Max and Sasha exercise a total of 20 hours each week. Max exercises 15 hours less than 4 times the

number of hours Sasha exercises. The system of equations shown below represents this situation, where

x represents the number of hours Max exercises and y represents the number of hours Sasha exercises.

How many hours do Max and Sasha exercise per week?

(x + y = 20

x - 4y =-15

Max exercises

hours a week and Sasha exercises

hours a week.

The values οf the trigοnοmetric functiοns are

sin( u+ v)=-(15/52 + (12√7)/52)

tan(u-v)=  -(15-12√7)/(36+5√7)

cοs( u + v)= (5√7)/52 - 36/52

Trigοnοmetric functiοns which are alsο knοwn as Circular Functiοns. It can be simply defined as the functiοns οf an angle οf a  right angled triangle. It explains  the relatiοnship between the angles and sides οf a triangle. The basic trigοnοmetric functiοns are sine(sin), cοsine(cοs), tangent(tan), cοtangent(cοt), secant(sec) and cοsecant(cοsec).

Given that sin u = 3/4 and cοs v = -5/13. (Bοth u and v are in Quadrant II.)

In Quadrant II the trigοnοmetric functiοn sin functiοn is pοsitive but cοs functiοn is negative.

From the trigonometric identity,

sin²u + cos²u =1 and sin²v + cos²v =1

Given sin u = 3/4                           cos v = -5/13

        cos u = -√(1-(3/4)²)                 sin v = √(1-(-5/13)²)

                  = -√(1-(9/16))                          = √(1-(25/169))

                  = - √7/4                                 = 12/13

71.

sin( u + v )

= sin u cos v + cos u sin v

= (3/4)(-5/13) + (-√7/4)(12/13)

= -15/52 - (12√7)/52

= -(15/52 + (12√7)/52)

73.

sin( u - v )

= sin u cos v - cos u sin v

= (3/4)(-5/13) - (-√7/4)(12/13)

= -15/52 + (12√7)/52

= -(15/52 - (12√7)/52)

cos(u - v)

= cos u cos v+ sin u sin v

= (-√7/4)(-5/13) + (3/4)(12/13)

= (5√7)/52 + 36/52

tan(u-v)

= \(\frac{sin(u-v)}{cos(u-v)}\)

= -(15-12√7)/(36+5√7)

75.

cos(u + v)

= cos u cos v- sin u sin v

= (-√7/4)(-5/13) - (3/4)(12/13)

= (5√7)/52 - 36/52

Hence, the values of the trigonometric functions are

sin( u+ v)=-(15/52 + (12√7)/52)

tan(u-v)=  -(15-12√7)/(36+5√7)

cos( u + v)= (5√7)/52 - 36/52

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Answer:

2000 miles.        

Step-by-step explanation:

If she has the car for  One day she can drive 2000 miles.

if she has the car for 2 days she can drive 1500

if she has the car for 3 days she can drive 1000

If she has the car for 4 days she can drive 500

The number of days Tallulah can afford to rent while staying within his budget is 4.2 days.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

The question has the following data as;

The amount charged =  $40

Rent per mile = $0.08

The mile to drive = 400 miles.

The Amount to spend = 200 dollars

The inequality would be written as;

40x + 0.08(400) ≤ 200

To solve for the value of x, this would be;

40x + 32 ≤ 200

40x ≤ 200 - 32

40x ≤ 168

We have to divide through by 40;

x ≤ 168/ 40

x ≤ 4.2

Hence we can say that the number of days Tallulah can afford to rent while staying within his budget is 4.2 days.

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Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

From the question, we have the following parameters that can be used in our computation:

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

2.56 feet / year to the nearest hundredth.

Step-by-step explanation:

Average rate = difference in height / number of years

= (3512-2712) / 312

= 800/312

= 2.56 feet / year

Answer:

40 goals.

Step-by-step explanation:

first you would want to do 30 divided by 15, because that's how many goals he makes per game, and multiply that (2) by 20.

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:

\(20x+240y/y\)

Step-by-step explanation:

1. Subtract the numbers

2. Evaluate the exponents

3. Subtract the numbers, again

4. Have a great day and thx for your inquiry :)

Answer:

Show the table or make ur question a little more clear so I can help

Step-by-step explanation:

Here is the required diagram .

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(0,3){2}{\line(1,0){4}}\qbezier(0,0)(0,0)(4,3)\qbezier(1,0)(1.2,0.35)(0.8,0.6)\qbezier(3,3)(2.8,2.65)(3.2,2.4)\put(2.5,0.02){\vector(1,0){0}}\put(1.5,3.02){\vector(-1,0){0}}\end{picture}\)

Alternate angles are equal .

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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Answer:

A) P(F | Fail) = 0.0195

B) i. Most bottles that fail inspection do not have a flaw.

C) P(NF | Pass) = 0.999999

D) ii: Most bottles that pass the inspection don't have a flaw.

E) probability in part C is very large and almost 100% and as such even if we fail a bottle which has no flaw, it is not a problem because we are sure that the ones that pass have no flaw.

Step-by-step explanation:

Let us first denote the terms:

F = The bottles have a flaw

NF = The bottles have no flaw

Pass = The bottles successfully passed the inspection test

Fail = The bottle failed the inspection test.

We are given:

P(F) = 0.0002

P(Fail | F) = 0.995

P(Pass | NF) = 0.99

Thus, probability of no flaw is;

P(NF) = 1 - P(F)

P(NF) = 1 - 0.0002

P(NF) = 0.9998

Also, probability that it passes the inspection when it has a flaw is;

P(Pass | F) = 1 - P(Fail | F)

P(Pass | F) = 1 - 0.995

P(Pass | F) = 0.005

Probability that it failed the test when It has no flaw is;

P(Fail | NF) = 1 - P(Pass | NF)

Thus;

P(Fail | NF) = 1 - 0.99

P(Fail | NF) = 0.01

A. Using Baye's theorem, we can find the probability that if fails inspection when it has a flaw;

P(F | Fail) = [P(Fail | F) × P(F)] / [(P(Fail | NF) × P(NF)) + (P(Fail | F) × P(F))]

P(F | Fail) = ((0.995) × (0.0002)/((0.01 × 0.9998) + (0.995 × 0.0002))

P(F | Fail) = 0.0195

B) probability in A is very small, thus;

We can say that majority of the bottles that fail inspection do not have a flaw.

C) using baye's theorem again, the probability that the bottle does not have a flaw if it passes the inspection. iis given by;

P(NF | Pass) = (P(Pass | NF) × P(NF)) / [(P(Pass | F) × P(F)) + (P(Pass | NF) × P(NF)]

P(NF | Pass) = (0.99 × 0.9998)/((0.005 × 0.0002) + (0.99 × 0.9998))

P(NF | Pass) = 0.999999

D) Probability in C above is very high, thus;

Most bottles that pass the inspection don't have a flaw.

E) probability in part C is very large and almost 100% and as such even if we fail a bottle which has no flaw, it is not a problem because we are sure that the ones that pass have no flaw.

Solution:

2b would be the greatest common factor (GCF) between both 10b^3 and 4b.

Hope this helps!

Step-by-step explanation:

x = number of heavy equipment operators

y = number of general laborers

x + y = 37 (37 people were hired)

out if this we get e.g.

x = 37 - y

124x + 82y = 3916 (daily rate for each role, in total 3916)

now we use the first equation in the second :

124(37 - y) + 82y = 3916

4588 - 124y + 82y = 3916

672 - 42y = 0

672 = 42y

y = 16

x = 37 - y = 37 - 16 = 21

21 heavy equipment operators were hired.

16 general laborers were hired.

Answer:

The independent variable is m, while the dependent variable is t.

Step-by-step explanation:

An independent variable is a variable that does not rely on another variable to change its outcome. In this case, the variable 'm' does not rely on the ride's total cost.

The dependent variable is a variable that depends on another variable to give its amount. In this case, 't' is the dependent variable, because it depends on how many miles were driven, in order to provide the correct answer.

t = $6 + ($1.50 x m)

3 miles: t = $6 + ($1.50 x m) or $10.50 = $6 + ($1.50 x 3)

4 miles: t = $6 + ($1.50 x m) or $12 = $6 + ($1.50 x 4)

5 miles: t = $6 + ($1.50 x m) or $13.50 = $6 + ($1.50 x 5)

6 miles: t = $6 + ($1.50 x m) or $15 = $6 + ($1.50 x 6)

7 miles: t = $6 + ($1.50 x m) or $16.50 = $6 + ($1.50 x 7)

8 miles: t = $6 + ($1.50 x m) or $18 = $6 + ($1.50 x 8)

9 miles: t = $6 + ($1.50 x m) or $19.50 = $6 + ($1.50 x 9)

10 miles: t = $6 + ($1.50 x m) or $21 = $6 + ($1.50 x 10)

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The given figure is a square base pyramid. The formula for determining the volume of a square base pyramid is expressed as

Volume = 1/3 x base area x height

From the diagram,

height = 1

base area = 1 x 1 = 1

Volume = 1/3 x 1 x 1

Volume = 0.333

Rounding to the nearest hundredth, volume of pyramid = 0.33 cubic yard

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

3 quarters

15 pennies

7 dimes

Step-by-step explanation:

5 times as many pennies as quarters would mean quarters x 5 equals pennies

3 quarters

15 pennies

7 dimes

You have to keep coming up with possible solutions to get the right one.

There are 5 times as many pennies as quarters, it adds up to $1.60, and it is 25 coins. This is the answer.

Answer: 141.26666666667

Step-by-step explanation:

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

=540

Step-by-step explanation:

10(3(25−6(22−19)+11))

=10(3(25−(6)(3)+11))

=10(3(25−18+11))

=10(3(7+11))

=10(3)(18)

=(10)(54)

=540

- it's a simplification process

Answer:

D) cannot factor

Step-by-step explanation:

D) cannot factor

D: cannot factor

it’s not factorable

Answer:

\(49.5 , -0.5\)

Step-by-step explanation:

\(a + b =49\\a - b = 0.5\\a= 49.5\\b= -0.5\)

\(x+y=49\\\underline{x-y=\dfrac{1}{2}}\\2x=49.5\\x=24.75\\\\24.75+y=49\\y=24.25\)

Those numbers are 24.75 and 24.25.

The ordered pair that is a solution of the system is (-3, -3), the second option.

There are two ways of finding this.

You can use your graph and identify which of the given pointes lies in the region where the two shaded areas intersect.

Another way, is replacing the values of the coordinate points in both inequalities and checking that both are true when evaluated in the point.

Here we will use the graph, because you already had it (and you can see a more precise graph in the image at the end).

We can see that the region os solutions is on the left side of the graph, and the only point that lies on there is (-3, -3)

So that point is the solution.

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Given:

The vertices of ΔABC are A(-4,4), B(-2,5), and C(-5,2).

The triangle ABC is reflected across the line y-axis to produce the image ΔA'B'C'.

To find:

The coordinates of ΔA'B'C'.

Solution:

If a figure is reflected across the y-axis, then

\((x,y)\to (-x,y)\)

Using this rule, we get

\(A(-4,4)\to A'(4,4)\)

\(B(-2,5)\to B'(2,5)\)

\(C(-5,2)\to C'(5,2)\)

Therefore, the vertices of the ΔA'B'C' are A'(4,4), B'(2,5) and C'(5,2).

Answer:

2:17 am

Step-by-step explanation:

3 hours after 10:46 would be 1:46

1:46 plus 31 minutes is 1:77 but there are only 60 minutes in an hour so 1:77 is 17 minutes after 2:00, or 2:17 am

The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:

Obtain the data for the medal winnings of the Top 10 NOCs

Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)

Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option

Add a title and labels to the chart to show the NOCs and their corresponding medal winnings

b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:

Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.

Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.

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