A steel rod that is 64 feet long must be cut into three pieces to fabricate the supports for a drill press. The longest piece is 3.09 times the shortest and the middle piece is 1.73 times the shortest. How long is each​ piece? Round nearest foot.

[tex]\text{Domain}\\\\y-9 > 0\to y>9\\\\------------------------\\\\\log_4(y-9)+\log_43=\log_481\qquad\text{use}\ \log x+\log y=\log(xy)\\\\\log_4[3(y-9)]=\log_481\qquad\text{use distributive property}\\\\\log_4(3y-27)=\log_481\iff3y-27=81\qquad\text{add 27 to both sides}\\\\3y=108\qquad\text{divide both sides by 3}\\\\\boxed{y=36}\in D\\\\Answer:\ \boxed{y=36}[/tex]

Answer:

y = 36

Step-by-step explanation:

log4 (y – 9) + log4 3 = log4 81.

We know from the property of logs that if the bases are the same, when we subtract logs, we can divide what is inside

loga (b) + loga (b) = loga (b*c)

Lets simplify the expression log4( (y-9)*3) = log4 (81)

Since the bases are the same, what is inside the parentheses on the left hand side  must be equal to what is inside the parentheses o the right hand side

(y-9)*3 = 81

Divide each side by 3

(y-9)*3 /3= 81/3

y-9 = 27

Add 9 to each side

y-9+9 = 27+9

y = 36

Answer:

150 and 240 are the two numbers having difference as 90 and ratio as 5 : 8.

Step-by-step explanation:

Since ratio of two numbers is 5 : 8 ,

lets assume two numbers be 5x and 8x.

Difference of two numbers = 8x - 5x = 90

⇒3x =90

⇒x = 90/3=30

so two numbers are 5x = 5 × 30 = 150 and 8x = 8 × 30 = 240

Hence 150 and 240 are the two numbers having difference as 90 and ratio as 5 : 8.

Answer:

174 packages of t-shirts    PLEASE GIVE BRAINLIEST

Step-by-step explanation:

139 x 5 = 695 t-shirts are needed

695 ÷ 4 = 173.75

Since you have to purchase whole packages of t-shirts you will need to buy 174 packages of t-shirts.  174 x 4 = 696 t-shirts

174 packages

Answer:

The value of the quantity after 186 hours is 2089.41

Step-by-step explanation:

We can use exponential formula

[tex]P(t)=a(1-b)^{\frac{t}{h} }[/tex]

a quantity with an initial value of 2100

so,

[tex]a=2100[/tex]

decays exponentially at a rate of 0.65% every 10 days

So, b=0.0065 when h=10*24=240

now, we can plug values

[tex]P(t)=2100(1-0.0065)^{\frac{t}{240} }[/tex]

now, we can plug t=186

and we get

[tex]P(186)=2100(1-0.0065)^{\frac{186}{240} }[/tex]

[tex]=2089.413[/tex]

Answer:

Q(186)  = 2089.463                    

Step-by-step explanation:

Formula for decaying exponentially:

Q(t) = Q_0 e^{-rt}

where, Q(t)= quantity at time t

Q_0 = initial quantity value (2100)

t = time (186 hours)

r = rate of decaying (0.65)

r = 0.65% = 10 days

1 day = [tex]\frac{0.0065}{10}[/tex]

1 hour = [tex]\frac{0.0065}{240}[/tex]

186 hours = [tex]\frac{0.0065*186}{240}[/tex]

rt = 0.00503

Q(186) = 2100*e^{-0.00503}

          = 2089.46

Answer:

306

Step-by-step explanation:

9 times 18= 162

24 times 6= 144

144+162=306

Answer:

123

Step-by-step explanation:

Assuming that 85% of the total was either adults or boys, we can subtract

100-85

=15

Therefore, that 15% is girls

820*.15

=123

Answer:

Step-by-step explanation:

Basically, in each option, you have to find the relationship between x and y (for one pair). Like in option #1 - how do you get 1.5 from 3? divide it by 2. Now you apply it for all numbers. It the outcome the same? No. 7 ÷ 2 ≠ 3.

You do the same process for all, until you are left with the last one. y = 50x

The last option is the answer.

Answer:

2072.56

Step-by-step explanation:

a=1030(1+0.06)^12

Answer:

$2072.60

Step-by-step explanation:

Every year you add on 6% so the multiplier  will be 1.06

so start off:

1030 x 1.06 = 1091.8

1091.8 x 1.06 = 1157.308

.......... you repeat this 12 times for every year and the final answer is

2072.6562366

you take that answer and round it to 2072.60

Hope this helps :)  

Final answer:

The man originally had $99. We determined this by setting up an equation based on the remaining amount after spending and misplacing portions of his money, then we solved for the original total.

Explanation:

To solve for the original amount of money the man had, let's call that amount x. First, he spent two-thirds of his money, which is (2/3)x. The remainder is x - (2/3)x = (1/3)x. He then misplaced one-third of this remainder which is (1/3) of (1/3)x = (1/9)x. So the portion he was left with is (1/3)x - (1/9)x = (2/9)x.

Since we know the final amount left is $22, we can express this as an equation:

To find x, we will divide both sides of the equation by (2/9):

When dividing by a fraction, we multiply by its reciprocal which is (9/2):

Therefore, the man originally had $99.

Answer:

The angle 6 measures 54 degrees

Step-by-step explanation:

Angle 6 is congruent to angle 7 ("-2x+34") as it is an opposite angle in straight line intersection. But angle 6 is congruent to angle 2 (-9x-36) due to the two horizontal lines being parallel. So we can write the following equality to determine the value of x:

-2x + 34 = -9x -36

7x = -70

==> x = -10

Now we can answer the question:  the angle 6 is

-2x + 34 = -2(-10)+34 = 54 degrees

Notice how the x-2 on the numerator and denominator cancel out, as well as the x+1. You are left with 8(x+2)/4 which is 2(x+2) which results in your answer, B, or 2x+4.

Answer:

As x decreases without bound, f(x) approaches the line y=3 .

As x increases without bound, f(x) increases without bound.

Step-by-step explanation:

From the given graph f(x), we can see that

When x  increases the value of y also increases

When x decreases  the y values goes close to 3 but it does not cross 3

As x goes to positive infinity , y approaches positive infinity

As x increases without bound, f(x) increases without bound.

As x goes to negative infinity, y values approaches +3

As x decreases without bound, f(x) approaches the line y=3

As x decreases without bound, f(x) approaches the line y=3 . As x increases without bound, f(x) increases without bound. Therefore, options A and B are correct answers.

The given function is f(x)=4 1/3x+3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph f(x), we can see that

When x increases the value of y also increases

When x decreases the y values goes close to 3 but it does not cross 3

As x goes to positive infinity, y approaches positive infinity

As x increases without bound, f(x) increases without bound.

As x goes to negative infinity, y values approaches +3

As x decreases without bound, f(x) approaches the line y=3

Therefore, options A and B are correct answers.

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The probability that a randomly selected light bulb will last between 750 and 825 hours is 34.13%. This is calculated through standardization of the desired range into z-scores, and reference to the standard normal distribution table.

The question is about finding the probability that a randomly selected light bulb will last between 750 and 825 hours, given that the life of light bulbs is normally distributed with a mean of 750 hours and a standard deviation of 75 hours.

Firstly, standardize the desired range by subtracting the mean and dividing by the standard deviation. This will give us the z-score: Z = (X - μ) / σ. For X = 750, Z1 = (750 - 750) / 75 = 0. For X = 825, Z2 = (825 - 750) / 75 = 1.

We can then use the Z-table or standard normal distribution table to find the probability associated with these z-scores. Since the z-score for 750 is 0, the probability is 0.5 (or 50%, as it's the mean). For z=1, the probability is 0.8413 (or 84.13%).

The probability that the bulb will last between 750 and 825 hours is then calculated by subtracting the smaller probability from the larger one: 0.8413 - 0.5 = 0.3413 or 34.13%

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To find the probability, calculate the z-scores for the values and use the standard normal distribution table which is 34.13%

To find the probability that a randomly selected light bulb will last between 750 and 825 hours, we need to calculate the z-scores for both values and then use the standard normal distribution table. The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation. For 750 hours, the z-score is 0, and for 825 hours, the z-score is (825 - 750) / 75 = 1.

Using the standard normal distribution table, the probability corresponding to a z-score of 0 is 0.5, and the probability corresponding to a z-score of 1 is 0.8413.

Therefore, the probability that a randomly selected light bulb will last between 750 and 825 hours is 0.8413 - 0.5 = 0.3413, or 34.13%.

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[tex]\left\{\begin{array}{ccc}9x-8y=2\\-3x-9y=-24&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}9x-8y=2\\-9x-27y=-72\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-35y=-70\qquad\text{divide both sides by (-35)}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the second equation}:\\\\-3x-9(2)=-24\\-3x-18=-24\qquad\text{add 18 to both sides}\\-3x=-6\qquad\text{divide both sides by (-3)}\\\boxed{x=2}\\\\Answer:\ \boxed{x=2}[/tex]

Answer:

x coordinate is 2

Step-by-step explanation:

We have given,

9x - 8y = 2   .........(1)

-3x - 9y = -24   ...............(2)

We use elimination method to eliminate y.

We multiply equation (1) by 9 and equation (2) by 8.

We get,

{ 9x - 8y = 2} × 9   or  81x - 72y = 18    -------------(3)

{-3x - 9y = - 24} × 8  or -24x - 72y = -192  -----------(4)

And subtract equation (4) from equation (3)

So , (81x - 72y ) - (-24x -72y)= 18 -(-192)

or 105x = 210

or x = 210/105

or x= 2

Hence we get x coordinate as x= 2

Answer:

(-6,-14)

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -\cfrac{4}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=-\cfrac{4}{5}(x-0) \\\\\\ y-7=-\cfrac{4}{5}x\implies y=-\cfrac{4}{5}x+7[/tex]

Rounded to the nearest tenth, the unit rate of calories per serving is approximately 141.3 calories.

To find the unit rate of calories per serving, divide the total calories (424) by the number of servings (3).

The unit rate is the amount of calories per serving. To find the unit rate, divide the total number of calories by the number of servings:

Unit rate = Total calories / Number of servings

Unit rate = 424 calories / 3 servings

Dividing 424 calories by 3 servings gives:

Unit rate = 424 / 3 ≈ 141.3 calories per serving

So, the unit rate of calories per serving is approximately 141.0 calories rounded to the nearest tenth or approximately 141.00 calories rounded to the nearest cent.

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Answer:

69% or 69/100

Step-by-step explanation:

It's experimental odds based off of experience.

The probability of getting a head on the next flip is 69%.

In order to determine the probability of getting a head on the next flip, we must first analyze the given data. The number of heads obtained in the first 100 flips is 69, while the number of tails is 31. Based on this information, we can calculate the proportion of heads to the total number of flips. The probability of getting a head on the next toss is therefore 69/100 = 0.69 or 69%.

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The required values of x and y is 9 and -36, respectively. The correct answer is option a.

Given that the system of equations:

y = -3x - 9                       (1)

y = (1/3)x - 39                  (2)

Setting the two equations equal to each other since they both equal y:

-3x - 9 = (1/3)x - 39

⇒ -3(3x) - 3(9) = (1/3)(3x) - 39(3)

⇒ -9x - 27 = x - 117

⇒ -9x - x = -117 + 27

⇒ -10x = -90

⇒ x = -90 / -10

⇒ x = 9

Substitute the value of x back in the equation (1),

y = -3(9) - 9

⇒ y = -27 - 9

⇒ y = -36

Hence, the solution to the system of equations is x = 9 and y = -36. The correct answer is option a.

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Answer:

48 pages

Step-by-step explanation:

So Colton's rate of using pages is:

9 pages/3 hours = 3 pages per hour.

Thus, we can find out how many pages he uses after 16 hours by multiplying

3 pages × 16 hours, which equals to 48 pages of notes.

Hope this helps!

Answer:

option B is correct.

[tex]2\sin^2r - 1[/tex]

Step-by-step explanation:

Given the expression: [tex]1-2\cos^2r[/tex]                      ......[1]

Using trigonometric identities:

[tex]\sin^2r+ \cos^2r = 1[/tex]

We can rearrange this as;

[tex]\cos^2r = 1-\sin^2r[/tex]      ......[2]

Substitute equation [2] into [1] we get;

[tex]1-2(1-\sin^2r)[/tex]

Using distributive property:  [tex]a\cdot (b+c) = a \cdot b + a\cdot c[/tex]

[tex]1- 2 +2sin^2r[/tex]

or

[tex]-1+2\sin^2r[/tex]

therefore, the given expression in terms of sine terms is; [tex]2\sin^2r-1[/tex]

Answer:

3p + 26  

Step-by-step explanation:

Let S = Sue's newspapers sold

     B = Bill's newspapers sold

     H = Harry's newspapers sold.

We have three conditions:

(1)   S = B + 26

(2)  B = 3H

(3)  H = p     Substitute (3) into (2)

(4) B = 3p     Substitute (4) into (1)

      S = 3p + 26

Sue sold 3p + 26 newspapers.

Let's keep in mind the conversion factors between mile, yard, feet and inches:

1 mile = 1760 yards

1 yard = 3 feets

1 feet = 12 inches

a) 3 mi. 26 yd.

We have:

8 mi. 133 yd. 2 ft. –

5 mi. 107 yd. 2 ft =

Here, we can simply do the substraction of each term, and we get:

(8-5) mi  (133-107) yd  (2-2) ft =

3 mi. 26 yd  0 ft =

3 mi. 26 yd.

b) 2 yd. 7 in.

We have:

2 yd. 2 ft. 6 in. –

0 yd.  1 ft. 11 in.

Here, we need to convert 1 feet into 12 inches and add them to the inches in the first term as follows:

2 yd. 2 ft. 6 in. = 2 yd. 1 ft. (6+12) in. = 2 yd. 1 ft. 18 in.

So now the subtraction becomes:

2 yd. 1 ft. 18 in. –

0 yd.  1 ft. 11 in.

and now we can simply do the substraction of each term, and we get:

(2-0) yd.  (1-1) ft.  (18-11) in. =

2 yd. 0 ft. 7 in. =

2 yd. 7 in.

c)  5 yd. 5 in.

We have:

6 yd.  0 ft. 0 in. –

0 yd.  2 ft. 7 in.

We have to "move" 1 yard into  feets and inches in the first term, as follows:

6 yd.  0 ft. 0 in. = 5 yd. 3 ft. 0 in. = 5 yd. 2 ft. 12 in.

And now the subtraction becomes:

5 yd. 2 ft. 12 in. -

0 yd.  2 ft. 7 in. =

5 yd.  0 ft. 5 in. =

5 yd. 5 in.

d) 8 in.

We have:

8 yd. 0 ft. 4 in. –

7 yd. 2 ft. 8 in.

Again, let's convert the first term, moving yards into feets and inches:

8 yd. 0 ft. 4 in. = 7 yd. 3 ft. 4 in. = 7 yd. 2 ft. (4+12) in. = 7 yd. 2 ft. 16 in.

So now the subtraction is:

7 yd. 2 ft. 16 in. -

7 yd. 2 ft. 8 in. =

0 yd. 0 ft. 8 in. =

8 in.

Answer:

15 points vertically.

Step-by-step explanation:

change -8 to 8, then add the 2 numbers in the y axis and you will get 15. brainliest?

Answer:

$43.40

Step-by-step explanation:

12 + 28

40

40 (1.085)    <<< sales tax

43.40

Answer: $43.40

Step-by-step explanation:

Total Cost of products (before sales tax): $12 + $28 = $40

After sales tax: ($40 × 108.5%) ÷ 100% = $43.4 = $43.40

Answer:

P₂ - P₁ = -11 100

Step-by-step explanation:

The profit for month 1 was P₁.

The profit for month 2 was P₂.

The difference in profit was

Diff. = P₂ - P₁

P₁ = 6400; P₂ = -4700

Diff. = - 4700 - 6400

Diff. =  -11 100

Answer:

Simplifying the expression eliminating the parentheses:

(-5 u^2 w)^3 = -125 u^6 w^3

Step-by-step explanation:

(-5 u^2 w)^3 = (-5)^3 (u^2)^3 (w)^3

(-5 u^2 w)^3 = (-5)(-5)(-5) u^(2 x 3) w^3

(-5 u^2 w)^3 = -125 u^6 w^3

Answer:

21.46 or 21.5

Step-by-step explanation:

To find the answer to this problem you must divide 877 by 4132, which gets you 0.2146. Then you multiply this answer by 100 to find the percentage; which in this case is 21.46, or 21.5 if you are rounding up. I hope my answer helped you!

887 is 21.47% of 4132, found by dividing 887 by 4132 and multiplying by 100.

To find out what percent 887 is of 4132, you need to use the formula for calculating percentages, which involves dividing the part by the whole and then multiplying the result by 100.

Here is how you can compute it step-by-step:

Divide 887 by 4132, which gives you approximately 0.2147.

Multiply this result by 100 to convert it into a percentage: 0.2147 * 100 = 21.47%.

Therefore, 887 is 21.47% of 4132.

Answer:

10 & 14

Step-by-step explanation:

10 + 14 = 24

14 - 10 = 4