Select the correct answer.
If no denominator equals zero, which expression is equivalent to 15/x-6 + 7/x+6?
A.
OB.
OC.
OD.
22 +132
²36
22-48
236
22
C.36
22 +48
²36

The quarterback should throw the ball at an angle of 53.1° in order for the receiver to catch it.

In order for the receiver to catch the ball, the horizontal component of the velocity vector making an angle of (x)°, should be equal to the velocity of the receiver's velocity. Mathematically, we can write that -

20 cos (x°) = 12

cos (x°) = 12/20

cos (x°) = 3/5

(x°) = cos⁻¹(3/5)

x = 53.1°

So, the quarterback should throw the ball at an angle of 53.1° in order for the receiver to catch it.

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Answer: [tex]\frac{10\sqrt{3}}{3}[/tex]

Step-by-step explanation:

To find this use TOA which is Tan = Opposite/Adjacent

so we have tan(30°) = y/10 and to isolate the "y" we multiply both sides by 10 to get 10tan(30°) = y

where y = [tex]\frac{10\sqrt{3}}{3}[/tex]

To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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Answer:

Same, same, same, different.

Step-by-step explanation:

Same x-coordinate of vertex because no horizontal movement.

Same y-coordinate of vertex because no vertical movement.

Same direction of opening because the exponents are equal and both coefficients are positive.

Different y value at x = 1. y value for x^2 is 1 while y value for 2x^2 is 2.

The volunteers feed the gorillas 36.5 tons of fruits and vegetables each year.

Each gorilla is fed 40 pounds of fruits and vegetables per day, and there are 5 gorillas in the family.

Therefore, the total amount of fruits and vegetables fed to the gorillas each day is:

40 pounds/gorilla x 5 gorillas = 200 pounds

To convert pounds to tons, we need to divide by 2000, since there are 2000 pounds in a ton.

200 pounds / 2000 pounds/ton = 0.1 tons

To calculate the amount of fruits and vegetables fed to the gorillas in a year, we need to multiply the daily amount by the number of days in a year:

0.1 tons/day x 365 days/year = 36.5 tons/year

Therefore, the volunteers feed the gorillas 36.5 tons of fruits and vegetables each year.

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The salesman traveled at an average speed of 55 miles per hour on his trip.

To find the average miles per hour, we need to find the total distance traveled and divide it by the total time taken.

Total distance traveled = 52 miles + 64 miles + 49 miles = 165 miles

Total time taken = 1 hour + 1 hour + 1 hour = 3 hours

Average speed = Total distance traveled / Total time taken

= 165 miles / 3 hours

= 55 miles per hour

Therefore, the salesman averaged 55 miles per hour on his trip.

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Answer:

$10.92

Step-by-step explanation:
We can label book (a), marker (b) and notebook (c)

A+B+C= total cost

If we subtract the total cost from the $40 we get Jamie’s change

A+B+C= $29.08

40 - 29.08 = 10.92

Therefore, your answer will be $10.92

Answer:

$523.54

Step-by-step explanation:

To find the present value of $600 after 3 years at 5% compounded monthly, we can use the present value formula which is PV = FV / (1 + r/n)^(n*t), where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of times compounded per year and t is the number of years  

In this case, we have FV = $600, r = 0.05 (5%), n = 12 (monthly compounding), and t = 3 years. Plugging these values into the formula gives us:

PV = $600 / (1 + 0.05/12)^(12*3) = $523.54

Therefore, the present value of $600 after 3 years at 5% compounded monthly is $523.54. I hope that helps!

When GH=5x+3 and CB = 2x + 4, GA is 13/3.

Since line CB is the midsegment of A GHJ:

CB = (GH + HJ) / 2

Since HJ = GH (because G is the midpoint of GHJ), substitute GH for HJ:

CB = (GH + GH) / 2

CB = GH

Since lines CB and GH are parallel, set their corresponding parts equal:

GH = CB

5x + 3 = 2x + 4

Solving for x:

5x - 2x = 4 - 3

3x = 1

x = 1/3

Now substitute x back into GH to find GA:

GH = 5x + 3

GH = 5(1/3) + 3

GH = 8 1/3

Since G is the midpoint of GH, GA = GH / 2:

GA = (5x + 3) / 2

GA = (5/3 + 3) / 2

GA = 13/3

Therefore, GA is 13/3.

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The distance between both houses is: 3839.75 ft

The Law of Cosines is simply a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be communicated as:

c² = a² + b² - 2abcos(C),

where:

c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Using law of cosines, the length AB is:

AB = 50² + 100² - 2(50 * 100) * cos 30

AB = 3839.75 ft

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A hypothesis test was conducted to determine if the proportion of online applications in 2004 was more than in 2009, using a significance level of .005. The test results show that there is not enough evidence to support the claim.

The null hypothesis is that the proportion of online applications in 2004 is equal to or less than the proportion in 2009. The alternative hypothesis is that the proportion of online applications in 2004 is greater than the proportion in 2009. Symbolically, we can write

H o: p2004 ≤ p2009

H a: p2004 > p2009

The significance level is given as 0.005. Since this is a one-tailed test (we are testing for a greater proportion in 2004), we will use a one-tailed critical value. Using a normal distribution table or calculator, we can find the critical value to be 2.576.

The test statistic for this hypothesis test is a z-score, which we can calculate using the formula

z = (P₁ - P₂) / √(P(1-P)(1/n₁ + 1/n₂))

where P₁ and P₂ are the sample proportions, n₁ and n₂ are the sample sizes, and P is the pooled proportion. In this case, we have

P₁ = 123/373 = 0.33

P₂ = 70/776 = 0.09

n₁ = 373, n₂ = 776

P = (123 + 70) / (373 + 776) = 0.157

Plugging these values into the formula, we get

z = (0.33 - 0.09) / √(0.157(1-0.157)(1/373 + 1/776))

z ≈ 8.48

Since the test statistic (8.48) is greater than the critical value (2.576), we can reject the null hypothesis. This means there is enough evidence to support the alternative hypothesis that the proportion of online applications in 2004 is greater than the proportion in 2009.

Based on the results of the hypothesis test, we can conclude that there is enough evidence to support the claim that the proportion of online applications in 2004 was more than the proportion of online applications in 2009. Therefore, the opposite answer in the given question is incorrect.

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The correct answer is option D. 250 milliliters, is the capacity of a small cup. This is a proportion exercise.

It is given that, the  total capacity of two large cups and two small cups is 1,500 milliliters. If the total capacity of one large cup and two small cups is 1,000 milliliters.

To find the capacity of a small cup

Let small cup capacity  be 's' and large cup capacity be 'l'

From the given information we can write,

2l + 2s = 1500

Then l + s = 750

one large cup and two small cups is 1,000 milliliters.

l + 2s = 1000

l + s + s = 1000

(l + s) + s = 1000

750 + s = 1000

s = 1000 - 750 = 250

The correct answer is option D. 250 milliliters

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Full Question:

The total capacity of two large cups and two small cups is 1,500 milliliters. If the total capacity of one large cup and two small cups is 1,000 milliliters, what is the capacity of a small cup?

A. 375 milliliters

B. 200 milliliters

C. 500 milliliters

D. 250 milliliters

a) The function that models the number of bacteria is n(t) = 8900[tex]e^{(0.126t)[/tex].

b) Rounding to the nearest hundred, we get the answer of 12100 bacteria after 2 hours.

c) It would take approximately 5.5 hours for the number of bacteria to double.

To model the growth of the bacteria population, we can use an exponential growth function of the form n(t) = n₀[tex]e^{(rt)[/tex], where n₀ is the initial population, r is the growth rate, and t is the time in hours.

(a) To find the growth rate, we can use the formula r = ln(N/N₀)/t, where N is the final population, N₀ is the initial population, and t is the time interval. Plugging in the given values, we get:

r = ln(10000/8900)/1 = 0.126

(b) To find the number of bacteria after 2 hours, we can simply plug in t=2 into the exponential function:

n(2) = 8900[tex]e^{(0.126*2)[/tex] = 12099.92

Rounding to the nearest hundred, we get the answer of 12100 bacteria after 2 hours.

(c) To find the time it takes for the number of bacteria to double, we can use the fact that the population doubles when n(t) = 2n₀. Substituting these values and solving for t, we get:

2n₀ = n₀[tex]e^{(rt)[/tex]

2 = [tex]e^{(rt)[/tex]

ln(2) = rt

t = ln(2)/r = 5.5 hours (rounded to one decimal place)

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There does not appear to be enough evidence to back the claim that individuals taking Lipitor have a higher risk of infection compared to those on the placebo.

To test the claim that the rate of infection for those treated with Lipitor was more than the rate of infection for those given a placebo at the .025 significance level, we will perform a hypothesis test using a two-proportion z-test.

Claim: p1 > p2

Opposite: p1 ≤ p2

P1 is the Lipitor group

P2 is the placebo group

The test is a right-tailed test.

Let's calculate the proportions and pooled proportion:

p1 = 86/220 = 0.3909

p2 = 88/260 = 0.3385

p = (86 + 88) / (220 + 260) = 0.3615

Now, we'll find the test statistic (z):

Using a calculator, we see that

z ≈ 1.255

The critical value (Zα) for a right-tailed test at a .025 significance level is approximately 1.96.

Since the test statistic (1.255) is below the critical value (1.96), we fail to reject the null hypothesis.

In conclusion: There does not appear to be enough evidence to back the claim that individuals taking Lipitor have a higher risk of infection compared to those on the placebo.

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A. $66,000 is least likely to be the average salary of another one of the groups.

If the sampling variability was low, it means that the averages of the different groups are expected to be similar to each other, and any differences are likely due to chance or random variation.

Given that the average salary of several groups was close to $56,000, it is unlikely that another group would have an average salary that is much higher or much lower than $56,000.

Therefore, the least likely average salary for another group is option A, $66,000, as this is much higher than $56,000 and would require a significant deviation from the other group averages, which is unlikely given the low sampling variability.

Option B, $58,000, and option D, $57,000, are closer to the expected average and therefore more likely to be the average salary of another group. Option C, $56,000, is obviously possible, since it is already an observed average.

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The square that has identical objects is the fourth square which had identical objects of a bar graph with 3 bars.

Objects that are absolutely identical share the same properties and features, meaning they cannot be differentiated from one another. Combinatorics is an area of mathematics and statistics focused on counting and organizing objects and this frequently requires identical objects to be used in calculations.

Looking at the fourth square, we see that there are two items which are identical and these are the bar graphs. These two items might have different orientations but they are identical.

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The surface area of the rectangular prism is 26/3 times larger than the surface area of the cube.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

For the cube, the dimensions are given as follows:

x, x and x.

Hence the surface area is:

S = 2 x 3x² = 6x².

For the rectangular prism, the dimensions are given as follows:

2x, 3x and 4x.

Hence the surface area is:

S = 2 x (2x(3x) + 3x(4x) + 2x(4x)) = 52x².

Hence the ratio is given as follows:

52x²/6x² = 26/3.

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The height of the water increasing at a rate of 0.05 m/min.

The Volume of a cylinder is

V = [tex]\pi r^{2} h[/tex]

where r is the radius and h is the height of the cylinder.

We are given that the radius r of cylinder is 5m and the water is filled at the rate of 4 ;

V = 25πh  ...(1)

Now, differentiating (1) with respect to time t,

dV/dt = 25πdh/dt

Substituting the value of dV/dt ;

4 = 25πdh/dt

dh/dt = 0.05 m/min

Hence, the water is increasing at the rate of 0.05 m/min.

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Answer:

Step-by-step explanation:

let’s take 59% of X = 23.6

So 59/100 * x = 23.6

59X/100 = 23.6

100/59* 59X/100 = 23.6 * 100/59

X = 40

The coordinates of the new figure would be: I' = (1, 3), J' = (5, 3), and H' = (0, -2).

To find the coordinates of the new figure we must identify the coordinates of the original figure and add 3 units to the first number and 1 unit to the second number. Below is the procedure:

I =

J =

K =

So, the correct coordinates would be: I' = (1, 3), J' = (5, 3), and H' = (0, -2).

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Answer:

8

Step-by-step explanation:

multiply 80 by 0.10 to get 8

We can see here that option C is the correct option that gives us the percentage bar graph that best represents the data.

A bar graph, also called a bar chart, is a form of graph that uses rectangular bars of equal width to depict data. Each bar's height or length reflects the value or frequency of the data it conveys. Discrete or categorical data are frequently compared and analyzed using bar graphs.

We see that from the data given, the total number of students =

44 + 55 + 55 + 66 = 220

Reading = 44/220 × 100% = 20%

Sports =  55/220 × 100% = 25%

Video Games =  55/220 × 100% = 25%

Music = 66/220 × 100% = 30%

Thus, option C is the correct answer.

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The most reasonable prediction for the next 200 visitors to the park using probability is :

D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.

Given that,

A survey of visitors at a national park was conducted to determine the preferred activity of each visitor to the park.

Total number of visitors who were surveyed = 80

The number of visitors who select each of the activity is given.

For the next 200 visitors,

Number of visitors who may select camping = (28 /80) × 200 = 70

Number of visitors who may select hiking trails = (22 /80) × 200 = 55

Number of visitors who may select water sports = (14 /80) × 200 = 35

Number of visitors who may select biking trails = (16 /80) × 200 = 40

Camping = 70 = 35 × 2 = water sports × 2

The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.

Hence the correct option is D.

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The complete question is given in the image and the options for the question are given below.

A. The number of visitors who prefer water sports will be 5 more than the number of visitors who prefer biking trails.

B. The number of visitors who prefer hiking trails will be 8 more than the number of visitors who prefer hiking trails.

C. The number of visitors who prefer camping will be 15 times the number of visitors who prefer hiking trails

D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.

Answer:

Step-by-step explanation:

y = -2/3(x) + 1, which is the line through the point (3, -1) and perpendicular to the line y = 3/2(x) + 3.

Since the diameter of this circle is 18 kilometers, the circle's area is 254.34 square kilometers.

In Mathematics and Geometry, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 18/2 = 9 kilometers.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = 3.14 × 9²

Area of circle = 254.34 square kilometers.

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