aldo has scored 77, 88, 77, 87, and 63 on his previous five tests. what score does he need on his next test so that his average (mean) is 79?

Answer: 540 cm²

Step-by-step explanation:To find the area of the dilated rectangle, we need to first find the dimensions of the new rectangle after it has been dilated by a factor of 3.

The length of the new rectangle will be 3 times the original length, which is:

10 cm x 3 = 30 cm

The width of the new rectangle will also be 3 times the original width, which is:

6 cm x 3 = 18 cm

Therefore, the area of the dilated rectangle will be:

30 cm x 18 cm = 540 cm²

Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

The width of the dumpster that minimizes its surface area is approximately 1.71 yards, and the length is approximately 3.42 yards.

The length of the rectangular dumpster is equal to two times its width, or 2x, if x is its width. The dumpster's height is not specified, however it is not necessary for this issue.

We need to determine the dumpster's size to reduce the amount of surface area it has. The following sources provide the rectangular dumpster's surface area:

A = lw + lh + lw

where w stands for width, l for length, and h for height.

Given that the container must hold [tex]20 yd3[/tex] of waste, we can use the formula for the volume of a rectangular solid to create the following sentence:

[tex]V = lwh = (2x) (x)\\h = 2x^2 h = 20\\h = 10/x^2[/tex]

Inputting this expression for h into the surface area A formula yields the following results:

[tex]A = 2lw + 2lh + 2wh = 2(x)(2x) + 2(x)(10/x) + 2(2x)(10/x) = 4(x)(2x) + 40(x)[/tex]

We can take the derivative of A with respect to x, set it equal to zero, and solve for x to determine the dimensions that minimise A:

[tex]dA/dx = 8x - 40/x^2 = 0\\8x = 40/x^2\\x^3 = 5\\x = (5)^(1/3)\\[/tex]

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To find out whether the community studied in Exercise 13 was unusual or not, a t-test should be utilized to determine whether the average loss observed was significantly different from the regional average.

T-test is a statistical test that assesses whether two population means are statistically different from one another. It is often used in hypothesis testing to determine whether there is a significant difference between two means.

A t-test is utilized when the mean of one variable for two groups is compared to the mean of another variable for those same two groups.

The steps to perform a t-test are given below:

Determine the level of significance (alpha).

Determine the degrees of freedom (DF) for the sample.

Determine the critical value of t.

Calculate the t-value.

Compare the calculated t-value with the critical value of t.

Draw a conclusion as to whether there is a significant difference between the two means or not.

A t-test can be performed using the following formula:

t = (X1 - X2) / [s (1 / n1 + 1 / n2)]

Where:

X1 and X2 are the means of the two samples.

s is the pooled standard deviation of the two samples.

n1 and n2 are the sample sizes for the two groups.

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Answer: We can solve the given inequality as follows:

|2x + 2| > 4

There are two cases to consider, depending on whether the expression inside the absolute value is positive or negative:

Case 1: 2x + 2 > 4

2x > 2

x > 1

Case 2: 2x + 2 < -4

2x < -6

x < -3

Therefore, the solution to the inequality is x < -3 or x > 1.

To graph the solution, we can plot the two critical points x = -3 and x = 1 on a number line, and shade the regions to the left of -3 and to the right of 1. This gives us the following graph:

<==================o-----------------o===================>

    x < -3       x > 1

The open circles indicate that the points -3 and 1 are not included in the solution, since the inequality is strict (|2x + 2| > 4).

Step-by-step explanation:

The confidence interval for variance is (0.29,0.58)

A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.

The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.

The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.

Since we have given that the sample size n= 54,

variance = 0.44

we need to find a 98% confidence interval to estimate the variance.

So, we will use Chi-square distribution,

For this, we will find

df=n-1 = 54-1 = 53,

the interval would be,

[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]

Hence the confidence interval is (0.29,0.58)

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A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.

As per the given information,

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.

Here we have to Find: How deep should the searchlight be.

First of all, we need to find the equation of the paraboloid of revolution.

Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).

So, the equation of the paraboloid is given by:

y² = 4ax

Where, a = 2 feet (distance of light source from vertex)

So, the equation of the paraboloid is:

y² = 8x ..... (1)

The opening of the paraboloid is given to be 5 feet across.

We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.

The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)

The equation of the plane is given by x = -2.5

Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.

We can substitute x = -2.5 in equation (1) to get:

y² = -20

Squaring both sides, we get:

y = ±√(-20)

Since y can only be positive (since we are considering the upper half of the paraboloid),

y = √(-20) = i√20 = 2√5 i

So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)

The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet

Hence, the depth of the searchlight should be 2.5 feet.

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The value of x is 7, and NM and OL are both equal to 37.

Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,

NM = OL

We also have the following information:

NM = x + 30

OL = 4x + 9

Substituting the first equation into the second equation, we get:

x + 30 = 4x + 9

Simplifying this equation, we get:

3x = 21

Therefore, x = 7.

Substituting this value back into the original equations, we get:

NM = x + 30 = 7 + 30 = 37

OL = 4x + 9 = 4(7) + 9 = 37

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The value of the interquartile range for the given subsample is 8.

The interquartile range (IQR) is a measure of the dispersion of a set of observations. It is defined as the difference between the third quartile and the first quartile (Q3-Q1). The subsample data is as follows: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. The interquartile range for the subsample data can be computed as follows:

Step 1: Arrange the data in ascending order: 18, 20, 21, 22, 24, 24, 25, 27, 28, 31, 35, 36.

Step 2: Find the median of the lower half of the data, which is called the first quartile, Q1. Here, the lower half of the data is 18, 20, 21, 22, 24, and 24. Hence, the median of the lower half of the data is the average of the two middle values, which is Q1 = (22 + 21)/2 = 21.5.

Step 3: Find the median of the upper half of the data, which is called the third quartile, Q3. Here, the upper half of the data is 24, 25, 27, 28, 31, 35, and 36. Hence, the median of the upper half of the data is the average of the two middle values, which is Q3 = (28 + 31)/2 = 29.5.

Step 4: Calculate the interquartile range as the difference between the third quartile and the first quartile: IQR = Q3 - Q1 = 29.5 - 21.5 = 8.

Therefore, the value of the interquartile range for the given subsample is 8.

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Answer:

B) 3

Step-by-step explanation:

219 / 73= 3

3 x 73= 219

Answer: 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think it equals 18 tens

Answer:

3 x 60 x 30 = 5400

Step-by-step explanation:

The total number of listings possible for the 14 teams in the local little league is 11,664. This is because there are 14 teams, so the number of possible listings is equal to 14! (14 factorial). 14! is equal to 1x2x3x4x5x6x7x8x9x10x11x12x13x14, which equals 11,664.

To further explain, 14! is the number of ways to arrange 14 items. This is because the first item can be arranged in 14 ways, the second item in 13 ways, the third in 12, and so on. This means that the total number of possible arrangements is 14x13x12x11x10x9x8x7x6x5x4x3x2x1, which equals 11,664.

Therefore, the total number of listings possible for the 14 teams in the local little league is 11,664.

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The measure of the larger acute angle of the right triangle is 73.7°. This can be calculated using trigonometry and the Pythagorean theorem.

The larger acute angle of the triangle can be found using trigonometry. First, we can find the length of the other leg using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs. Plugging in the values we get: 4² + b² = 12², solving for b we get b = √(12² - 4²) = 8√3. Now we can use inverse tangent to find the larger acute angle: tan⁻¹(opposite/adjacent) = tan¹⁽⁸√³/⁴⁾ ≈ 73.7°. So, the measure of the larger acute angle is 73.7°.

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The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.

Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

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Answer:

290

Step-by-step explanation:

Answer:

The ring-shaped region has an inner radius of 10m and a width of 3m. To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle. The area of a circle is given by A = πr^2, where r is the radius. Therefore, the area of the outer circle is A1 = π(10+3)^2 = 169π m^2 and the area of the inner circle is A2 = π(10)^2 = 100π m^2. Subtracting these two areas gives us: A1 - A2 = (169π - 100π) m^2 = 69π m^2. Therefore, the area of the shaded region is approximately 216.27 m^2 (69π ≈ 216.27) .

The probability that the arborist will break a saw chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking is 0.007

We are given the probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw.

The time that he spends on each saw are 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking.

Let us find the probability that he will break a chain when he uses the small climbing saw.

P(small climbing saw) = 1/2P(Break a chain using small climbing saw) = 0.004

Using the medium limbing saw: P(medium limbing saw) = 3/8P(Break a chain using medium limbing saw) = 0.008

Using the large felling and bucking saw: P(large felling and bucking saw) = 1/8P(Break a chain using large felling and bucking saw) = 0.04

Now, to find the probability that he will break a chain on a day, we use the weighted average. Probability is a weighted average because the probability of breaking the saw chain is different for each saw that he uses.

Hence, the probability that he breaks a saw chain when he uses each saw is weighted according to how much time he spends on that saw.

P = P(small climbing saw)* P(Break a chain using small climbing saw) + P(medium limbing saw) * P(Break a chain using medium limbing saw) + P(large felling and bucking saw) * P(Break a chain using large felling and bucking saw)P = (1/2 * 0.004) + (3/8 * 0.008) + (1/8 * 0.04)P = 0.007

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The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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(a) The probability that there is exactly one car and exactly one bus during a cycle is 0.020.

(b) The probability that there is at most one car and at most one bus during a cycle is 0.105.

(c) The probability that there is exactly one car during a cycle is 0.100, and the probability that there is exactly one bus during a cycle is 0.200. The probability that there is exactly one car is also 0.050.

(a) To find the probability that there is exactly one car and exactly one bus during a cycle, we need to look at the cell in the table where x = 1 and y = 1. This cell has a probability of 0.020. Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.020.

(b) To find the probability that there is at most one car and at most one bus during a cycle, we need to add up the probabilities of the cells where either x = 0 or x = 1, and either y = 0 or y = 1. These cells are

x = 0, y = 0: 0.025

x = 0, y = 1: 0.010

x = 1, y = 0: 0.050

x = 1, y = 1: 0.020

Adding up these probabilities, we get

0.025 + 0.010 + 0.050 + 0.020 = 0.105

Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.105.

(c) To find the probability that there is exactly one car during a cycle, we need to add up the probabilities of the cells where x = 1. These cells are

x = 1, y = 0: 0.050

x = 1, y = 1: 0.020

x = 1, y = 2: 0.030

Adding up these probabilities, we get

0.050 + 0.020 + 0.030 = 0.100

Therefore, the probability that there is exactly one car during a cycle is 0.100.

To find the probability that there is exactly one bus during a cycle, we need to add up the probabilities of the cells where y = 1. These cells are

x = 0, y = 1: 0.010

x = 1, y = 1: 0.020

x = 2, y = 1: 0.050

x = 3, y = 1: 0.060

x = 4, y = 1: 0.040

x = 5, y = 1: 0.020

Adding up these probabilities, we get

0.010 + 0.020 + 0.050 + 0.060 + 0.040 + 0.020 = 0.200

Therefore, the probability that there is exactly one bus during a cycle is 0.200.

Finally, the probability that there is exactly one car can also be obtained by summing the probabilities of the cells in the first row of the table

0.025 + 0.010 + 0.015 = 0.050

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The surface area of the triangular prism Milo paints red is equal to 186 square centimeters.

The triangular prism have two triangle and three rectangle faces, so we shall calculate for each area of the faces and add them to get the surface area of the triangular prism as follows:

area of triangle = 1/2(base × height)

area of one triangle face = 1/2(6 cm × 4 cm)

area of one triangle face = 12 cm²

area of two triangle faces = 2 × 12 cm² =24 cm²

area of one rectangle face = 10.8 cm × 5 cm

area of one rectangle face = 54 cm²

area of three rectangle faces = 162 cm²

area of the triangular prism = 24 cm² + 162 cm³

area of the triangular prism = 186 cm²

Therefore, the surface area of the triangular prism Milo paints red is equal to 186 square centimeters.

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The Answer of the given question based on the triangle is angle ∠α ≈ 56.4° degrees , angle ∠β ≈ 33.6° degrees , side C ≈ 14.4° units.

In a right triangle, the hypotenuse is the longest side and it is opposite the right angle. It is the side that is directly opposite the right angle and is always opposite the largest angle of the triangle. The hypotenuse is also the side that connects the two legs of the right triangle. The length of hypotenuse can be found using Pythagorean theorem.

From the problem statement, we know that angle ∠gamma = 90° degrees, which means that BC is the hypotenuse of the right triangle. We also know that side A = 12 and side B = 8.

Using Pythagorean Theorem, we can find length of  hypotenuse by:

c² = a² + b²

c² = 12² + 8²

c² = 144 + 64

c² = 208

c = √(208)

c ≈ 14.4

So the length of BC is approximately 14.4 units.

To find the altitude CA, we can use the formula for the area of a right triangle:

area = (1/2) * base * height

Since angle gamma = 90° degrees, the altitude CA is equal to the length of side A:

CA = A = 12 units.

Now we can use the trigonometric ratios to find the acute angles∠α and :

sin(α) = opposite/hypotenuse = CA/c

sin(α) = 12/14.4

α ≈ 56.4° degrees

Since α and gamma are complementary angles (they add up to 90° degrees), we can find β using the following formula:

β = 90 - α

β ≈ 33.6° degrees

Therefore, the unknown values for the given right triangle are:

angle ∠α ≈ 56.4° degrees

angle ∠β ≈ 33.6° degrees

side C ≈ 14.4° units.

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Answer:

18.72

Step-by-step explanation:

48% is 0.48 as a decimal

0.48*39=18.72

Answer:

$57

Step-by-step explanation:

12*4.75=57

At alpha equal to 0.01 there is enough evidence to reject the claim that is the chance of a false positive.

When reducing the alpha from 0.05 to 0.01 reduces the chance of a false positive also called a Type I error, it makes it harder to detect differences with a t-test and with any significant results one might obtain would be more trustworthy but there would probably be less of them.

We know that:

probability > 0.1: no evidence,

then, probability between 0.05 and 0.1: weak evidence

then, probability between 0.01 and 0.05: evidence

then, probability between 0.001 and 0.01: strong evidence

and probability < 0.001: very strong evidence

The alpha level set relates to the formal decision made rather than this informal interpretation, but both can be reported together.

Lower alpha levels are sometimes used while carrying out multiple tests at the same time and a common approach is to divide the alpha level by the number of tests being carried out.

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The  probability that at least 3 customers out of the first 6 will buy bread is 88.3% that is option B.

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

The formula used is :

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

65% of customers who come into this store buy bread, hence p = 0.65.

A sample of 6 customers is taken, hence n = 6.

The probability that at least 3 customers out of the first 6 will buy bread is given by:

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

In which

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

P(X = 3) = C₆,₃(0.65)³ x (0.35)³ = 0.2355

P(X = 4) = C₆,₄(0.65)⁴ x (0.35)² = 0.328

P(X = 5) = C₆,₅(0.65)⁵ x (0.35)¹ = 0.2437

P(X = 6) = C₆,₆(0.65)⁶ x (0.35)⁰ = 0.0754

Then,

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

= 0.2355 + 0.328 + 0.2437 + 0.0754 = 0.8826

The probability that at least 3 customers out of the first 6 will buy bread is 0.8826 ≈ 88.3%.

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Complete  question;

A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?

23.5%

88.3%

11.7%

76.5%

Optiοn A : Side AD is οppοsite tο the angle ACD in the given triangle ADC.

Every triangle has 3 sides and thus 3 angles. Each side οf a triangle has 2 angles οf it fοrmed at the 2 endings οf the side and οne angle is the οne present οppοsite tο the side.

Thus, fοr each side, 2 angles are tοuched and 1 angle at the οppοsite is called the οppοsite angle tο that side.

Here, the triangle is ADC.

The 3 angles οf the triangle are : ADC, ACD, and CAD

Fοr side AD,

The twο angles A ( CAD ) and D( ADC ) are cοnnected with the side AD and are adjacent tο it.

The third angle C ( CAD ) is nοn-adjacent tο side AD and is οppοsite tο it. Hence, Optiοn D is cοrrect.

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The system of equation with the same solution with 2x + 2y = 16 3x  - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.  Therefore, let's solve the system of equation as follows;

2x + 2y = 16

3x  - y = 4

multiply equation(ii) by 2

2x + 2y = 16

6x - 2y = 8

add the equations

8x = 24

x = 24  / 8

x = 3

y = 3x - 4

y = 3(3) - 4

y = 9 - 4

y = 5

Therefore,

2x + 2y = 16

6x - 2y = 8

add the equation

8x = 24

x = 24  / 8

x = 3

Therefore,

2(3) + 2y = 16

6 + 2y = 16

2y = 16 - 6

2y = 10

y = 5

Therefore, the equation with the same solution is 2x + 2y = 16

6x - 2y = 8.

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