Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both
Spanish and biology. What is the probability that a student selected at random takes
Spanish or Biology? Simplify the fraction!

The side AB measures option 2. [tex]\sqrt{20}}[/tex] units long.

Step-by-step explanation:

Step 1:

The coordinates of the given triangle ABC are A (4, 5), B (2, 1), and C (4, 1).

The sides of the triangle are AB, BC, and CA. We need to determine the length of AB.

To calculate the distance between two points, we use the formula [tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}.[/tex]

where ([tex]x_{1},y_{1}[/tex]) are the coordinates of the first point and ([tex]x_{2},y_{2}[/tex]) are the coordinates of the second point.

Step 2:

For A (4, 5) and B (2, 1), ([tex]x_{1},y_{1}[/tex]) = (4, 5) and ([tex]x_{2},y_{2}[/tex]) = (2, 1). Substituting these values in the distance formula, we get

[tex]d=\sqrt{\left(2-4\right)^{2}+\left(1-5}\right)^{2}} = \sqrt{\left(2\right)^{2}+\left(4}\right)^{2}}=\sqrt{20}}.[/tex]

So the side AB measures [tex]\sqrt{20}}[/tex] units long which is the second option.

The given terms combine to form 9.047 in decimal form. The mathematical conversions are based on division by powers of ten and understanding how to move the decimal point for correct place value representation.

The question asks us to express a sum of three terms in decimal form. The terms are: 9x1, 4x1/100, and 7x1/1000.

To simplify, the first term is just 9, as anything multiplied by one remains unchanged.

The second term, when simplified, is 4 divided by 100, which is 0.04.

The third term, 7 divided by 1000, simplifies to 0.007. Adding these three numbers together gives us the decimal form of the expression.

Using the knowledge of powers of ten, we know that dividing by powers of 10 moves the decimal point to the left a number of places equal to the exponent.

For instance, when we divide 1.9436 by 1000, we get 0.0019436.

Converting whole numbers to decimals and vice versa involves moving the decimal point and keeping track of the moves with powers of ten, as seen with the example of 965 becoming 9.65 x 10².

With this understanding, the sum of the terms is as follows: 9 + 0.04 + 0.007, which equals 9.047. This combines whole numbers and decimal fractions into one rounded decimal form.

Answer:

The answer is 12 x 5= 60

Step-by-step explanation:

Each number from the 5 digits becomes used with each other number that is used 5 x. This creates 4*2 =16 3^3=27 +2^3=16 +1^1 = 60

Answer:

x + 3

Step-by-step explanation:

1. The area of a rectangle is length times width.

A = LW

2. Solve for the width by dividing both sides of the equation by the length:

W = A / L

3, Plug in the expressions for A and L:

W = (3x² + 9x) / 3x

W = (3x² / 3x) + (9x / 3x)

W = x + 3

Answer:

Radius  =  7 cm

Diameter  =  7 cm  ×  2  =  14 cm

Step-by-step explanation:

The radius of the circle is 7 cm, and the diameter is 14 cm.

Given that the radius (R) of a circle is 7 cm, we can determine both the radius and diameter of the circle.

Radius: The radius is the distance from the center of the circle to any point on its boundary. Thus, the radius provided is 7 cm.

Diameter: The diameter is twice the radius, as it stretches from one edge of the circle to the other, passing through the center. Therefore, the diameter is calculated as follows:

Diameter = 2 × Radius

Diameter = 2 × 7 cm

Diameter = 14 cm

So, the diameter of the circle is 14 cm.

To summarize, the radius is 7 cm and the diameter is 14 cm.

Answer:

I think the answer is -3, i'm not sure tho :(

Step-by-step explanation:

Answer: -17.425

Step-by-step explanation:

Answer:

3,420

Step-by-step explanation:

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 28\frac{1}{2}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:120=\frac{120}{1}\\=\frac{57}{2}\cdot \frac{120}{1}[/tex]

[tex]\mathrm{Cross-cancel\:common\:factor:}\:2\\=\frac{57}{1}\cdot \frac{60}{1}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}\\=\frac{57\cdot \:60}{1\cdot \:1}[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:57\cdot \:60=3420\\=\frac{3420}{1\cdot \:1}\\ \\\mathrm{Apply\:rule}\:\frac{a}{1}=a\\3420[/tex]

Hope this helps you!

Have a good night!

Answer:

1. 1

2. 10

3. 12

Step-by-step explanation:

When rolling two number cubes, there are 36 possible combinations. There are 6 combinations that yield a sum of 7, so the probability is 1/6. Tamara should expect a sum of 7 about 24 times when she rolls the cubes 144 times.

When rolling two number cubes, there are 36 possible combinations. To find out how many times Tamara should expect the sum of the two cubes to be equal to 7, we need to determine the number of combinations that result in a sum of 7.

From the chart provided, we can see that there are 6 combinations that yield a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Since there are 6 favorable outcomes out of 36 possible outcomes, the probability of rolling a sum of 7 is 6/36 or 1/6.

To calculate the number of times Tamara should expect a sum of 7 when she rolls the cubes 144 times, we can multiply the probability by the number of trials: (1/6) * 144 = 24.

Answer:

1296π m^3

Step-by-step explanation:

The volume of a cylinder is given by

V=πr^2h

We are given the diameter.  To find the radius, divide the diameter in half.

r = d/2 = 24/2 = 12

Substituting in what we know

V = pi * (12)^2 * 9

V = pi *1296 m^3

Answer:

V=1296π m3

Step-by-step explanation:

3.14(12)^2(9)

3.14(144)(9)

3.14(1296)

Answer:

16 and -15

Step-by-step explanation:

Let the numbers be x and y

x+y = 1 ..............(1)

5x + 4y = 20 .........(2)

Solve simultaneously using elimination method by multiplying equation 1 by 5 to eliminate x

5x + 5y = 5

5x + 4y = 20.   Subtract the eqns from each other

---------------------

5y - 4y = 5-20

y = -15

Put value of y into equation 1

x+y = 1

x -15 = 1

Add 15 to both sides

x = 1+15

x = 16

Therefore the numbers are 16 and -15

I hope this was helpful, please mark as brainliest

Y-intercept is 45

Slope: (50-45)/(0.5-0)=5/0.5=10

y=10x+45

Answer: a) y=10x+45

Answer:

Step-by-step explanation:

g(4)=4²/4+7=11

g(-2)=(-2)²/4+7=4/4+7=1+7=8

average rate of change over the interval [-2,4]=(g(4)-g(-2))/4-(-2))

=(11-8)/6

=3/6

=1/2

Answer:

-1/2

Step-by-step explanation:

To find the average rate of change (ARC)  of the function g over the interval [-2,4]  we need to take the total change in the function value over the interval (which is the difference of its values at the endpoints) and divide it by the length of the interval:

ARC [−2,4] =g(4)-g(-2)/4-(-2)

​

Note that this is the same as finding the slope of the line connecting the points on the graph that correspond to the endpoints of the interval:

Answer:

-1/6

Step-by-step explanation:

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

m=(-5-(-6))/(-2-4)

m=(-5+6)/-6

m=1/-6

Answer:

speed in meters per seconds = 5x

speed in kilometers per hour = 18

Step-by-step explanation:

The speed is the distance over the time

Given the speed of the stone x meters in 0.2 seconds

So, speed = [tex]\frac{x}{0.2}[/tex] = [tex]\frac{5*x}{5*0.2} = \frac{5x}{1}[/tex] = 5x meters per seconds

To convert from meters per seconds to kilometers per hour :

1 kilometer = 1000 meters ⇒ 1 meters = 0.001 kilometer

1 hour = 3600 seconds ⇒ 1 second = 1/3600 hour

[tex]\frac{meter }{second } = \frac{0.001\ km }{(1 /3600) \ hour} =\frac{3600}{1000} \frac{km}{hour} = 3.6 \ km/hour[/tex]

So, 5x meters per seconds = 5x * 3.6 = 18 kilometers per hour

Final answer:

Calculate the speed of the stone in meters per second and kilometers per hour based on the given distance and time traveled.

Explanation:

The speed of the stone can be calculated as follows:

Speed in meters per second = Distance / Time = x / 0.2 seconds

Speed in kilometers per hour = (x / 0.2) * 3.6

Answer: [tex]2,160\ ft^3[/tex]

Step-by-step explanation:

The first step is to find the ratio of the lengths.

According to the information given in the exercise, one the solids has edges of  12 feet and the other solid has edges of 24 feet.

Therefore, the ratio of the length of the smaller solid to the length of the is the following:

[tex]k=\frac{24\ ft}{12\ ft}\\\\k=2[/tex]

Now, the ratio to the volumes of the smaller solid to the other one is the following:

[tex]k^3=2^3=8[/tex]

Then, knowing that the volume of the smaller solid is:

[tex]V_s=270\ ft^3[/tex]

You get that the volime of the larger solid is:

[tex]V_l=270\ ft^3*8\\\\V_l=2,160\ ft^3[/tex]

To find the volume of the larger solid, we cube the ratio of the edge lengths, which in this case is 2. Then, we multiply the volume of the smaller solid by this cubed ratio to get the volume of the larger solid, which is 2160 cubic feet.

The student's question involves finding the volume of a solid similar to another solid, given the edge lengths and the volume of the smaller solid. Since the solids are similar, the ratio of their edges will be the same as the ratio of the sides, the squares of the ratio of the surfaces, and the cubes of the ratio of their volumes. For the solids in the question, the ratio of their edges is 24/12=2. Therefore, the ratio of their volumes will be 23=8.

Given the volume of the smaller solid is 270 cubic feet, the volume of the larger solid will be 270 multiplied by the volume ratio, which is 8. So the volume of the larger solid V is calculated by V = 270 x 8 = 2160 cubic feet.

Answer:

X = 9

Step-by-step explanation:

| | Wearing a Watch | Not Wearing a Watch |

|------------|-----------------|---------------------|

| Wearing a Belt | 43.36% | 22.38% |

| No Belt | 20.28% | 13.99%

The Breakdown

To create a relative frequency table, we need to calculate the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not.

First, let's calculate the total number of people:

Total = 62 + 32 + 29 + 20 = 143

Now, let's calculate the percentages:

Percentage of belt wearers who wear a watch:

= (Number of belt wearers who wear a watch / Total) × 100

= (62 / 143) *×100

≈ 43.36%

Percentage of belt wearers who do not wear a watch:

= (Number of belt wearers who do not wear a watch / Total) × 100

= (32 / 143) × 100

≈ 22.38%

Percentage of people without belts who wear a watch:

= (Number of people without belts who wear a watch / Total) × 100

= (29 / 143) × 100

≈ 20.28%

Percentage of people without belts who do not wear a watch:

= (Number of people without belts who do not wear a watch / Total) × 100

= (20 / 143) × 100

≈ 13.99%

Using these percentages, we can create the relative frequency table:

| | Wearing a Watch | Not Wearing a Watch |

|------------|-----------------|---------------------|

| Wearing a Belt | 43.36% | 22.38% |

| No Belt | 20.28% | 13.99% |

This table shows the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not.

Answer:

Mr. Reynolds used 32 ounces of peanuts to make trail mix.

Step-by-step explanation:

One pound is equal to sixteen ounces! Simply, multiply the number of pounds by 16!

2 pounds x 16 ounces = 32 ounces

Hope this helps! :)

Answer:

[tex]0.42 - 0.994\sqrt{\frac{0.699(1-0.699)}{83}}=0.370[/tex]

[tex]0.42 + 0.994\sqrt{\frac{0.699(1-0.699)}{83}}=0.470[/tex]

The 68% confidence interval would be given by (0.370;0.470)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 68% of confidence, our significance level would be given by [tex]\alpha=1-0.68=0.32[/tex] and [tex]\alpha/2 =0.16[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-0.994, z_{1-\alpha/2}=0.994[/tex]

The proportion os persons who work 40 hours or more is 1-0.301= 0.699

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values obtained we got:

[tex]0.42 - 0.994\sqrt{\frac{0.699(1-0.699)}{83}}=0.370[/tex]

[tex]0.42 + 0.994\sqrt{\frac{0.699(1-0.699)}{83}}=0.470[/tex]

The 68% confidence interval would be given by (0.370;0.470)

There are 453.592grams in 1 pound

in one pound their are 453.59237 grams.

and as my estimate is 454 grams

I hope this helps

The requried equation of the line in slope-intercept form is y = -2x + 16.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept of the line.

We can use the two given points on the line (0, 16) and (8, 0) to find the slope of the line:

slope = (y₂ - y₁) / (x₂ - x₁)

= (0 - 16) / (8 - 0)

= -2

Next, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y₁ = m(x - x₁)

We can choose either of the two given points to plug in as (x1, y1). Let's choose the point (0, 16):

y - 16 = -2(x - 0)

Simplifying this equation, we get:

y - 16 = -2x

y = -2x + 16

Therefore, the equation of the line in slope-intercept form is y = -2x + 16.

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Answer:

yes, it is a perfect square trinomial because the square of binomial are (x-0.375) (x-0.375)

Answer:

-5x + 5/6 (Could also be written like: 5/6 - 5x )

Step-by-step explanation:

−6x+8/6−3/2x−1/2+5/2x

First add like terms

−6x−3/2x+5/2x = -5x

8/6−1/2=5/6

Then put the two answers together to form completed simplified equation.

-5x + 5/6 (Could also be written like: 5/6 - 5x )

Hope this helped!

Answer:

-5x + 5/6

Step-by-step explanation:

-6x + 8/6 + (-3/2x) + (-1/2) + 5/2x

-6x + (-3/2x) + 5/2x + 8/6 + (-1/2)

-7 1/2 + 2 1/2x + 1 2/6 + (-1/2)

-5x + 8/6 + (-1/2)

-5x + 5/6

Please tell me if I'm wrong, maybe consider brainliest.

Answer:

3x − y = 5,

2x + 3y = −15

Which value can the first equation be multiplied by to form opposite values on the y-term? 3

The solution to the system of equations is (0, -5).

Multiply by 3.

Solution is x=0, y=-5.

The coefficients of y are -1 and 3.

If we multiply the first equation by 3. Then the coefficients of y will be 3 and -3. They are opposite values.

After multiplying the first equation by 3 we get:

[tex]3(3x - y) = 3(5)\\9x-3y=15[/tex]

Then we add it with the second equation.

[tex]9x-3y+2x+3y=15-15\\11x=0\\x=0[/tex]

Using x=0 in 3x - y = 5 we get:

[tex]3(0) - y = 5\\0-y=5\\y=-5\\[/tex]

Solution is x=0, y=-5.

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Answer:

Markup: $54.60 Retail Price: $236.60

Step-by-step explanation:

Multiply 182 by 30% or 0.30. Then, add your product to the original price.

The mark up price is $ 54.60  and retail price is $236.60.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Cost of suit= $182

Mark up = 30%

Now, the mark up price

= 182 x 30/100

= 182 x 0.3

= $54.60

and, the retail price= 182+ 54.60

                                = $236.60

Hence, the mark up price is $ 54.60  and retail price is $236.60

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Answer:

2

Step-by-step explanation:

Answer: [tex]x=2.4[/tex]  or [tex]x=\frac{12}{5}[/tex] mark as brainliest please!

Step-by-step explanation:

[tex]12+5x=24\\-12 -12\\5x=12\\x=\frac{12}{5} \\x=2.4[/tex]

Answer:

The answer is n < -7

Step-by-step explanation:

First, you have to move all the numbers to one side:

(-5) - (-7) > 9 + n

-5 + 7 > 9 + n

9 + n < 2

n < -7

(Hope this can help)