Given x = 60°, tan x/2 can be rewritten as which of the following?

1-cos60/1-2sin^260

+- SQRT 1-cos60/1+cos60

tan60/2tan^260

+- SQRT 1-cos60/2

Answer:

Yes they are proportional!

The factors of 28 that we can use in these fractions are 4 and 7.  To find if these are proportional, just simplify 8/28.  To do so divide the numerator (top) and the denominator (bottom) both by 4...

8/28 / 4 = 4/7

Now that you have both with the same denominator, you can evaluate if 3/7 and 4/7 are proportional.  In this case they are.

Hope this helps! :)

Final answer:

Hannah initially has 8/9 of a pound of birdseed, and after using 2/3 of a pound, she has 2/9 of a pound remaining, which is calculated by finding a common denominator and subtracting the second fraction from the first.

Explanation:

Hannah initially has 8/9 of a pound of birdseed. After filling her bird feeders with 2/3 of a pound of birdseed, we need to subtract the amount she used from what she started with to find out how much birdseed she has left. The calculation we'll use is:

(initial amount) - (amount used) = (amount remaining)

In fractional form, this becomes:

8/9 - 2/3

To subtract these fractions, we need a common denominator. The smallest common denominator for 9 and 3 is 9. We can convert 2/3 to 6/9 by multiplying the numerator and the denominator by 3. After this step, the subtraction is straightforward:

8/9 - 6/9 = 2/9

Hence, Hannah has 2/9 of a pound of birdseed remaining.

Answer: The value of x = 90°

and the value of y = 43°

Step-by-step explanation:

Since we have given that

In ΔABC,

∠B=∠C=47°

As we know that "Sum of all three angles of a triangle is 180° ".

So, it becomes,

[tex]\angle A+\angle B+\angle C=180\textdegree\\\\\angle A+47\textdegree+47\textdegree=180\textdegree\\\\\angle A+94\textdegree=180\textdegree\\\\\angle A=180\textdegree-94\textdegree\\\\\angle A=86\textdegree\\\\So,\\\\y=\frac{86}{2}=43\textdegree[/tex]

Similarly,

Now, in ΔABD,

[tex]\angle A+\angle B+\angle ADB=180\textdegree\\\\43\textdegree+47\textdegree+\angle ADB=180\textdegree\\\\90\textdegree+\angle ADB=180\textdegree\\\\\angle ADB=180\textdegree-90\textdegree\\\\\angle ADB=90\textdegree[/tex]

Hence, the value of x = 90°

and the value of y = 43°

Answer:

[tex]\$4701.80[/tex]

Step-by-step explanation:

Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate and she gets a loan payoff of 60 months,

We know that,

[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]

Where,

PV = Present value of annuity = 25000,

r = rate of interest of each period = [tex]\dfrac{7}{12}[/tex]% monthly

n = number of periods = 60 months,

Putting the values,

[tex]\Rightarrow 25000=P\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right][/tex]

[tex]\Rightarrow P=\dfrac{25000}{\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]}[/tex]

[tex]\Rightarrow P=\$495.03[/tex]

Hence total amount paid is,

[tex]=495.03\times 60=\$29,701.80[/tex]

Therefore interest amount is,

[tex]=29,701.80-25,000=\$4701.80[/tex]

Answer:

16 inches

Step-by-step explanation:

2 1/4 = 9/4 inches

Number of pieces = 36 / 9/4

= 36 + 4/9

= 16 inches

Answer:

D. 16

Step-by-step explanation:

I divided 36 from 2.25.

[tex]15a^2+45=0\qquad\text{subtract 45 from both sides}\\\\15a^2=-45\qquad\text{divide both sides by 15}\\\\a^2=-3<0\\\\\text{NO REAL SOLUTION}\\\\\text{in the complex set}\\\\a^2=-3\to a=\pm\sqrt{-3}\\\\a=\pm\sqrt{(-1)(3)}\\\\a=\pm\sqrt{-1}\cdot\sqrt3\\\\\boxed{a=-i\sqrt3\ \vee\ a=i\sqrt3}\\\\------------------\\\\i=\sqrt{-1}[/tex]

Answer:

I think the answer is b

Step-by-step explanation:

Because Mark has a better probability of getting at least  something

Answer:

C) It is not a fair game. Evan has the advantage.

Step-by-step explanation:

Mark's expected value is 3/6×$1 = $0.50.

Evan's expected value is 2/6×$2 = $0.67.

Cayla's expected value is 1/6×$3 = $0.50.

_____

Evan's expected value exceeds that of the other players. It is not fair.

Answer:

4th degree

Step-by-step explanation:

We can use a technique called finite differences.

In column 1  put the differences  between the y values  (y2-y1)

Keep adding columns with the differences until they become constant.

Column 2 is column1 differences  (-2- -30) etc

Column3 is column 2 differences

Column 4 is column3 differences

The differences in column4 are the same, so we can stop

This will be a 4th degree polynomial

x    y          column 1               column 2      column 3        column 4

-2  30        

-1   0                 -30                    

0   -2               -2                           28

1      0               2                           4               -24

2     30           30                          28               24              48

3    160           130                        100               72               48

4      510        350                       220               120             48

Answer:

4th degree ...........

Answer: 20

Step-by-step explanation:

h(x) = |3x| - 1

h(7) = |3(7)| - 1

      = |21| - 1

      =  21  - 1

      = 20

Look at the picture.

Use the Pythagorean theorem to calculate x:

[tex]x^2=2^2+4^2\\\\x^2=4+16\\\\x^2=20\to x=\sqrt{20}\approx4.47\ cm[/tex]

[tex]A_1=\dfrac{8+6}{2}\cdot4=14\cdot2=28\ cm^2\\\\A_2=3\cdot6=18\ cm^2\\\\A_3=3\cdot4.47=13.41\ cm^2\\\\A=4A_1+2A_2+2A_3\\\\A=4\cdot28+2\cdot18+2\cdot13.41=174.82\ cm^2\approx175\ cm^2\\\\1mL\to1cm^2[/tex]

Answer:

When we add 9 to the function we are shifting the function up 9 units.

Step-by-step explanation:

If it were added inside the function, it woulds shift it left or right.

But since it is outside the function, we will shift it up or down

When we add 9 to the function we are shifting the function up 9 units.

Answer:

add 9 to the function we are shifting the function up 9 units

Step-by-step explanation:

Answer:

1st number = 18

2nd number = -5

Step-by-step explanation:

Let x be first number and y be the 2nd number.

We have been given that first number plus twice a second number is 8. We can represent this information as:

[tex]x+2y=8...(1)[/tex]

We are also given that twice the first number plus the second totals 31. We can represent this information as:

[tex]2x+y=31...(2)[/tex]

Now let us solve our system of equations using substitution method.

From equation (1) we will get,

[tex]x=8-2y[/tex]

Substituting [tex]x=8-2y[/tex] in equation (2) we will get,

[tex]2(8-2y)+y=31[/tex]

[tex]16-4y+y=31[/tex]

[tex]-4y+y=31-16[/tex]  

[tex]-3y=15[/tex]  

[tex]y=\frac{15}{-3}[/tex]

[tex]y=-5[/tex]

Therefore, the second number is -5.

Now let us substitute y=-5 in equation (1).

[tex]x+(2*-5)=8[/tex]

[tex]x-10=8[/tex]

[tex]x=8+10[/tex]

[tex]x=18[/tex]

Therefore, the first number is 18.

The numbers are x = 18 and y = -5.

The question involves a system of linear equations and requires solving for two unknown numbers. Using variables to represent these numbers, the system can be written as:

First equation: x + 2y = 8,

Second equation: 2x + y = 31.

To solve this system, follow these steps:

Multiply the first equation by 2, obtaining the equation 2x + 4y = 16.

Subtract the second equation from this result to eliminate x, leading to 3y = -15.

Divide by 3 to find y = -5.

Substitute y = -5 into any original equation to solve for x.
Using the first equation: x + 2(-5) = 8, therefore x = 18.

The solution to the system is x = 18 and y = -5.

Answer: hot dog = $1.75

Step-by-step explanation:

Let h represent hot dogs and c represent bags of chips.

Customer 1: 4h + 2c = 9.00  →  3(4h + 2c = 9.00)  →  12h + 6c =  27.00

Customer 2: 5h + 3c = 11.75 → -2(5h + 3c = 11.75)  → -10h - 6c = -23.50

                                                                                       2h        =    3.50

                                                                                      ÷2               ÷2    

                                                                                        h        =    1.75

Final answer:

The cost of one hot dog is determined to be $1.75.

Explanation:

To find the cost of a hot dog, we will use the information given in two different customer purchases to set up a system of linear equations. Let's define H as the cost of one hot dog and C as the cost of a bag of chips. The first customer buys 4 hot dogs and 2 bags of chips for $9.00, which gives us the first equation:

4H + 2C = 9.00 ...(1)

The second customer buys 5 hot dogs and 3 bags of chips for $11.75, which provides us with the second equation:

5H + 3C = 11.75 ...(2)

With two equations, we can solve for H by either substitution or elimination. Let's multiply equation (1) by 3 and equation (2) by 2 to eliminate C:  

Subtracting equation (4) from equation (3) gives us:

2H = 3.50

And dividing both sides by 2:

H = 1.75

Therefore, the cost of one hot dog is $1.75.

Answer:

80 mg

Step-by-step explanation:

By proportion the daily allowance is 200 * 100/250

= 200 * 10/25

=  80 mg

Answer: 838860

=========================================

Plug in x = 0 to find y = f(x)

f(x) = 4^(2x+1)

f(0) = 4^(2*0+1)

f(0) = 4

The point (0,4) is on the function curve

Plug in x = 5 and compute

f(x) = 4^(2x+1)

f(5) = 4^(2*5+1)

f(5) = 4194304

The point (5, 4194304) is on the function curve

Once you have these two points, you use the slope formula to compute the average rate of change

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

m = (4194304 - 4)/(5-0)

m = 838860

The slope of the line through the two points found earlier is m = 838860, so this is the average rate of change on f(x) for the interval from x = 0 to x = 5.

Answer: [tex]\bold{x=\dfrac{c}{a-b},\qquad x=7}[/tex]

Step-by-step explanation:

Move all of the x's to one side and everything else on the other.

ax = bx + c

ax - bx = c      subtracted bx from both sides

x(a - b) = c       factored out the like term of "x" on left side

[tex]x=\dfrac{c}{a-b}[/tex]          divided both sides by (a- b)

2x = x + 7  → a = 2, b = 1, c = 7

                    [tex]x=\dfrac{7}{2-1}[/tex]

                     x = 7

Check:

2x = x + 7

-x    -x      

x =       7

Answer:F=−20d+1500

Step-by-step explanation:he amount of filling used to make each dumpling is constant, so we're dealing with a linear relationship.

We could write the desired formula in slope-intercept form: F=\greenD md+\maroonD bF=md+b. In this form, \greenD mm gives us the slope of the graph of the function and \maroonD bb gives us the yy-intercept. Our goal is to find the values of \greenD mm and \maroonD bb and substitute them into this formula.

Hint #22 / 3

We know that each dumpling Dominik makes decreases the filling remaining by 2020 grams, so the slope \greenD mm is \greenD{-20}−20, and our function looks like F=\greenD{-20}d+\maroonD bF=−20d+b.

We also know that Dominik has 15001500 grams of filling initially, so the yy-intercept \maroonD{b}b is \maroonD{1500}1500.

Hint #33 / 3

Since \greenD{m}=\greenD{-20}m=−20 and \maroonD{b}=\maroonD{1500}b=1500, the desired formula is:

The function's formula for the grams F of filling remaining as a function of d, the number of dumplings Dominik makes, is given by:F(d) = 1500 - 20d

To derive this formula, we start by considering the total amount of filling Dominik has, which is 1500 grams. Each dumpling uses 20 grams of filling. Therefore, if Dominik makes d dumplings, he will have used 20d grams of filling. To find the remaining filling, we subtract the amount used from the total amount initially available:

[tex]\[ F(d) = \text{Total filling} - (\text{Filling per dumpling} \times \text{Number of dumplings}) \] \[ F(d) = 1500 - (20 \times d) \] \[ F(d) = 1500 - 20d \][/tex]

This function gives us the amount of filling, in grams, that remains after Dominik has made d dumplings.

When a = 1, the equation becomes x² - 6x = -13.

To rewrite the equation 8x² - 48x = -104 with the coefficient of x² as 1,

you can divide the entire equation by 8,

which is the coefficient of x²:

(8x² - 48x) / 8 = (-104) / 8

Now, simplify:

x² - 6x = -13

So, when a = 1, the equation becomes x² - 6x = -13.

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Answer:

79.38 miles per hour

Step-by-step explanation:

average speed =  miles covered / hours

= 515.97 / 6.5

=  79.38

Answer:    79.38 miles per hour

Step-by-step explanation:

Given : Distance covered by rally car race course = 515.97 miles

Time taken to complete the course by winning car = 6.5 hours

The average speed of the winning car = ( Distance covered by rally car race course) ÷  (Time taken to complete the course by winning car)

= (515.97)÷ (6.5) miles per hour

= 79.38 miles per hour

Hence, the average speed of the winning car =  79.38 miles per hour.

Answer:

Step-by-step explanation:

1. If you work these out in detail, they are tedious, but not difficult. Fortunately, you can take advantage of certain clues to simplify the work.

___

2. You know the -x as an argument of the function will flip the curve left-to-right, so only C and D are potential choices. One way to resolve the ambiguity is to see what the function value is for x=0. You find they are the same:

... f(0) = root(3)(0 -1) = g(0) = root(3)(-0-1) = root(3)(-1)

Only graph C has the two curves crossing at x=0.

___

f(x) = root(3)(x -1) is a shift to the right of the parent function root(3)(x).

Replacing x by -x reflects that function across the y-axis, so what was a shift to the right now becomes a shift to the left, as seen in graph C.

Answer:

$3.15

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ration of weight of nickel, zinc, and copper in an alloy is 4:1:2

The weight of alloy can be written as

4x + x + 2x = 35 Kg

7 x = 35 Kg

X = 35 Kg/7

X = 5kg

The weight of nickel the alloy = 4 x 5 = 20 Kg

The weight of zinc in the alloy= 1 x 5 = 5kg

The weight of copper in the alloy = 2 x 5 = 10 kg

Answer:

Let X be the amount of each metal needed to make 35 Kg of this alloy.

We know that an alloy is composed of nickel, zinc and copper in a proportion

4:1:2. Therefore, we have:

[tex]4X+1X+2X = 35[/tex]

[tex]7X = 35[/tex]

[tex]X=\frac{35}{7}[/tex]

[tex]X=5[/tex] Kg

Therefore, there are [tex]5 \times 4 =20[/tex] kg of nickel, [tex]1 \times 5 =5[/tex] kg of zinc, and [tex]2 \times 5 = 10[/tex] kg of copper needed to make 35 kg of this alloy

Answer:

x = 53 degrees

Step-by-step explanation:

Alternate exterior angles are equal if  two parallel lines are cut by a transversal.

 If  m and n are parallel, then

3x-28 = 2x+25

Subtract 2x from each side.

3x-28-2x = 2x+25-2x

x-28 =25

Add 28 to each side.

x-28+28 = 25+28

x = 53

Answer:

D

Step-by-step explanation:

The new one would have a long gap between the Q3 and the maximum of the box and whisker plot, therefore it should create a positive skew.

Answer:

D

Step-by-step explanation:

It will be positively skewed (skewed right), because that means that the longer segment would be on the right side of the median.

140 is a major outlier and a lot larger than the more central numbers. However, it's only 1 number, so the median (location of the "box") would remain similar or the same. The end on the right, however, would move far to the right, extending the "line" on that side.

The error is in Step-4.

A negative exponent does NOT mean that the number turns negative. A negative exponent means the number is in the denominator.

(4)⁻⁴ means (1/4⁴) .  That's (1/256) .  All positive numbers.

Answer:

a) 5.4%  

Step-by-step explanation:

a) We will use the binomial distribution, with n = 100 and p(success) = 0.95

We need to calculate

P(X=x) = [tex]\binom{n}{x}p^{x}q^{n-x}[/tex]

P(X ≤91) =  [tex]\sum_{k=1}^{91}\binom{100}{k}0.95^{k}0.5^{n-k}[/tex]

As we know that binomial distribution can be approximated to normal distribution if np≥5 and nq≥5 as in this case.

Therefore, P(x,n,p) →N[tex](\mu, \sigma )[/tex]

[tex]\mu[/tex] = np = 95

[tex]\sigma[/tex] = √npq = 2.`79

P(X≤91) ≅ P(X≤91.5)  = P( Z≤[tex]\frac{91.5-95}{2.179}[/tex]

                                 =  P( Z≤ -1.6)

                                 = 0.054

Probability = 5.4%

b) If the probability was less than 5% then we must say that the DHL Shipping company don not ships 95% of its orders on time but as we can see that the probability is more that 5% that is 5.4%. So, we cannot say that the company does not ships the orders on time. But we cannot say with confirmation, we need more samples so as to judge accordingly.

The correct statement that interprets the confidence interval is option A: We have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

The correct answer is A. We have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

The confidence interval shows that we are 95% confident that the true mean of the population of all data speeds at the airports is between 13.05 Mbps and 22.15 Mbps.

The other options are incorrect.

Option B states that we have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the sample mean of the data speeds at the airports.

This is incorrect because the confidence interval is for the population mean, not the sample mean.

Option C states that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.

This is also incorrect because we can never be 100% sure that the true mean is within the confidence interval.

Option D states that the limits of 13.05 Mbps and 22.15 Mbps contain 95% of all of the data speeds at the airports.

This is incorrect because the confidence interval is for the mean of the population, not for all of the data speeds in the population.

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