substituting n=30, we get:

\(FV = $5000 \times [(1.03^{20}+1)(1.02)^{80}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{40}-1]/(0.02)\)

Simplifying this expression gives:

\(FV = $5000 \times (1.03^{20} \times 1.02^{80} + 1.03^{10} \times 1.02^{40})\)

Using a calculator, we get:

\(FV = $5000 \times (10.4619 + 1.7958)\)

\(FV = $62,297.36\)

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(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

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The background info has less than 50 members, it may lead to insufficient data for making statistic significant conclusions. It's important to have a larger sample size for reliable results and accurate analysis.

A subgroup in the background information has less than 50 members, it may be more difficult to draw statistically significant conclusions or generalize findings to a larger population. This is because the smaller the sample size, the larger the margin of error and the less reliable the data may be. It is still possible to conduct research on small subgroups and draw valid conclusions if appropriate methods are used.

Researchers may need to use alternative statistical analyses or consider qualitative methods to explore the subgroup in more detail. Ultimately, the validity of the findings will depend on the quality of the data collected and the methods used to analyze it.

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Using compound interest, it is found that:

a) He will have paid $18,774 in total.

b) He paid $4,774 more than the price of the car.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, the parameters are:

\(P = 14000, r = 0.049, n = 12, t = \frac{72}{12} = 6\).

Item a:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(6) = 14000\left(1 + \frac{0.049}{12}\right)^{12 \times 6}\)

\(A(6) = 18774\)

He will have paid $18,774 in total.

Item b:

18774 - 14000 = $4,774.

He paid $4,774 more than the price of the car.

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Answer:

Three digit number to be divisible by 5 , the last digit should be 5 or 0

_ _ _5

Two remaining places can be filled in 4×3=12

_ _ _0

Two remaining places can be filled in 3×3=9 (0 cannot be filled in the first place, it will become 2 digit number).

Total =12+9=21

Répondre:  \(\frac{5x5}{24}\)

Commentez si vous voulez l'explication :D

1. The total amount of candy is 1,080 pieces of candy.

2. Each student would get 72 pieces of candy.

Answer:

each student will get 5 pieces of candy

Step-by-step explanation:

20+15+25+12 =72

72 divided by 15 = 5

Answer:

11

Step-by-step explanation:

those alternate angles are equal to each other

5x+4=59

5x=55

x=11

Answer:

(5x + 4) = 59

5x = 59 - 4

5x = 55

x = 55/5

x = 11

The length of side a is 10/3, and the length of the hypotenuse c is 2√(34)/3.

To find the length of side a, we can use the tangent of angle A. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, tan(A) = 5/12, which means that the length of side a is 5/12 times the length of the adjacent side. Since we know that side b is 2, we can calculate a = \((5/12) * 2 = 10/3\).

To find the length of the hypotenuse c, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we know that side b is 2 and side a is 10/3. Let's denote the length of c as x. Applying the Pythagorean theorem, we have \((10/3)^2 + 2^2 = x^2\). Simplifying this equation, we get \(100/9 + 4 = x^2\). Combining the terms, we have 100/9 + 36/9 = \(x^2\), which gives us \(136/9 = x^2\). Taking the square root of both sides, we have \(x = \sqrt{(136/9)} = \sqrt{(136)/} \sqrt{(9)} = \sqrt{(136)/3} = 2\sqrt{(34)/3}\).

Therefore, the lengths of the missing sides are a = 10/3 and c = \(2 \sqrt{(34)/3}\).

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Answer:

25p^2 + 4 + 20p

Step-by-step explanation:

(5p + 2)^2 = (5p)^2 + (2)^2 + 2 × 5p × 2

= 25p^2 + 4 + 20p

Answer:

Combine like terms, although the provided answer is missing a "-" sign in front of the "13."  

Step-by-step explanation:

Combine like terms.  The -7 and -6 can be added to produce -13.

The correct result is -13 - 2x^2 = -2x^2 + 1  [Not _13- 2x² = _2x² + 1

Perhpas the initial equation is written incorrectly(?)

The news article related to a current, specific U.S. trade barrier issue is given below.

Trade barriers are government-induced restrictions on international trade.The barriers can take many forms, including the following:

Tariffs,Non-tariff barriers to trade, Import licenses, Export licenses,Import quotas, Subsidies, Voluntary Export Restraints, requirements, Embargo, Currency devaluation, Trade restriction.

Trade barriers such as tariffs raise prices and reduce available quantities of goods and services for U.S. businesses and consumers, that lead to lower income, reduced employment, and lower economic output.

An increase in U.S. trade barries may also result in a decline in international trade in the United States.

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The point S is selected during the construction as Point S can be placed anywhere along the segment drawn through point R. That is option C.

A congruent segment is defined as the type of segment that is said to be equal in measurement with another segment.

That is , the length of line segment PQ = RS.

When constructing the line segments, Point S can be placed anywhere along the segment drawn through point R. Thai is because the measure of PQ has been taken with the compass and this can be drawn anywhere from point R.

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Answer:

35

Step-by-step explanation:

Law of cosines

c^2=a^2+b^2-2ab(cos(A))

14^2=11^2+8^2-2(11)(8)Cos(A)

A=93.5833

Law of Sines

Sin(A)/a=Sin(B)/a

Sin(93.5833)/11=Sin(B)/8

B=34.7719

If she obtained a different equation or made an error during the conversion process, then that would be the error.

if she correctly converted the equation to standard form, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, and plugged in the given values, she should have obtained the equation:

(x - 4)^2 + (y + 2)^2 = 16

what is equation?

In mathematics, an equation is a statement that asserts the equality of two mathematical expressions. It typically involves one or more variables that can take different values, and the equation is true only for certain values of those variables. Equations are used to model various phenomena in mathematics, science, engineering, and other fields. They are often used to solve problems, to make predictions, and to describe the relationships between different variables or quantities.

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Answer:

-7 over 9

Step-by-step explanation:

To add fractions, find the LCD and then combine.

Option 1. Bar chart and option 2. Histograms are appropriate data displays for the given data about Training for a marathon.

A bar chart can be used to display the frequency or count of each distance category. The horizontal axis can represent the distance categories and the vertical axis can represent the frequency or count. The bars represent the frequency or count of each category.

A histogram can be used to display the frequency or count of each distance category as well as the distribution of the data. The horizontal axis represents the distance categories and the vertical axis represents the frequency or count. The bars represent the frequency or count of each category and are placed next to each other. The range of the data can be easily seen in a histogram.

A line plot, stem-leaf plot, and circle plot are not appropriate data displays for this data set. A line plot is used to display a small data set with discrete values. A stem-leaf plot is used to display a small data set with discrete values as well. A circle plot is used to display the relative sizes of different categories or parts of a whole.

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Complete Question:

The table shows the distance hakeem jogged when training for a marathon. He wants to highlight the mean and range in a data display. Select the appropriate data displays for the given data.

Miles Jogged: 12, 17, 13, 10, 8, 8, 21, 12, 21.

1. Bar chart.

2 histogram

3. line plot,

4. stem leaf plot.

5. circle plot.

Answer:

64 cups

Step-by-step explanation:

1 gallon = 16 cups

Therefore, 4 gallons = 4 x 16 = 64 cups

Answer:

64

Step-by-step explanation:

hope this helps!!! :)

An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.

The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.

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A dependent variable is the variable that being check in a scientific experiment.

The dependent variable is "dependent" on the other independent variable. As the experimenter alter the independent variable, the change in the dependent variable is observed and recorded. When you take data in an experiment, the dependent variable is the one being advised.

A scientist is testing the effect of light and dark on the efforts of moths by turning a light on and off. The independent variable is the amount of light and the moth's reply is the dependent variable.

A change in the independent variable (total amount of light) straight source a change in the dependent variable (moth behavior).

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Answer:

10

Step-by-step explanation:

2+10+18+14+6= 50

then divide by 5 to get mean = 10

Answer:

the answer is 10

Step-by-step explanation:

if you add up all the numbers you get 50

and if you divide it by the number of results, in this case 5, you get 10!

y=x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

Y=x

Step-by-step explanation:

it's a straight line passing by the center (0,0) at 45°

You can tell because Y is equal to X for every value of X and the points you posted fall in this case.

The speed of the air or water increases and its pressure decreases as it circles the longer-path side of the sail or keel. The air or water will attempt to migrate from the side of high pressure to the side of low pressure as it moves along the sail or keel in response to the consequent pressure difference.

Theoretical displacement hull speed is determined by the following equation: velocity in knots = 1.35 x waterline length in feet squared.

Use x to symbolise the slower boat's speed.

Therefore, the faster boat's speed would be x + 20 mph.

They met for 8 hours, hence the distance they travelled overall during that period is depicted as

Distance: (x + 20) * 8 + x * 8

Thus, we have

Distance: 16x plus 160

At twilight, the two boats were separated by 400 kilometres.

The distance equation is as follows.

400 = 16x + 160

Analyze similar terms

16x = 240

multiply by 16

x = 15

Remember that

20 mph faster boat equals x.

Thus, we have

Speedier boat = 15 plus 20

Speedier boat = 35

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