What happens to spoons when they work too hard (riddle)

Answer:

$3.52

Step-by-step explanation:

Lavender oil: $18.75/oz

Lemon oil: $15.90/oz

0.2 × $18.75 + 0.3 × $15.90 - 5 = $3.75 + $4.77 - $5 = $3.52

The Solution.

The total number of people surveyed = 750.

The number of age group 41 - 50 that favored the Do-It-Yourself books = 69

The percentage of the people in age group 41 - 50, and favored the Do-It-Yourself books is calculated as below:

Hence, the correct answer is 9 percent.

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

In order to find the area of a triangle in the Cartesian coordinate system, we need to find the length of two sides of the triangle, and the angle between them.

We can use the distance formula for the length of the sides and the dot product of vectors for the angle between them.

Then we can use the formula for the area of a triangle which is:

Area=12|A||B|sinθArea=12|A||B|sinθ

where θ is the angle between vectors A and B.

The dot product of vectors A and B is given by:

A⋅B=|A||B|cosθA⋅B=|A||B|cosθ

Thus, the angle between A and B is given by:

θ=cos−1A⋅B|A||B|θ

 =cos−1A⋅B|A||B|

We will now proceed with finding the length of sides and angle between vectors.

We need to find the area of a triangle with vertices P(1,0,1),Q(−2,1,3), and R(4,2,5).

Let A be the position vector of point P, B be the position vector of point Q, and C be the position vector of point R.

The position vectors of these points are:

A=⟨1,0,1⟩B=⟨−2,1,3⟩C=⟨4,2,5⟩

The side lengths are:

|AB|=∥B−A∥=√(−2−1)2+(1−0)2+(3−1)2

                  =√(−3)2+12+22

                  =√14|BC|

                  =∥C−B∥

                  =√(4+2)2+(2−1)2+(5−3)2

                  =√62|CA|=∥A−C∥

                  =√(1−4)2+(0−2)2+(1−5)2

                  =√42

The direction vectors of the two sides AB and BC are given by:

B−A=⟨−2−1,1−0,3−1⟩

      =⟨−3,1,2⟩C−B

      =⟨4+2,2−1,5−3⟩

      =⟨6,1,2⟩

Thus, we can find the angle between them using the dot product of the two vectors:

AB⋅BC=(−3)(6)+(1)(1)+(2)(2)

          =−18+1+4

          =−13|AB||BC|

∴cosθ=−13√14(√62)

∴θ=cos−1−13√14(√62)

Now we can use the formula for the area of a triangle:

Area=12|AB||BC|sinθ

       =12√14(√62)sin(θ)

       =12√14(√62)sin(cos−1(−13√14(√62)))

        =√14(√62)2sin(cos−1(−13√14(√62)))

        =√14(√62)2sin(133.123°)

        =√14(√62)2×0.8767≈1.819 square units

Therefore, the area of the triangle with vertices P(1,0,1),Q(−2,1,3), and R(4,2,5) is 1.819 square units.

Determine whether the lines L1​ and L2​ are parallel, skew or intersecting. If they intersect, find the point of intersection.

L1​: 2x−3=y−4=3z−1

L2​: 4x−1=−21y−3=5z−4

First, we will write each equation in parametric form.

L1​: x=3t2+32, y=t+42, z=13t+12L2​:

x=141−52t, y=31+25t, z=44t−54

We will now equate x, y, and z from both the equations.

L1​: 3t2+32=141−52t, t+42=31+25t, 13t+12=44t−54⇔13t=13⇔t=1

L1​: x=12,y=5,z=25L2​: x=12,y=5,z=25

Therefore, the lines L1​ and L2​ are not parallel or skew but intersecting at the point (1,5,2).

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Answer:

x ∈ { ( 6 + \(\sqrt{23}\) * i) , { ( 6 - \(\sqrt{23}\) * i) }

Step-by-step explanation:

Given: \(x^2-12x+59=0\)

First, collect like terms. \(x^2\) and -12x, 59 and 0:

\(x^2-12x=0-59\)

+59 is changed to -59 when transferred. Then subtract:

( x - 12 ) x = -59

Finally divide both sides by -59:

x ∈ { ( 6 + \(\sqrt{23}\) * i) , { ( 6 - \(\sqrt{23}\) * i) }

Answer:

Can't explain but

9:12

12:16?

Answer:

First, in standard notation, we must define our zero.

In this case, would make sense to define the zero in the surface of the water.

(below is a number line so you can see the process to think this)

Then if the whale is swimming 60ft bellow the surface of the water, then the first position of the whale is:

-60

Now the whale goes up 30ft, then the new position of the whale is:

-60ft + 30ft = -30ft.

The correct option is A:

The equation is -60 + 30 = -30. The whale is 30 feet below the water's surface.

(you wrote that the equation was equal to +30 instead of -30 in the option A, i supposed that it was a typo)

Answer:

I belive the answer is A.

Step-by-step explanation:

Answer:

27)  (7 + 9) · 3 / 6 = 48/6 = 8

28) (-7)² - 3(-7)(4) = 49 - (-84) = 133

Step-by-step explanation:

The contribution of the Monday absences to the calculation of the chi-square test statistic would depend on the size of the observed and expected frequencies in that cell relative to the other cells in the table.

Without more information about the specific claim being tested and the data being analyzed, it is difficult to provide a precise answer. However, in general, if the claim being tested involves a comparison of the frequency of absences on Mondays to the frequency of absences on other days of the week, then the number of Monday absences would likely be one of the variables included in the calculation of the chi-square test statistic.

The chi-square test is a statistical test that is used to determine if there is a significant association between two categorical variables. In order to perform the test, the observed frequencies of each category of each variable are compared to the expected frequencies, which are calculated based on the assumption of independence between the variables. The difference between the observed and expected frequencies is then squared, divided by the expected frequency, and summed across all categories of both variables to obtain the chi-square test statistic.

If the claim being tested involves a comparison of the frequency of absences on Mondays to the frequency of absences on other days of the week, then the number of Monday absences would likely be one of the categories of one of the variables included in the calculation of the chi-square test statistic. For example, if the data were organized into a contingency table with one variable representing the day of the week and the other variable representing the frequency of absences on that day, then the number of Monday absences would be one of the cells in the table. The contribution of the Monday absences to the calculation of the chi-square test statistic would depend on the size of the observed and expected frequencies in that cell relative to the other cells in the table.

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Using it's concept, it is found that the percent increase in the amount of iron per serving was of 50%.

It is given by the increase divided by the initial value, and subtracted by 100%.

In this problem:

Hence the percent increase is given by:

P = 0.6/1.2 x 100% = 50%.

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Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

Answer:

A=1,2,3

B=x^2 is the answer

Answer:

there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Step-by-step explanation:

To choose three different members from the club to be president, vice president, and treasurer, you can follow these steps:

Step 1: Calculate the number of ways to choose the president:

Since there are 15 club members in total, the number of ways to choose the president is 15.

Step 2: Calculate the number of ways to choose the vice president:

After selecting the president, there are 14 remaining members. The number of ways to choose the vice president from these 14 members is 14.

Step 3: Calculate the number of ways to choose the treasurer:

After selecting the president and vice president, there are 13 remaining members. The number of ways to choose the treasurer from these 13 members is 13.

Step 4: Calculate the total number of ways to choose the president, vice president, and treasurer:

Since each step is independent, you can multiply the number of choices at each step: 15 * 14 * 13 = 2,730.

Therefore, there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Answer:

y+4 _<_ 10

Step-by-step explanation:

Answer:

4+y>10

Step-by-step explanation:

Pls give Brainliest!

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Answer:

v = 87.96 cubic inches

Step-by-step explanation:

v = πr²h

v = π2²(7)

v = 3.14(4)(7)

v = 12.57(7)

v = 87.96

Answer:

125.7 in^3

Step-by-step explanation:

V = 125.663706143592

V = 125.7 in^3

Maria skied a distance of 2.55 km, taking 0.425 hours (25.5 minutes) going up and 0.075 hours (4.5 minutes) skiing down.

To find out how far Maria skied and for how long, we'll use the given information and apply the distance-rate-time formula. The formula is Distance = Rate × Time.
First, let's convert the given 30 minutes into hours since the rates are in km/hr.
30 minutes = 30/60 = 0.5 hours.
Let x be the distance Maria skied up and down, and let t1 and t2 be the time taken to go up and down, respectively.
For the ski lift(going up):
Distance = Rate × Time
x = 6 × t1
For skiing down:
Distance = Rate × Time
x = 34 × t2
Since the round trip took 0.5 hours, we have:
t1 + t2 = 0.5
Now we have a system of equations:
x = 6 × t1
x = 34 × t2
t1 + t2 = 0.5
From the first equation, we can express t1 as:
t1 = x/6
From the second equation, we can express t2 as:
t2 = x/34
Now substitute these expressions into the third equation:
(x/6) + (x/34) = 0.5
To solve for x, find a common denominator (in this case, 102) and combine the fractions:
(17x + 3x) / 102 = 0.5
20x = 51
x = 51/20
x = 2.55 km
Now, we can find t1 and t2:
t1 = x/6 = 2.55/6 = 0.425 hours
t2 = x/34 = 2.55/34 = 0.075 hours
So, Maria skied a distance of 2.55 km, taking 0.425 hours (25.5 minutes) going up and 0.075 hours (4.5 minutes) skiing down.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{0}}}}}\)

Step-by-step explanation:

\( \sf{1 - 3x = 1 - x}\)

Move x to left hand side and change it's sign

Similarly, move 1 to right hand side and change it's sign

\( \dashrightarrow{ \sf{ - 3x + x = 1 - 1}}\)

Collect like terms

\( \dashrightarrow{ \sf{ - 2x = 0}}\)

Divide both sides by -2

\( \dashrightarrow{ \sf{ \frac{ - 2x}{ - 2} = \frac{ 0}{ - 2}}} \)

Calculate

\( \dashrightarrow{ \sf{ x = 0}}\)

Hope I helped!

Best regards! :D

L'Hospital's rule applies to the limit of the ratio of two functions when the limit of the function as x approaches a certain value.

In the limit expression, a and b are positive integers, but they do not equal 0, so L'Hospital's rule can't be applied.

L'Hospital's rule applies to the limit of the ratio of two functions when the limit of the function as x approaches a certain value, say c, approaches zero or infinity and the other function also approaches zero or infinity at the same point c. Therefore, L'Hospital's rule applies to the limit of the expression of the form:

lim ( f(x) / g(x) ) as x --> c

where, f(x) and g(x) are functions of x and c is a real number such that

In the limit expression, a and b are positive integers, but they do not equal 0, so L'Hospital's rule can't be applied.

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Answer:

x- intercept = (- 7.5, 0 ) , y- intercept = (0, 5.5 )

Step-by-step explanation:

the x- intercept is where the line crosses the x- axis

the line crosses the x- axis at - 7.5 , so

x- intercept = (- 7.5, 0 )

the y- intercept is where the line crosses the y- axis

the line crosses the y- axis at 5.5 , so

y- intercept = (0, 5.5 )

answer = ) 100.80

Step-by-step explanation:

I subtracted the people who payed on the 1st of the month which was 4 from the total 12 memebers. I got 8, then that 8 payed on the 2nd of the month so I multiplied 8 by 12.60

Answer:

A

Step-by-step explanation:

d≈5.09

Using the formulas

C=2πr

d=2r

Solving for d

d=C/π=16/π≈5.09296

Answer:

The price per unit of chocolate bars is £0.3.

Step-by-step explanation:

The cost of 4 chocolates bars is  £1.20.

The cost of 1 chocolate bars is \(\frac{1.20}{4}\)

The cost of 1 chocolate bars is £0.3.

Answer: $4.80 (us dollars)

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

30 ÷1.5

each person eats 1.5 pounds

Answer:

C

.....................

Answer:

salary = $ 500 + 0.105 sales

Step-by-step explanation:

Weekly Income = 500 + 0.105S   where S= weekly sales

in x, y math format that's

y=500+0.105x

Economics often uses Q for quantity and Y for income

so,

Y=500+0.105Q

Hope this answer helps you :)

Have a great day

Mark brainliest

Step-by-step explanation:

-(x + 4) - 3x = x

-x - 4 - 3x = x

-x - 3x - 4 = x

-4x - 4 = x

-4 = 5x

-4/5 = x

x = -4/5

Answer: 45%

Step-by-step explanation:

90 votes / 200 votes =  0.45

Now, let's convert this to percentage

=> 0.45 * 100% = 45%

.Thus, the student candidate was able to accumulate 45% of the voters out of 200.

Answer:

There are a total of 200 voters for the student council election. Now, one student who is a candidate was able to get 90 votes out of 200. Let's find out how much percentage did he or she get for the votes

.=> 90 votes / 200 votes =  0.45

Now, let's convert this to percentage

=> 0.45 * 100% = 45%

.Thus, the student candidate was able to accumulate 45% of the voters out of 200.

Step-by-step explanation: The answer

Answer: Option A, B, E are correct.

A. 8^x •8^x = 64^x

B. 8^2x = 64^x

C. 8•8^2x = 8^{1 + 2x}

D.8^2•8^x = 8^{2 + x}

E. (8•8)^x = 64^x

F. 8•8^x = 8^{1 + x}

The exact length of the curve is 8/3 (5sqrt(26) - 1).

To find the length of the curve, we can use the arc length formula:

L = ∫\([a,b]sqrt(dx/dt)^2 + (dy/dt)^2 dt\)

where a and b are the starting and ending values of the parameter t, and dx/dt and dy/dt are the derivatives of x and y with respect to t, respectively.

Plugging in the given equations, we get:

\(dx/dt = 24t\)

\(dy/dt = 24t^2\)

Therefore,

\((sqrt(dx/dt)^2 + (dy/dt)^2) = sqrt((24t)^2 + (24t^2)^2) = sqrt(576t^2 + 576t^4)\)

Substituting these expressions into the arc length formula, we get:

L = ∫\([0,2]sqrt(576t^2 + 576t^4) dt\)

We can factor out 576t^2 from the square root:

L = ∫\([0,2]sqrt(576t^2(1 + t^2)) dt\)

And then simplify the expression inside the square root:

L = ∫\([0,2]24t sqrt(1 + t^2) dt\)

This integral can be evaluated using the substitution\(u = 1 + t^2, du/dt = 2t, dt = du/2t:\)

L = ∫\([1,5]12 sqrt(u) du\)

Now we can use the power rule of integration to evaluate this integral:

\(L = [8/3 u^(3/2)]_1^5 = 8/3 (5sqrt(26) - 1)\)

Therefore, the exact length of the curve is 8/3 (5sqrt(26) - 1).

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