Anne is taking courses in both mathematics and English. She estimates her probability of passing mathematics at 0. 42 and passing English at 0. 47 , and she estimates her probability of passing at least one of the courses at 0. 7. What is the probability that Anne could pass both courses?

Answer:

<

Step-by-step explanation:

√7 ≈ 2.66

14/5 = 2.8

2.66 < 2.8

√7 < 14/5

Best of Luck!

Answer:x − x^{2} − 1.

Step-by-step explanation:

.

The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

To determine whether the set S is linearly independent or linearly dependent.The set is linearly independent. This is because the only way to make a linear combination of vectors equal to the zero vector is to have all the coefficients equal to zero.

A linear combination of vectors is the sum of a scalar multiple of each vector in the set. We must check if the equation a(-2,2,4) + b(1,9,-2) + c(2,3,-3) = (0,0,0) has only the trivial solution, i.e., a=b=c=0. This gives us the system of equations,-2a + b + 2c = 01a + 9b + 3c = 02a - 2b - 3c = 0We can solve the system of equations by using Gauss-Jordan elimination. The augmented matrix for the system is:[-2 1 2 0][1 9 3 0][2 -2 -3 0]Let's use elementary row operations to simplify the matrix.

We can swap the first and second rows since the first element in the second row is 1.[1 9 3 0][-2 1 2 0][2 -2 -3 0]We can then add twice the first row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][-2 1 2 0][0 16 3 0]We can then add nine times the first row to the second row to eliminate the leading coefficient in the second row.[1 9 3 0][0 17 15 0][0 16 3 0]We can then add -16/17 times the second row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][0 17 15 0][0 0 -117/17 0]We see that the only solution is a=0, b=0, and c=0. Therefore, the set S is linearly independent.

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There is no possible width for the rectangle with the given dimensions and area.

The area of the rectangle is given by the product of its length and width.

We know the length of the rectangle is 2x + 1, so we can write:
Area = (2x + 1) * Width

We are also given the expression for the area:
4x4 + 2x³ + 8x² - 20x - 12

We can factor this expression to get:
(2x + 3)(2x - 1)(x² + 2)

So the possible values of the area are (2x + 3)(2x - 1)(x² + 2).

We can set each factor equal to zero to find the possible values of x:
2x + 3 = 0, 2x - 1 = 0, or x² + 2 = 0

Solving for x, we get:
x = -3/2, x = 1/2, or x = ±√(-2)

However, we cannot have a negative value for the width of a rectangle. Therefore, the only possible value for x is 1/2.

Substituting x = 1/2 into the expression for the length of the rectangle, we get:
2x + 1 = 2(1/2) + 1 = 2

So the length of the rectangle is 2.

Substituting x = 1/2 into the expression for the area, we get:
4(1/2)4 + 2(1/2)³ + 8(1/2)² - 20(1/2) - 12 = 0

Simplifying, we get:
4 + 1 + 2 - 10 - 12 = -15

Therefore, there is no possible width for the rectangle with the given dimensions and area.

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Coach Burke's emphasis on proper hitting mechanics during Tuesday's practice at the ball field led to impressive results among the players. By focusing on elements such as stance, grip, and swing, the players were able to improve their overall hitting performance.

Their increased hitting distance can be attributed to several factors.

First, a balanced and comfortable stance allowed the players to transfer their weight effectively and generate more power in their swings. Secondly, a firm yet relaxed grip on the bat helped maintain proper bat control, ensuring that the players were able to hit the ball with maximum force. Additionally, an efficient and smooth swing, with a proper follow-through, allowed the players to make solid contact with the ball, thus increasing the hitting distance.

As a result of Coach Burke's guidance in refining these aspects of hitting mechanics, the players were able to hit the ball off the outfield fence and even over the fence during batting practice.

This improvement in hitting distance is a testament to the importance of mastering the fundamentals of baseball and the impact of quality coaching on player performance.

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Answer:

The width and the length of the pool are 12 ft and 24 ft respectively.

Step-by-step explanation:

The length (L) of the rectangular swimming pool is twice its wide (W):

\( L_{1} = 2W_{1} \)

Also, the area of the walkway of 2 feet wide is 448:

\( W_{2} = 2 ft \)

\( A_{T} = W_{2}*L_{2} = 448 ft^{2} \)

Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle).

The total area is related to the pool area and the walkway area as follows:

\( A_{T} = A_{1} + A_{w} \)    (1)          

The area of the pool is given by:

\( A_{1} = L_{1}*W_{1} \)        

\( A_{1} = (2W_{1})*W_{1} = 2W_{1}^{2} \)  (2)          

And the area of the walkway is:

\( A_{w} = 2(L_{2}*2 + W_{1}*2) = 4L_{2} + 4W_{1} \)    (3)          

Where the length of the bigger rectangle is related to the lower rectangle as follows:                  

\( L_{2} = 4 + L_{1} = 4 + 2W_{1} \)   (4)        

By entering equations (4), (3), and (2) into equation (1) we have:

\( A_{T} = A_{1} + A_{w} \)

\(A_{T} = 2W_{1}^{2} + 4L_{2} + 4W_{1}\)                

\(448 = 2W_{1}^{2} + 4(4 + 2W_{1}) + 4W_{1}\)            

\( 224 = W_{1}^{2} + 8 + 4W_{1} + 2W_{1} \)

\( 224 = W_{1}^{2} + 8 + 6W_{1} \)

By solving the above quadratic equation we have:

W₁ = 12 ft

Hence, the width of the pool is 12 feet, and the length is:

\( L_{1} = 2W_{1} = 2*12 ft = 24 ft \)

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.

I hope it helps you!                                                                                          

Answer:

0.53333333333

Step-by-step explanation:

pls give me brainlest

Answer:

8/15 or 0.5333

Step-by-step explanation:

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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Answer:

B

Step-by-step explanation:

- 9.2(8x - 4) + 0.7(2 + 6.3x) ← distribute parenthesis

= - 73.6x + 36.8 + 1.4 + 4.41x ← collect like terms

= -73.6x + 4.41x + 36.8 + 1.4

= - 69.19 + 38.2

Answer:

the answer is B.-69.19x+38.2

A box can be filled completely using 5 layers of 6 units cubes. The volume of the box is 30 units.

What do you mean by volume?

A measurement of three-dimensional space is volume. Commonly, it is numerically quantified using a range of imperial or US customary measures as well as SI-derived units. Volume and length (cubed) are symbiotically linked. Instead of thinking of a container's volume as the amount of space it takes up, it is more typical to think of it as its capacity. In other words, a container's volume is determined by how much liquid or gas it can hold.

Given in the equation

6 unit cubes and 5 layers total the number of layers in the box. Thus, the volume can be determined below-

=6*5

=30

Hence the volume of the box is 30

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The height of the building from which the angle of elevation is 32 degrees is 127.87m.

The angle of elevation is found to be 32 degrees and when moving 50 closer to the building, the angle of elevation is 53.

Let us say that the height of the building is X.

Now, let us say the distance between the building and the person is Y.

So, we write,

tan(32°) = X/Y

Also, tan(53°) = X/(Y-50)

0.62 = X/Y and 1.32 = X/(Y-50)

0.62Y = 1.32Y - 66

66 = 0.32Y

Y = 206.25 m

Now, we know, X = 206.25m x 0.62

X = 127.87m

So, the height of the building is 127.87m.

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Answer:

6.04 inches.

Step-by-step explanation:

Corbin want's to make a model, in which every 100 feet would be shown by 1 inch.

The monument is 604 feet in height.

Divide 604 with 100:

604/100 = 6.04

The height of Corbin's model would thereby be 6.04 inches.

~

Answer: 6.25 inches

Step-by-step explanation:

Answer:

11/35

Step-by-step explanation:

\(\( \cos (\theta+2\pi) \)\) will have the same value as \(\( \cos (\theta) \).\)

\(\( \cos (\theta+2\pi) = \frac{6}{13} \).\)

To determine the value of \(\( \cos (\theta+2\pi) \)\), we can use the periodicity of the cosine function.

The cosine function has a period of \(\( 2\pi \),\) which means that adding or subtracting \(\( 2\pi \)\) to the angle does not change the value of the cosine.

Since \(\( \theta \)\) is in the first quadrant and \(\( \cos (\theta) = \frac{6}{13} \),\) we know that \(\( \cos (\theta) \)\) is positive.

Adding \(\( 2\pi \)\) to \(\( \theta \)\) will keep it in the first quadrant.

So, \(\( \cos (\theta+2\pi) \)\) will have the same value as \(\( \cos (\theta) \).\)

Therefore, \(\( \cos (\theta+2\pi) = \frac{6}{13} \).\)

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Answer:

$900.47

Step-by-step explanation:

you minus $50.47 (%6) from $900.47

The total cost of an $849.50 laptop after adding a 6% sales tax will be equal to $900.47.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the data provided in the question,

Price of laptop = $849.50

A tax of 6% on the Price of the laptop, so the tax will be,

849.50 × 6/100 = $50.97

Then, the total cost of the Laptop will be,

$849.50 + $$50.97 = $900.47

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The interval does not contain 0, so we can conclude that there is evidence that some washers get damaged during shipment. However, the interval is quite wide, so we cannot be very precise about the proportion of damaged washers.

A confidence interval is a range of values that are constrained by the statistic's mean and that is likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.

a. To construct a confidence interval for the proportion of appliances that get damaged during shipment, we need to check if the following assumptions and conditions are met:

1. Random sampling: The sample of 60 washers should be a random sample from the population of all washers that the manufacturer ships.

2. Independence: The status of one washer being damaged should not affect the status of any other washer. This assumption is reasonable if the washers are inspected and handled independently of each other.

3. Success-Failure Condition: Both the number of successes (washers with damage) and failures (washers without damage) in the sample should be at least 10. In this case, we have 5 successes and 55 failures, so the success-failure condition is met.

If all the assumptions and conditions are met, then we can construct a confidence interval for the proportion of damaged appliances.

b. We can use the formula for the confidence interval for a proportion:

CI = p ± z√(p(1-p)/n)

where:

p = proportion of damaged appliances in the sample

z = critical value from the standard normal distribution for the desired level of confidence (95% in this case)

n = sample size

In this case, we have:

p = 5/60 = 0.0833

z = 1.96 (from a standard normal distribution table for a 95% confidence level)

n = 60

Plugging in the numbers, we get:

CI = 0.0833 ± 1.96√(0.0833(1-0.0833)/60)

CI = 0.0833 ± 0.063

So the 95% confidence interval for the proportion of damaged appliances is (0.020, 0.146).

c. We are 95% confident that the true proportion of damaged appliances in the population of all washers shipped by this manufacturer is between 0.020 and 0.146.  

The interval does not contain 0, so we can conclude that there is evidence that some washers get damaged during shipment. However, the interval is quite wide, so we cannot be very precise about the proportion of damaged washers.

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Let's evaluate the limit using l'Hôpital's Rule when it is convenient and applicable:

The evaluated limit using l'Hôpital's Rule is 5.

Given limit,

lim (x -> 0) (sin(5x) / x)

Since both the numerator and denominator approach 0 as x approaches 0,

we can apply l'Hôpital's Rule.

Step 1: Differentiate the numerator and the denominator with respect to x.
- Derivative of sin(5x) with respect to x: 5*cos(5x)
- Derivative of x with respect to x: 1

Step 2: Apply l'Hôpital's Rule:
lim (x -> 0) (5*cos(5x) / 1)

Step 3: Evaluate the limit:
As x approaches 0, cos(5x) approaches cos(0) = 1.

Therefore, the limit is: 5*1 = 5

So, the evaluated limit using l'Hôpital's Rule is 5

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The probability that a randomly chosen young adult has at least a high school education can be found using the rule of probability called the "complement rule".

To find the answer, we need to subtract the probability that a randomly chosen young adult does not have at least a high school education from 1. In other words:

Probability of having at least a high school education = 1 - Probability of not having at least a high school education.

By using this rule, we can calculate the probability.

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True. Birth statistics typically include data on both live births and fetal deaths.

Fetal deaths refer to the loss of a pregnancy before the fetus is delivered and can be classified as either early or late fetal deaths, depending on the gestational age at the time of the loss. While the focus of birth statistics is often on live births, tracking fetal deaths is important for monitoring the health of pregnant women and identifying potential risks or problems with pregnancy. In the United States, fetal death statistics are typically collected by state health departments and reported to the National Vital Statistics System. These statistics provide important information for researchers, healthcare providers, and policymakers working to improve maternal and fetal health outcomes.

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The probability for sample mean tax is less than $7,900 is 0.1894.

μ = population mean = 8,040

σ = standard deviation = 5,000

n = amount of sample = 1,000

\(\bar x\) = sample mean = 7,900

The probability for sample mean tax can be calculated using z test formula.

P(x < 7,900) = P(z < \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}\) )

= P(z < \(\frac{7,900 - 8,040}{\frac{5,000}{\sqrt{1,000}}}\))

= P(z < \(\frac{-140}{\frac{5,000}{31.622}}\))

= P(z < -0.88)

Using z table for P(z < -0.88). So,

= 0.1894

Thus, the probability is 0.1894 for sample tax mean is less than $7,900.

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Answer:

Function F is odd

Step-by-step explanation:

just took the edmuntum/plato test. I included my answer

The function F is an odd function.

A function f(x) is even if f(-x) = f(x), for all values of x in D(f) and it is odd if f(-x) = -f(x), for all values of x. The graph even function is symmetric with respect to the y-axis and the graph of an odd function is symmetric about the origin.

According to the  question

Function F(x) = \(8x^5+4x^3+5x\)

To check whether function is odd or even

Let x = -x

Now, Substituting -x in f(x)

F(-x) = \(8(-x)^5+4(-x)^3+5(-x)\)  

i.e

F(-x)  = \(-8x^5-4x^3-5x\)

or

F(-x)  = \(-(8x^5+4x^3+5x)\)

F(-x)  = - F(x)

As per definition of odd function

if f(-x) = -f(x), for all values of x. it is a odd function

Therefore, it is a odd function

When graph will be plotted

We can observe that symmetry about the origin.

Hence, the function F is an odd function.

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Answer:

C. (0.4,2.9)

Step-by-step explanation:

When x = .4 the y values are getting the closest to each other

Averaging the y values

(2.8 + 3)/2 = 2.9  is a good approximation to the solution

There were 1542 yes votes

Parameters:

Total votes = 2570

Ratio of yes votes to no votes = 3:2

Sum of ratios = 3 + 2 = 5

The given statement means if 2570 was divided into 5, yes votes take 3 part of the votes, and no votes take the remaining 2.

So

Yes Votes = (3/5)*2570

= 1542

No Votes = (2/5)*2570

= 1028

If 90 pens with black ink were ordered, the total number of pens ordered would be 216.

To solve this problem, we need to find the ratio between the total number of pens and the number of pens with black ink. We can then use this ratio to determine the total number of pens when given the number of pens with black ink.

Let's calculate the ratio for the first set of data:

Ratio = (Pens with Black Ink) / (Total Pens) = 60 / 144

We can simplify this ratio by dividing both the numerator and denominator by their greatest common divisor, which is 12:

Ratio = 5 / 12

Now, we can use this ratio to find the total number of pens when 90 pens with black ink are ordered:

Total Pens = (Pens with Black Ink) / Ratio = 90 / (5 / 12)

Dividing 90 by 5/12 is the same as multiplying 90 by the reciprocal of 5/12:

Total Pens = 90 * (12 / 5) = 216

Therefore, if 90 pens with black ink were ordered, the total number of pens ordered would be 216.

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Answer:

second option is correct (for question no 20)

Step-by-step explanation:

coordinate points are:

(3,1) = (x1,y1)

(5,9) = (x2,y2)

slope (m) = y2-y1/x2-x1

=9-1/5-3

=8/2

=4

Now using slope intercept form

y=mx + b

y=4x + b

since the line passes through the point (3,1) it satisfies the equation

y=4x + b

1=4*3 + b

1-12 = b

-11 = b

substituting the value of b in equation

y=4x + b

y=4x +(-11)

y=4x - 11

Answer:

this. question is not clear please send clear question

We can conclude that -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the following two functions -

y = -x

AND

y = x

Refer to the graphs attached for both the functions -

y = - x     and     y = x

The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.

We can conclude that -

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Given:

Find-:

How many times greater the radius of Saturn is than the radius of Earth

Explanation:-

Let "x" times greater than the radius of Saturn is than the radius of Earth

So,

So Saturn's radius is 9.407 times greater than the radius of the earth.

Step-by-step explanation:

Step-by-step explanation:

The general equation for a circle is

\( {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \)

where (h, k) is the coordinates of the center of the circle and r is the radius. Since the circle passes through (4, 4) and (-4, -4), its center is located at the origin, which means its equation becomes

\( {x}^{2} + {y}^{2} = {( \sqrt{ {4}^{2} + {4}^{2} } )}^{2} = 32\)