Look at the table showing prices of different items at a store.

Items for Sale
Paperbacks
$10.65 for 3
Notebooks
$14.36 for 4
Puzzles
$11.85 for 3
Picture Frames
$15.20 for 4

Which items cost less than $3.75 per item?
picture frames and paperbacks
puzzles and notebooks
picture frames and puzzles
paperbacks and notebooks

Answer:

The answer to this question is --> 0.40

Step-by-step explanation:

simply do the division.

as a fraction is basically nothing else than a division of the upper number by the lower number.

2 divided by 5

2/5 = 0.4

remember, how division works :

first the outmost left digit(s) divided by the digits of the right number. we use the same number of digits on both sides.

2 / 5 = 0

the first step gives us a 0, because 2 cannot be divided by 5.

then we pull down the next digit from the left side.

if we don't have any (as in this case), we simply pull a 0.

20 / 5 = 0.4

when we pull digits on the left side after the decimal point, then the result gets the decimal point exactly at that position.

20/5 = 4, so the 4 goes into the first position after the decimal point.

and therefore, the final result is

2/5 = 0.4

Justin's speed on his way to his parents' house was 42 mph. Therefore, his speed on his way back home was 18 mph slower, or 18 mph.

Let's use x mph to represent the pace at which Justin was travelling to his parents' house. Then, as he travelled 24 mph slower owing to the terrible weather, his speed on the way back would be (x - 24) mph.

By dividing the distance he drove by his speed, one may determine how long it took Justin to drive to his parents' house, or:

Time is a function of both speed and distance.

Similar to how long it would take Justin to drive back home:

Time is a function of distance and speed (x - 24)

Justin drove for a total of 12 hours, so we can construct the following equation:

420/x + 420/(x-24) = 12

By multiplying both sides of the equation by x(x-24), we may simplify the equation and find the value of x. After some algebraic fiddling, we arrive at:

\(x^2 - 24x - 840 = 0\)

We can find the value of x by using the quadratic formula:

\(x = (24 +- \sqrt{(242 + 41840)}) / 2\) or x = -18

We can determine that Justin was travelling at a speed of 42 mph as he made his way to his parents' home because the speed cannot be negative. Thus, he travelled at a speed of 18 mph less on the way back home.

We can confirm the following to see if the solution is accurate:

420/42 + 420/18 = 10 + 23.33 = 33.33

Justin did, in fact, drive for a total of 12 hours, proving that our answer is accurate.

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The expected frequencies are approximately 38 for each entrance. The degrees of freedom for the chi-squared test are 3. The critical value for the rejection region can be obtained.

The null hypothesis (H0) states that all four entrances are used equally, while the alternative hypothesis (Ha) suggests that there is a difference in the usage of the entrances. The expected frequencies can be calculated by dividing the total number of people (150) equally among the four entrances (150/4 = 37.5). However, since frequencies must be whole numbers, we can approximate the expected frequencies as 38 for each entrance.

The degrees of freedom for a chi-squared test in this case are (number of categories - 1) = (4 - 1) = 3. The critical value, based on a 10% level of significance, would be obtained from the chi-squared distribution table for 3 degrees of freedom.

To make a statistical decision, we compare the calculated test statistic (8.755) with the critical value. If the calculated test statistic exceeds the critical value, we reject the null hypothesis and conclude that there is evidence of a difference in the usage of the entrances. However, if the calculated test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and do not have sufficient evidence to conclude a difference in entrance usage.

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Answer: x=48

Step-by-step explanation:

first add 9 to both sides

then add 27 to 9 to get 36

multiply both sides by 3/4 the reciprocol of 4/3

and youll get x=36 x (4/3)

simply to a single fraction then

then divide 144 by 3  to get 48

Answer:

the increase is by 2

Step-by-step explanation:

You can add 17 plus 2 or subtract 17 from 19.

Answer:

2?

Step-by-step explanation:

Answer:

1: 180-degree Rotation.

2: Reflection across the X-Axis

3: Translation 3 units left, and 3 units up.

Step-by-step explanation:

Answer:

180-degree Rotation.

Reflection across the X-Axis

Translation 3 units left, and 3 units up.

Do great on your text!!! :3

Answer:

989000

Step-by-step explanation:

Answer: 100,000 = 989,000

5x - y - 13 = 0  is the equation of the plane

To find the equation of the plane, we need two pieces of information: a point on the plane, and the normal vector of the plane.

We are given a point on the plane: P0(2, -3, -5).

To find the normal vector of the plane, we need to use the fact that the plane is perpendicular to the given line. The direction vector of the line is <1, 5, 0>, since the line has parametric equations x=2+t, y=-3+5t, z=-3, and the vector <1, 5, 0> is the coefficient vector of the parameter t in these equations.

Any vector that is perpendicular to <1, 5, 0> will be a normal vector of the plane. One such vector is <5, -1, 0>, which we can verify by taking the dot product of this vector with <1, 5, 0>:

<5, -1, 0> · <1, 5, 0> = 5(1) + (-1)(5) + 0(0) = 0

Thus, the normal vector of the plane is <5, -1, 0>.

Now we can use the point-normal form of the equation of a plane:

ax + by + cz = d

where <a, b, c> is the normal vector of the plane, and (x, y, z) is any point on the plane. Substituting in the values we have:

5(x - 2) - 1(y + 3) + 0(z + 5) = 0

Simplifying:

So the equation of the plane is:

5x - y - 13 = 0

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The probability of getting at least 2 1's in 4 spins is:

1 - 0.7383 = 0.2617 or approximately 26.17%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To calculate the probability that at least 2 of the spins result in a 1, we can use the complement rule and subtract the probability that fewer than 2 of the spins result in a 1 from 1.

The probability of getting exactly 0 1's in 4 spins is:

(3/4)⁴ = 0.3164

The probability of getting exactly 1 1 in 4 spins is:

4 * (1/4) * (3/4)³ = 0.4219

So the probability of getting 0 or 1 1's in 4 spins is:

0.3164 + 0.4219 = 0.7383

Therefore, the probability of getting at least 2 1's in 4 spins is:

1 - 0.7383 = 0.2617 or approximately 26.17%.

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The question is given below as

Now, we will have to replace the blank spaces with letters a and b

Cross multiply both sides, we will have

By comparing coefficients, we will have

By comparing the second coefficient, we will have

Hence,

The complete equation will be

Answer:

see explanation

Step-by-step explanation:

f(x) = x² , then

f(3.5) = 3.5² = 12.25

which means the area of a square with a side of length 3.5 units is 12.25 units²

The area of a square with a side of length 3.5 units is 12.25 square units.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

Given that, the area for any square is given by the function f(x) = x², where x is the length of a side of the square

f(x) = x²

f(3.5) = 3.5²

f(3.5) = 12.25

Hence, The area of a square with a side of length 3.5 units is 12.25 square units.

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If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.

On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.

Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.

Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.

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To find the angle between two non-zero vectors,

we will use the formula: θ=cos−1(v.w/|v||w|)

where θ is the angle between two non-zero vectors v and w, v.w is the dot product of vectors v and w, and |v| and |w| are the magnitudes of vectors v and w, respectively

.The given vectors are:

v= (√2, √2, 0) and w= (1, -2, 2)

The dot product of v and w is given by:v.w = (√2 × 1) + (√2 × -2) + (0 × 2) = √2 - 2√2 = -√2

Thus,θ = cos⁻¹(-√2/√6)θ ≈ 135°

Since the calculated angle is 135°, which is not equal to 45°,

the statement "The angle between two nonzero vectors v = (√2, √2, 0) and w = (1, -2, 2) is 45" is an Error.

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Answer:

81 cm square

Step-by-step explanation:

the answer is 121.5cm^2

To find the zeros of y = tan(2x), we need to solve the equation sin(2x) = 0 to determine the x-values where sin(2x) is zero. These x-values will correspond to the zeros of the function tan(2x).

To find the zeros of the function y = tan(2x), we can utilize the fact that tan(x) is equal to sin(x)/cos(x).

Given y = tan(2x), we can rewrite it as:

y = sin(2x) / cos(2x)

Now, let's consider the numerator of this expression, which is sin(2x). If we set sin(2x) equal to zero, we can determine the values of x that make the numerator zero:

sin(2x) = 0

By solving this equation, we can find the zeros of sin(2x). The solutions will be the values of x for which sin(2x) equals zero.

Similarly, we can look at the denominator of the expression y = sin(2x) / cos(2x), which is cos(2x). If cos(2x) equals zero, the denominator will be zero, which leads to undefined values for y. These points will be vertical asymptotes of the function tan(2x).

To find the zeros of y = tan(2x), we need to solve the equation sin(2x) = 0 to determine the x-values where sin(2x) is zero. These x-values will correspond to the zeros of the function tan(2x).

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The equation of the line that satisfies the given conditions and passes through the point (3,8) and is perpendicular to the y-axis is x=3. This can be answered by the concept of Simple equations.

A line perpendicular to the y-axis is parallel to the x-axis, and since it passes through the point (3,8), its equation can be written as x = 3. This is because for any point on this line, the x-coordinate will always be 3, and the y-coordinate can be any value, which means the line will be a vertical line passing through (3,8).

Therefore, the equation of the line that satisfies the given conditions and passes through the point (3,8) and is perpendicular to the y-axis is x=3, which is in standard form

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Answer:

\(-\frac{5}{2}\)

Step-by-step explanation:

G(-6 , 2) = (x1 , y1)

J(-4 , -3) = (x2 , y2)

slope = y2 - y1/x2 - x1

=-3-2/-4-(-6)

=-5/-4+6

=-5/2

Answer:

4x+6y<=10

Step-by-step explanation:

The linear inequality that describes the graph is 4x+ 6y ≤ 10.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

As, The bold straight line passes through the points (1,1) and (-2, 3).

so, equation of line will be

(y- 1) = (3-1)/ (-2-1) (x-1)

y-1 = 2 / (-3) (x-1)

-3y + 3 = 2x - 2

-3y -2x = -5

If we multiply by 2 both side we get

-6y - 4x = -10

4x+ 6y= 10

So, the required inequality for gray area is 4x+ 6y ≤ 10.

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Answer:

\(y=-\frac{4}{3} x+2\)

Step-by-step explanation:

In order to write an equation that represents a line, you have to write it in Slope-Intercept Form.

Slope-Intercept Form: y = mx+b

Where b represents the Y-intercept

Where m represents the Slope

**********************************************

That's all you need to know about Slope-Intercept Form!

How do we get started?

Well first off, take a look at the graph and spot two points that are shown

The two points will be: (0, 2) and (3, -2)

Then use the two points to Solve for the Slope of the line!

m = slope

m = \(\frac{y2-y1}{x2-x1}\)       Second y - first y/ Second x - First x

m = \(\frac{-2-2}{3-0}\)        

m = \(\frac{-4}{3}\)           Turn the whole answer negative since there's a negative

m = \(-\frac{4}{3}\)           Final Answer

so the slope of the line is -4/3

Now we need to get the Y-intercept of the line!

Easy we don't need to solve just look how many units the graph goes up in y-axis?

2 units

so the y-intercept of the line is 2

Equation: y = -4/3x + 2

Answer:

Proton

Step-by-step explanation:

The charge on the proton and electron are exactly the same size but opposite. Neutrons have no charge. Since opposite charges attract, protons and electrons attract each other.

Hope this helps you luv!

Given:

The point is (1,-2).

To find:

The quadrant in which the point (1,-2) lies.

Solution:

We know that,

In first quadrant, both coordinates are positive, i.e., (x,y).

In second quadrant, x coordinate is negative but the y-coordinate is positive, i.e., (-x,y).

In third quadrant, both coordinates are negative, i.e., (-x,-y).

In fourth quadrant, x coordinate is positive but the y-coordinate is negative, i.e., (x,-y).

Where, x and y are two non-negative values.

In the given point (1,-2) the x coordinate is positive but the y-coordinate is negative.

Therefore, the point (1,-2) lies in fourth quadrant.

The constants that make the vectors ⟨b+3,−1⟩ and ⟨b,10⟩ orthogonal are b = -5 and b = 2.

To find the constant b that makes the vectors ⟨b+3,−1⟩ and ⟨b,10⟩ orthogonal, we need to check if their dot product is zero.

The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.

So, we have:

⟨b+3,−1⟩ · ⟨b,10⟩ = (b+3)(b) + (-1)(10) = \(b^2\) + 3b - 10

For the vectors to be orthogonal, their dot product should be zero.

Therefore, we set the dot product equal to zero and solve for b:

\(b^2\)+ 3b - 10 = 0

This equation can be factored as:

(b + 5)(b - 2) = 0

Setting each factor equal to zero gives us two possible values for b:

b + 5 = 0  -->  b = -5

b - 2 = 0  -->  b = 2

So, the constants that make the vectors orthogonal are b = -5 and b = 2.

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Answer:

\(m = \frac{14 - 7}{2 - 0} = \frac{7}{2} \)

\(14 = \frac{7}{2} (2) + b\)

\(14 = 7 + b\)

\(b = 7\)

\(y = \frac{7}{2} x + 7\)

Answer:

The slope between the points (-2, -1) and (4, 3) is \(\frac{3}{2}\)

Step-by-step explanation:

First, we must know the equation for finding the slope.

\(Slope(m) = \frac{y2-y1}{x2-x1}\)

Next, we plug in the coordinate points.

\(m=\frac{4-(-2)}{3-(-1)}\)

\(m=\frac{6}{4}\)

Finally, we simplify this answer.

\(Slope = \frac{3}{2}\)

Answer:

Amy is (21.6 - 14.4) 7.2 km/hr faster than Bill.

Distance = speed / time

Amy's speed

40 minutes = 40/60 = 2/3 hours

14.4 = speed / 2/3

Speed = 14.4 * 3/2 = 21.6 km/ hr

Bill speed

60 minutes = 1 hour

Speed = 14.4 km / hr.

Answer:

56 ≤ 13x

Step-by-step explanation:

The minimum requiremenet is 56 g, so set 13x greater than 56 g.

Answer:

5x-30

Step-by-step explanation:

x+15+4x-45

5x+14-45

5x-30

The expected frequency of South campus and passed will be 36.5. Calculating the total number of students who took the aptitude exam is the first step in determining the expected frequency of South campus and passing.

Total number of students = 42 + 31 + 58 + 69 = 200

The marginal totals for South campus and passed need to be calculated as:

Marginal total for South campus is 42 + 58 = 100

Marginal total for passed is 42 + 31 = 73

Using the following formula, we can now know the anticipated frequency for the South campus and passed:

Expected frequency = (row total * column total) / grand total

Expected frequency for South campus and passed = (100 * 73) / 200 = 36.5

Therefore, the expected frequency of South campus and passed=36.5.

In the event that there is no appreciable difference between the two campuses' pass rates, this statistic represents the anticipated number of students who passed the aptitude exam at the South campus.

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