Sue either travels by bus or walks when she visits the shops. The probability that she catches the bus TO the shops is 0. 4 the probability that she catches the bus FROM the shops is 0. 7

Answer:

14g-30

Step-by-step explanation:

Combine like terms

11g+3g-9-21

14g-30

Answer: I posted a picture

Step-by-step explanation:

The given argument is invalid by giving values for the predicates p and q over the domain = But both P(a) = p(b) = f There doesn’t exist any x, such that p(x) is true

What is Values?

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.

Given,

fx( p(x) – a(x))

f.(p(x))

fx (a(x))

Let p(a)=T

P(b) = F

And a(a) = T

A(b) = T

So, p(a)=a(a)

=T

P(a) – a(b)

= T

And p(b)=T

So, f.(p(x)-a(x))

Fx(p(x))are T

But we have a (a) + A(b) =T

So, there doesn’t exist any x, such that (x) is true

Hence fX (a(x)) Doesn’t follow from the given statement.

This argument is include

b) fx(p(x) v a(x))

fx (a(x))

fx p(x)

Let P(a) = F

P(b) = F

And a(a) = F

A(b) = T

So, p(b) v a(b) = T

A(a) = F

= ft((x))

But both P(a) = p(b)

= f There doesn’t exist any x, such that p(x) is true

Hence fx p(x)) Dose’t follow from the given statements.

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The correct distance for placing the brake anchor is 6 feet away from the base of the tree.

Let's break down the information given:

Vince measured 24 feet away from the base of the tree because the bungee cord is 24 feet long.

He added 18 extra feet to allow the bungee cord to stretch to capacity.

Vince placed the brake anchor 42 feet from the base of the ending tree.

The flaw in Vince's process lies in his failure to account for the additional stretch of the bungee cord. By placing the brake anchor at 42 feet, he did not consider the extended length the bungee cord would reach.

To find the correct distance, we need to subtract the total length of the bungee cord, including the additional stretch, from the distance Vince measured. Let's calculate this step by step:

Total length of the bungee cord, including extra stretch:

24 feet (length of the bungee cord) + 18 feet (extra stretch) = 42 feet

Distance the brake anchor should be placed away from the base of the tree:

24 feet (Vince's measurement) - 42 feet (total length of the bungee cord) = -18 feet

The negative result indicates that Vince's anchor should be placed 18 feet closer to the base of the tree than his initial measurement. This means

=> (24 feet - 18 feet) = 6 feet.

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The probability that the difference between the sample means will be within 0.05 units of the difference between the population means μ₁ − μ₂ is required.

a) The difference between the sample means, X - Y, is approximately normally distributed with mean μ₁ − μ₂ and variance (σ₁²/n₁) + (σ₂²/n₂), where σ₁² and σ₂² are the variances of populations A and B, respectively. In this case, σ₁² = 0.01 and σ₂² = 0.02. The probability can be found by calculating the area under the normal distribution curve between -0.05 and 0.05. Using the known parameters and the z-score formula, the probability can be determined.

b) If n₁ = n₂ = n, the variance of the difference between the sample means is (σ₁²/n) + (σ₂²/n) = (0.01/n) + (0.02/n). We want this variance to be within 0.04 units with a probability of 0.9. By setting up the appropriate equation and solving for n, we can find the required sample size that satisfies this condition.

The calculations involve applying the properties of the normal distribution and solving equations to find the desired probabilities and sample sizes.

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Assuming that the events of each executive receiving a pay raise are independent, we can use the multiplication rule for independent events to find the probability that all four received a raise.

Let's denote the event that an executive receives a raise by "R". Then, the probability that an executive receives a raise is P(R) = 0.78, and the probability that an executive does not receive a raise is P(not R) = 1 - P(R) = 0.22.

The probability that all four executives receive a raise is:

P(R and R and R and R) = P(R) x P(R) x P(R) x P(R)

= 0.78 x 0.78 x 0.78 x 0.78

= 0.37 or 0.0037 (rounded to 4 decimal places)

Therefore, the probability that all four executives received a raise when they asked for one is approximately 0.0037 or 0.37%.

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Answer:

x = 14
y = 15.5

Correct option is E, The slope of a line perpendicular to y = -10/4 x + 5 is 4/10

The slope of the parallel line is undefined and the slope of the perpendicular line is 0.

Yes, the slope of a line perpendicular to the line 10x + 4y = 20 is indeed -4.

To find the slope of a perpendicular line, we can find the negative reciprocal of the slope of the original line.

The slope of line 10x + 4y = 20 can be found by solving for y and writing the line in slope-intercept form (y = mx + b), where m is the slope.

By solving for y in the equation 10x + 4y = 20:

10x + 4y = 20

4y = -10x + 20

y = -10/4 x + 20/4

y = -10/4 x + 5

So the line is in the form y = -10/4 x + 5, which is the slope-intercept form of a line where the slope (m) is -10/4 and the y-intercept (b) is 5.

Now, to find the slope of a line perpendicular to this line, we need to find the negative reciprocal of the slope of this line. The negative reciprocal of -10/4 is 4/10.

hence,. the slope of a line perpendicular to y = -10/4 x + 5 is 4/10

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Answer:

Explanation:

Here, we want to plot the graph of z1 plus z2

Firstly,let us identify the coordinates of z1 and z2

We can get this from the graph provided

z1 is (8,-4)

z2 is (-2,-3)

The sum of these two will be : (6,-7)

To plot this, we draw dotted vertical line at the point x = 6 and dotted horizontal line at the point y = -7

Wherever these two dotted lines meet is the point z

Answer:

Step-by-step explanation:

3x

Answer:

\(m<NLM = 30\)

Step-by-step explanation:

1. Approach

The easiest way to solve this problem is to find the degree measure of the parameter (x). Use the fact that line (LN) is a diameter to solve for (x), beacause the angle measure of a circle on either side of the diameter is (180) degrees. One can then find the measure of arc (mNM), and then find the measure of the angle (<NLM) using the inscribed angles theory.

2. Find the measure of (x)

A diameter is the largest chord or segment in a circle. It intersects a circle at two points and runs through the center of a circle. The degree measure of a circle on either side of the diameter is (180) degrees. As per the given image, line (LN) is a diameter. The arcs (mLM) and (mNM) make up half of the circle, or rather one side of the diameter. With this information, one can form an equation and solve for the parameter (x) using this information:

\((mLM)+(mNM)=180\)

Substitute,

\((mLM)+(mNM)=180\)

\((13x-10)+(7x-10)=180\)

Simplify,

\((13x-10)+(7x-10)=180\)

\(20x-20=180\)

Inverse operations,

\(20x-20=180\)

\(20x=200\)

\(x=10\)

3. Find the measure of angle (<NLM)

The inscribed angles theorem states that an angle with its vertex on the circumference (outer edge) of a circle is equal to half of the surrounding arc. One can form an equation and solve for the measure of angle (<NLM).

\(m<NLM=\frac{1}{2}(mNM)\)

Substitute,

\(m<NLM=\frac{1}{2}(mNM)\)

\(=\frac{1}{2}(7x-10)\)

\(=\frac{1}{2}(7(10)-10)\\\\=\frac{1}{2}(70-10)\\\\=\frac{1}{2}(60)\\\\=30\)

The value of x is 9/10.

The given equation is \(\frac{4x+9}{2\frac{1}{3} } =\frac{3x}{0.5}\).

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

Now, \(\frac{4x+9}{\frac{7}{3} } =\frac{3x}{\frac{1}{2} }\)

⇒(4x+9)×3/7=3x×2

⇒12x+27=42x

⇒30x=27

⇒x=9/10

Therefore, the value of x is 9/10.

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Answer:

25

Step-by-step explanation:

f(x)=-x^2-10x

Let x = -5

f(-5)=-(-5)^2-10(-5)

     = -25+50

      =25

Answer:

4a) 110 square centimetres

4b) 127 square centimetres

6) 292 square centimetres

8) 800 tiles

Step-by-step explanation:

4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:

a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:

A = 12 * 15 = 180 square centimetres

The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:

a = 10 * 7 = 70 square centimetres

Therefore, the area of the shaded part is:

A - a = 180  - 70 = 110 square centimetres

b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:

A = 13 * 11 = 143 square centimetres

The unshaded part has dimensions 8 cm by 2 cm. Its area is:

a = 8 * 2 = 16 square centimetres

Therefore, the area of the shaded part is:

A - a = 143 - 16 = 127 square centimetres

6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.

The frame has dimensions 24 cm by 18 cm. Therefore, its area is:

A = 24 * 18 = 432 square centimetres

The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:

a = 14 * 10 = 140 square centimetres

Therefore, the background area of the space not covered by the photograph is:

A - a = 432 - 140 = 292 square centimetres

8) The floor has dimensions 8 m by 4 m. The area of the floor is:

A = 8 * 4 = 32 square centimetres

Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:

a = 0.2 * 0.2 = 0.04 square metres

The number of tiles that are needed is the area of the floor divided by the area of each tile:

A / a = 32 / 0.04 = 800 tiles

Answer: it is a true equation.  

Step-by-step explanation:

the values of x and y that make the points (1,2,3), (5,7,1), and (x,y,2) collinear are x = 2 and y = 4.

Let's consider the direction ratios of the given points:

Point 1: (1, 2, 3)

Direction ratios: (1-0, 2-0, 3-0) = (1, 2, 3)

Point 2: (5, 7, 1)

Direction ratios: (5-1, 7-2, 1-3) = (4, 5, -2)

Point 3: (x, y, 2)

Direction ratios: (x-1, y-2, 2-1) = (x-1, y-2, 1)

Since the direction ratios should be proportional, we can set up the following proportion:

(1, 2, 3) / (4, 5, -2) = (x-1, y-2, 1) / (4, 5, -2)

This gives us the following ratios:

1/4 = (x-1)/4

2/5 = (y-2)/5

3/-2 = 1/-2

Simplifying these ratios, we get:

1 = x - 1

2 = y - 2

3 = 1

Solving these equations, we find:

x - 1 = 1

x = 2

y - 2 = 2

y = 4

Therefore, the values of x and y that make the points (1,2,3), (5,7,1), and (x,y,2) collinear are x = 2 and y = 4.

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Answer:

2 cm²

Step-by-step explanation:

Perimeter of a rectangle = perimeter of a square + perimeter of a square

2 congruent squares, side by side

The perimeter of the two squares = 6*sidelength.

Perimeter of a rectangle = 6 cm

The perimeter of the two squares = 6 * length

= 6l

Perimeter of a rectangle = The perimeter of the two squares

6 = 6l

l = 6/6

l = 1

Length = 1 cm

What is the total area of the squares.

Area of a square = lenght²

Area of two squares = 2(length ²)

= 2(1²)

= 2(1)

= 2 cm²

The number of weeks when Jim and Sally would have the same amount of money is 20 weeks.

The expression that can be used to represent the amount of money Jim would have in his account after x weeks is: $1,250 + 27.50x.

The expression that can be used to represent the amount of money Sally would have in his account after x weeks is: $1,400 + $20x.

In order to determine the number of weeks when they would have the same amount of money, the two expressions must be equal to each other.

$1,250 + 27.50x =  $1,400 + $20x

Combine similar terms

$1,400 - $1,250 = $27.50x - $20x

150 = $7.50x

x = 150 / 7.50 = 20 weeks

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The answer you are looking for is 1/5(a+34).

Solution/Explanation:

"Of"="multiplication (x)."

So, therefore, write it like this, to get the better picture and visualization,

1/5 times the sum of a number "a" and "34."

"Sum" obviously is related to "addition."

So, therefore, we can simplify the algebraic expression a little bit more,

1/5 times (a+34).

Now, we can finally write it like this.

1/5x(a+34).

The more proper way to write it, however is like this:

1/5(a+34).

So, therefore, the final answer is 1/5(a+34).

I hope that this has helped you. Enjoy your day, and take care!

The given statement is required in the form of an algebraic expression.

The statement is a fifth of the sum of number a and 34.

The sum means addition

So, the sum is \(a+34\)

The statement states a fifth of which, means multiplied by \(\dfrac{1}{5}\)

The algebraic expression will be the product of \(\dfrac{1}{5}\) and \((a+34)\)

The algebraic expression is \(\dfrac{1}{5}(a+34)\)

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Answer:

the story of my life

Step-by-step explanation:

good luck <3

Answer:

(14.2k - 1.1m + 5.5n) cm

Step-by-step explanation:

Perimeter of a triangle = side A + side B + side C

Side A = (5.8k+3.3m)cm

Side B = (8.4k-2.4n)cm

Side C = (7.9n-4.4m)cm

Perimeter of a triangle = side A + side B + side C

= (5.8k+3.3m) + (8.4k-2.4n) + (7.9n-4.4m)

= 5.8k + 3.3m + 8.4k - 2.4n + 7.9n - 4.4m

Collect like terms

= 5.8k + 8.4k + 3.3m - 4.4m - 2.4n + 7.9n

= (14.2k - 1.1m + 5.5n) cm

Therefore, the perimeter of the triangle = (14.2k - 1.1m + 5.5n) cm

Answer:

Step-by-step explanation: 20x+15(160-x)=2625

20x+2400-15x=2625

5x=225

x=45

160-x=115

rate of first mechanic= $45/hr

rate of second mechanic=$115/hr

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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The student from the first class performs better when comparing their scores using z-scores.

To compare the students' performances, we will calculate their z-scores, which show how many standard deviations away their scores are from the mean of their respective classes.

For the student from the first class:
z-score = (Score - Mean) / Standard Deviation
z-score = (62 - 56) / 9
z-score ≈ 0.67

For the student from the second class:
z-score = (83 - 75) / 15
z-score ≈ 0.53

The student from the first class has a higher z-score (0.67) compared to the student from the second class (0.53). This means the student from the first class performed better relative to their classmates.

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This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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The number of water distributed is 5265

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

There are 27 volunteer organizations.

each organization has 5 volunteers

therefore the number if volunteers is 27 × 5 = 135

each volunteers distributed 39 bottles

therefore the number of bottles distributed = 39 × 135 = 5265 bottles

therefore 5265 bottles were distributed

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Answer:

13in

Step-by-step explanation:

remember it's the same angle width.

Answer:

Hey :D

Step-by-step explanation:

Answer:

B: y=sinx

Step-by-step explanation:

the parent sine function is a repeating function that goes from 0 to 1, with sin(0)=0 sin(pi/2)=1 sin(pi)=0 sin(3pi/2)=-1 and sin(2pi)=0, π≈3.1415926 and we see on this graph that the graph matches at all these major points.

the cosine parent function is essentially the same thing but shifted to the left by π/2. It is essential to familiarize yourself with the unit circle and the key angles and their respective sin and cosine values.

The answer is y = sin x!!