Finn read an article claiming that 50% of Americans have brown hair,
20% have black hair, 20% have blonde hair, and
10% have red hair. He wondered if the hair colors of students at his school followed this distribution, so he took a random sample of
50 students and recorded their hair colors. Here are his results:
Color Brown Black Blonde Red
Students
17 14 14 5
He wants to use these results to carry out a
�
2
χ
2
\chi, squared goodness-of-fit test to determine if the distribution of hair colors at his school disagrees with the claimed percentages.

Choose 1 answer:
(Choice A)
�
2
=
5.76
;
0.10
<
P-value
<
0.15
​

χ
2
=5.76;
0.10 ​

A
�
2
=
5.76
;
0.10
<
P-value
<
0.15
​

χ
2
=5.76;
0.10 ​

(Choice B)
�
2
=
5.76
;
0.20
<
P-value
<
0.25
​

χ
2
=5.76;
0.20 ​

B
�
2
=
5.76
;
0.20
<
P-value
<
0.25
​

χ
2
=5.76;
0.20 ​

(Choice C)
�
2
=
6.05
;
0.10
<
P-value
<
0.15
​

χ
2
=6.05;
0.10 ​

C
�
2
=
6.05
;
0.10
<
P-value
<
0.15
​

χ
2
=6.05;
0.10 ​

(Choice D)
�
2
=
6.05
;
0.15
<
P-value
<
0.20
​

χ
2
=6.05;
0.15 ​

D
�
2
=
6.05
;
0.15
<
P-value
<
0.20
​

χ
2
=6.05;
0.15 ​

Step-by-step explanation:

a) To calculate the amount that Eric will receive after the 6 years, we need to use the formula for simple interest:

I = P * r * t

Where:

- I is the interest earned

- P is the principal amount (the initial investment)

- r is the interest rate (as a decimal)

- t is the time period (in years)

In this case, Eric invested $10,000 at an interest rate of 8% for 6 years. So we can plug in these values:

I = 10,000 * 0.08 * 6

I = 4,800

The interest earned is $4,800. To find the total amount that Eric will receive after the 6 years, we need to add the interest to the principal:

Total = P + I

Total = 10,000 + 4,800

Total = 14,800

Therefore, Eric will receive $14,800 after the 6 years.

b) The total interest that Eric will earn is already calculated in part a) and it is $4,800.

Theoretical probability is the likelihood of an event occurring based on mathematical reasoning or analysis, rather than on empirical or experimental data.

Probability refers to the likelihood of a particular event or outcome occurring. It is a measure of the chance of an event happening, and is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, physics, engineering, and finance, to make predictions and inform decision-making.

Here,

It is calculated using the laws of probability and assumes that all outcomes are equally likely to occur. Theoretical probability is often used in situations where it is not possible or practical to conduct experiments or collect data, such as in mathematical or statistical modeling.

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Answer:

A:0 Noone goes higher than 40. b: 5 miles

Answer:

Only the set of ordered pairs is one-to-one

Step-by-step explanation:

You have three right

The last one:
A function is one-to-one if and only if, for every value of y there is only one value of x

The mapping diagram is not one-to-one since for two values of x, x = -3 and x = 5 we get the same y value of 6

The set of ordered pairs is a one-to=-one since for every value of y there is a unique value for x

Answer: 680

Step-by-step explanation:

Answer:

The location of the point (4, 2) is to the right of the triangle RST, therefore,

a dilation from the left or a contraction from the right is required.

The dilation of ΔRST that would result in a line segment with slope of 2

that passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered 12,2

Step-by-step explanation:

Answer:

93%

Step-by-step explanation:

651/700 houses were for sale. Write that as a percentage.

651/700=0.93

0.93=93%

Answer: y=1x+6

Step-by-step explanation:

goign up by 1/1 y intercpt is 6

The vertical shape of the graph will be the same as that of the first rocket, assuming both rockets have the same initial velocity and acceleration.

1.I agree with Serena that we can draw the graphs for the other two rockets by shifting the functions. We can use the same equation and just adjust the values of the horizontal and vertical shifts.

2. The equation f(t) = -6t² represents a quadratic function, which has a parabolic shape when graphed. If we apply a transformation to this function, such as a vertical or horizontal shift, the shape of the graph will change accordingly.

3. The term 82.14 likely represents the maximum height achieved by the rocket, since the equation f(t) = -6t² gives the height of the rocket as a function of time. The value of h(t) = 82.14 corresponds to a specific time when the rocket reaches its maximum height.

4. If the second rocket is launched 3 seconds after the first one, the graph of the second rocket will be shifted horizontally by 3 units to the right compared to the graph of the first rocket. This represents a time delay of 3 seconds between the two launches.

5. The equation of the second rocket would be f(t) = -6(t-3)², assuming that the second rocket has the same initial velocity and acceleration as the first rocket but is launched 3 seconds later.

6. Since the third rocket is launched 3 seconds after the second rocket and from a tall platform, its graph will be shifted horizontally to the right by 6 units compared to the graph of the first rocket.

9. A: Based on the graph, the third rocket was launched at approximately 5:20 PM.

B: Based on the graph, the first rocket lands at approximately 5:15 PM.

C: Based on the graph, all three rockets are in the air between approximately 5:10 PM and 5:25 PM, so the approximate interval during which all three rockets are in the air is 15 minutes.

Therefore,  spends an additional 6 seconds in the air before landing. The vertical shape of the graph will depend on the specifics of the rocket's launch and trajectory.

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The conversion of 1/12in to milliters  can be expressed as 2.117mm

Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. As an illustration, if you had 1,000 interactions and 50 conversions, your conversion rate would be 5% because 50 x 1,000 = 5%.

The proportion of users who perform the intended action is known as the conversion rate. The proportion of website visitors who make a purchase there serves as the prototypical illustration of conversion rate.

We can  1/12in to milliters by using the conversion rate, which 1inch = 25.4mm,and this can be used to make the conversion as:

If  1inch = 25.4mm

 1/12 = X mm

Xmm =  (1/12 *25.4mm)/ 1inch

=2.117mm

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complete question:

How much is 1/12in to milliters?

The probability that one-half of the selected people will have high blood pressure is given as follows:

P(X = 13) = 0.0004684.

The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.

The mass probability formula is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters, along with their meaning, are listed as follows:

The parameter values for this problem are given as follows:

n = 26, p = 0.2.

One-half of 26 is of 13, hence the probability is given as follows:

P(X = 13) = 26!/(13! x 13!) x (0.2)^13 x (0.8)^13

P(X = 13) = 0.0004684.

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The length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.

The angles of a triangle are the angles formed by its sides. The sum of the angles of a triangle is always 180 degrees, which is a fundamental property of this shape. There are different types of triangles, based on their side lengths and angle measures. For example:

A scalene triangle has three sides of different lengths and three different angles.

An isosceles triangle has two sides of equal length and two equal angles.

An equilateral triangle has three sides of equal length and three equal angles.

A right triangle has one angle that measures 90 degrees (a right angle), and the side opposite to it is called the hypotenuse.

Triangles have many important properties and applications in mathematics, physics, and engineering. They can be used to calculate distances, angles, areas, volumes, and many other quantities. Triangles are also used in the construction of buildings, bridges, and other structures, as well as in art, design, and other fields.

We can use the trigonometric ratio of sine to solve for x:

sin(42) = opposite/hypotenuse

sin(42) = x/5

To solve for x, we can multiply both sides by 5 and simplify:

x = 5*sin(42)

x ≈ 3.4 (rounded to the nearest tenth)

Therefore, the length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.

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Hence, in answering the stated question, we may say that As a result, graphs  P75 equals 80.375.

Mathematicians use graphs to visually explain or chart events or variables. A graph point often indicates a connection between one thing and another. A graph, a non-linear data structure, is constituted of nodes (vertices) and edges. Glue the nodes, which are also called as vertices. This graph has E=1, 2, 1, 3, 2, 4, and (2.5) edges and V=1, 2, 3, 5. (3.5). (4.5). Graphical representations of exponential growth in analytical charts (bar charts, pie charts, line charts, and so on). a graph of a logarithmic triangle.

To get the value of P75, the 75th percentile, we need to discover the score where 75% of the scores fall below it.

z = (x - μ) / σ

where x is the score to be converted, is the mean, and is the standard deviation.

So we can write:

0.75 = P(Z ≤ 0.675)

where Z is the standard normal variable with a mean of 0 and a standard deviation of 1.

We can now rearrange the formula for the z-score to solve for the score x:

x = μ + zσ

Plugging in the values we have:

x = 77.4 + (0.675)(5) (5)

x = 80.375

As a result, P75 equals 80.375.

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Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore, LDFE = 35°

what is  parallel lines ?

Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.

In the given question,

Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.

Corresponding angles are pairs of angles that are in the same relative position at the intersection of two lines that are crossed by a third line, called a transversal. More specifically, corresponding angles are formed when a transversal intersects two parallel lines.

Corresponding angles are congruent, which means they have the same measure or degree of angle

Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore,

LAEG = LDFE

So, LDFE = 35°. .

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Answer:

Step-by-step explanation:

because we know 1 hour is 60 min so 3 hours would be 60x3=180 then you do 3x23.7=71 12x11.2=134 so in total he has 23.7 per hour and 11.2 for 3 hours

Answer:

Step-by-step explanation:

rate of the plane be x

distance traveled by plane = 420 miles

time taken by plane = 420/x

distance traveled by car =120 miles

rate of car = x-120

time taken by car = 120 / x-100

the time taken by both are same

420/x = 120/ x-100

420(x-100)=120x

420x-42000 = 120x

420x-120x=42000

300x= 42000

x=42000/300

x=140 mph the speed of the plane

We reject the null hypothesis and come to the conclusion that there is adequate evidence at the 0.02 level.

The rejection of a correct null hypothesis during hypothesis testing is referred to as a Type I mistake. As a result, we get the incorrect conclusion that there is a large difference between two groups or variables. A false positive is another name for a Type I mistake.

Failure to reject a faulty null hypothesis is a Type II mistake. This means that we get the incorrect conclusion that there is no difference between two groups or variables when there actually is one. False negative is another name for a Type II mistake.

The valve generates a mean pressure of 4.7 lbs/square inch, which is the null hypothesis:

H0: μ = 4.7

The other possibility is that the valve does not generate 4.7 lbs/square inch of mean pressure:

Ha: μ ≠ 4.7

Since we are comparing the single sample mean to a known population mean and we are aware of the population variance, we can test this hypothesis using a one-sample t-test. The test statistic is determined by dividing the sample mean (x) by the population mean, the sample size (n), and the population standard deviation (s).

We obtain the following by plugging in the values:

t = (4.6 - 4.7) / (0.9 / √(240))

t = -4.15

Using a two-tailed test and a t-distribution table with 239 degrees of freedom (240 - 1), we can get the crucial t-value as follows:

T critical equals 2.571

We reject the null hypothesis and come to the conclusion that there is adequate evidence at the 0.02 level that the valve does not operate in accordance with specifications since our computed t-value (-4.15), which is in the rejection area (t -2.571 or t > 2.571), falls within this range.

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Based on the image, we can break 9 × 4 into two expressions as 4 groups of 9 or 9 groups of 4. This equals 36.

It should be noted that to break 9 x 4 up into two expressions, you can use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.

So, we can rewrite 9 x 4 as:

9 x 4 = 9 x (3 + 1)

Using the distributive property, we can expand this expression as:

9 x (3 + 1) = (9 x 3) + (9 x 1)

Simplifying, we get:

9 x 4 = 27 + 9

Therefore, we have broken up 9 x 4 into two expressions: 27 and 9. This will give 36.

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Answer:

34

Step-by-step explanation:

16x-12= 9x-11 + 9x-11

16×-12=18x-22

10=2x

5=x

WT= 9x-11=9(5)-11

WT=45-11

WT=34

Answer:

(1,2)

Step-by-step explanation:

The solution to a system of equations is the point at which the lines defined by the equations intersect.

On this graph, we can see that the lines meet a point on the graph that is at 1 on the x-axis (horizontal axis) and at 2 on the y-axis (vertical axis).

In Cartesian coordinates, this is written in the format (x, y):

(1, 2)

Answer:

NO= 18

Step-by-step explanation:

If we dissect the image, we can see that triangle LMN there are two similar triangles; triangle LMN and smaller triangle OPN. By definition of similar triangles, corresponding parts of similar triangles will have the same ratios. So, as we can see, sides NP and NM are corresponding. The ratio of the two sides is 24/44 (just put the smaller side over the longer side). Simplified, the ratio is 6/11. So, we know that the opposite sides' ratio will also be 6/11. So, all we have to do is multiply NL (33) by 6/11, which equals 18.

Check:

24/44=6/11, and 18/33=6/11, so the ratios are the same.

Using null hypothesis,

a. Hzero : μ = 22

Hone : μ > 22

b. All requirements are satisfied.

c. Reject Hzero

d. There is sufficient evidence to support the claim that the students who complete the core curriculum are ready for college-level mathematics. (Score above 22 on average).

The null hypothesis is used to make decisions when employing data and statistical tests. The null hypothesis, or Hzero, claims that there is no difference in the characteristics of the two samples. A null hypothesis is, in general, a statement of no difference. The null hypothesis must be rejected in order to accept the alternative hypothesis.

a. Given,

μzero = 22.

n = 200

x = 22.6

s = 3.9

α = 0.05

Claim is mean is more than 22.

The claim is either null or alternative hypothesis. The null hypothesis states that the population mean is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

Hzero : μ = 22

Hone : μ > 22

b. Requirements t-distribution hypothesis test: Simple random sample, sampling distribution of the sample mean is approximately normal & independent sample results.

Simple random sample: Satisfied, because exercise prompt states that the sample is a random sample.

All requirements are satisfied.

c. Classical approach:

Determine the value of test statistics,

t = 2.176

Determine the critical values from the students' T-distribution table with

df = n - 1 = 200 -1 = 199 > 100

t = 1.660

2.176>1.660

⇒ Reject Hzero

d. There is sufficient evidence to support the claim that the students who complete the core curriculum are ready for college-level mathematics. (Score above 22 on average).

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Answer:

To solve this problem, we can use the central limit theorem and the standard normal distribution.

The central limit theorem states that the distribution of sample means is approximately normal, with a mean equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Let X be the systolic blood pressure of an individual in the population. We know that X is normally distributed with a mean of 120 and a standard deviation of 8.

Let Y be the sample mean blood pressure of a sample of 20 individuals. Then Y is also normally distributed, with a mean of 120 and a standard deviation of 8 / sqrt(20) = 1.7889.

We want to find the probability that the sample mean blood pressure is greater than 123. We can standardize this value using the standard normal distribution as follows:

Z = (Y - 120) / (8 / sqrt(20))

P(Y > 123) = P(Z > (123 - 120) / (8 / sqrt(20)))

= P(Z > 1.3363)

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 1.3363 is approximately 0.0918.

Therefore, the probability that the mean blood pressure for a sample of 20 people will be greater than 123 is approximately 0.0918.

Answer:

Second one

Step-by-step explanation:

The absolute maximum value occur (3, 4.033) at point x = 3

The function given in the problem is g(x) = 3x³e⁻ˣ

differentiating the function

g(x) = 3x³e⁻ˣ

g'(x) = 3x³(-e⁻ˣ) + e⁻ˣ(9x²)

g'(x) = e⁻ˣ(-3x³ + 9x²)

equating to zero

0 = e⁻ˣ(-3x³ + 9x²)

0 = -3x³ + 9x²

3x³ = 9x²

x = 3

checking intervals close to 3: the check is done using numbers at the left and right to 3 and this numbers will be sufficiently close.

We choose 1 and 5, when the value of g'(x) increases from positive to negative then maximum value occurs

at x = 1, g'(1) = e^(-1)(-3(1)³ + 9(1)²) = 2.2073

at x = 3, g'(3) = e^(-3)(-3(3)³ + 9(3)²) = 0

at x = 5, g'(5) = e^(-5)(-3(5)³ + 9(5)²) = -1.0107

We can say that x = 3 is point of local maxima

g(3) = 3(3)³e^(-3) = 4.03275 = 4.033

from calculation the absolute maximum value occurs at (3, 4.033)

From the graph the absolute maximum value for the domain -1 ≤ x ≤ 5 occurs at (3, 4.033)

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76 is m<BFD in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

 m<AFC + m<BFD = 180°

   (7x-8)° +   m<AFC = 180°

   (5x+6)° +  m<BFD =  180°

(7x-8)° = (5x+6)

 2x = 12

    x = 14

m<BFD=(5x+6)°

       = 5 * 14 + 6

        = 70 + 6

          = 76

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In response to the question, we may say that  Value total: 60 cents plus equation 240 cents plus 300 cents equals $3.00.

The equals symbol (=), which indicates equivalence, connects two statements in a mathematical equation. An algebraic equation's mathematical assertion proves the equality of two mathematical propositions. The equal sign, for instance, places a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. Use a mathematical formula to understand how the two sentences on opposite sides of a letter relate to one another. Usually, the logo corresponds to the particular programme. An example would be 2x - 4 = 2.

Let's define our variables first:

Let x represent the amount of quarters in the machine.

10x + 5(8x) = 300

When we simplify and find x, we obtain:

10x + 40x = 300

50x = 300\sx = 6

Hence, the machine has six dime coins. We may determine the quantity of nickels by using the connection between the number of dimes and nickels:

8x = 8(6) = 48

There are 48 nickels in the machine as a result.

Verifying our response:

6 dime is 6 times 10 cents, or 60 cents.

48 nickels is 48 x 5 cents, or 240 cents.

Value total: 60 cents plus 240 cents plus 300 cents equals $3.00.

The vending machine has 48 nickels and 6 dimes, thus our answer is right.

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The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

What is the Gaussian method?

The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.

To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:

Machining department: 1200x + 1800y + 3000z = 1050(60)

Inspection department: 2400x + 1200y = 1160(60)

Assembly department: 600x + 3000y = 830(60)

Simplifying these equations, we get:

Machining department: 20x + 30y + 50z = 3150

Inspection department: 8x + 4y = 232

Assembly department: x + 5y = 139

Now we can use the Gaussian method to solve for x, y, and z:

Step 1: Write the augmented matrix:

| 20 30 50 | 3150 |

| 8 4 0 | 232 |

| 1 5 0 | 139 |

Step 2: Use row operations to get the matrix in row echelon form:

R2 → R2 - 4/5 R3

R1 → R1 - 20R3

| 0 -2 50 | 850 |

| 0 2 -4   | -28 |

| 1 5 0     | 139 |

R2→ -1/2 R2

R1 → R1 + R2

| 0 1 -25 | 407 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R1→ R1 - R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R3→ R3 - 5R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R1→ -1/23 R1

| 0 0 1 | -17 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R2 → R2 + 2R3

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 10 | 65 |

R3 → R3 - 10R1

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 0 | 235 |

Step 3: Read off the solution from the row echelon form:

z = -17

y = 96

x = 235

Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

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Answer:

y = 8 is the smaller number.

Step-by-step explanation:

Sove the system by adding the two equations together, one on top of the other. Add from the top, down.



x + y = 20

x - y = 4

________

2x = 24

Divide by 2.

x = 12

Put this back into either original equation.

x + y = 20

12 + y = 20

Subtract 12.

y = 8

The numbers are 12 and 8.

8 is the smaller number.