If s(x) = x - 7 and f(x) = 4x²-x + 3, which expression is equivalent to (t*s) (x)?

Based on the task content given; the solution to the equation for x 3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0 is 2 203/231

3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0

(3 1/2 × 2 1/5x) - (3 1/2 × 4 2/3) - 5 5/6 = 0

(7/2 × 11/5x) - (7/2 × 14/3) - 35/6 = 0

77/10x - 98/6 - 35/6 = 0

77/10x = 98/6 + 35/6

77/10x = 98+35 / 6

77/10x = 133/6

x = 133/6 ÷ 77/10

= 133/6 × 10/77

= 1330/462

x = 2 406/462

= 2 203/231

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Did not understand "full working pliz".

Answer:

  1∠22.5°, 1∠112.5°, 1∠202.5°, 1∠292.5°

Step-by-step explanation:

A root of a complex number can be found using Euler's identity.

For some z = a·e^(ix), the n-th root is ...

  z = (a^(1/n))·e^(i(x/n))

Here, we have z = i, so a = 1 and z = π/2 +2kπ.

Using r∠θ notation, this is ...

  i = 1∠(90° +k·360°)

and

  i^(1/4) = (1^(1/4))∠((90° +k·360°)/4)

  i^(1/4) = 1∠(22.5° +k·90°)

For k = 0 to 3, we have ...

 for k = 0, first root = 1∠22.5°

  for k = 1, second root = 1∠112.5°

  for k = 2, third root = 1∠202.5°

  for k = 3, fourth root = 1∠292.5°

Answer:

3/10

Step-by-step explanation:

There are totally 5 disks. On the first pick, there are 3 red discs. So

P(red disc on first pick ) = 3/5

Assuming that a red disc has been picked the first time, there will be 2 red discs and 2 blue discs so

(P red disc on second pick given red disc on first pick) = 2/4

P(red disc on both picks) = 3/5 x 2/4 = 3/10

a) [tex]\angle QST[/tex]

b) Arc QT

c) Arc QRS

d) 105 degrees

e) 255 degrees

Answer: 45%

Step-by-step explanation:

Given:

Find:

The number of groups which contains 9 is 9 and the total number of groups are 20.

So,

P = 9 / 20 = 0.45 = 45%

Therefore, the experimental probability is 45%

g(x) is a translation of 6 units downwards.

Here we have the function:

y = f(x) = 3x + 1

Notice that the y-intercept of f(x) is:

f(0) = 3*0 + 1 = 1

The y-intercept of f(x) is y = 1.

Now, we know that the y-intercept of g(x) is -5. then:

g(x) = 3x - 5 = f(x) - 6

Meaning that g(x) is a translation of 6 units downwards.

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Answer:

translated 2

units up

g(x)= f(x-2)

Step-by-step explanation:

Answer: No

Step-by-step explanation:  proportional means corresponding in size or amount to something. However, the number of her sit-ups isn't consistent, so it isn't proportional to the time she spends doing them.

The equation for the reflected function is:

g(x) =  (1/2)*(3)^(-x)

Here we know that function g(x) is a reflection of f(x) across the y-axis.

Remember that the reflection is written as:

g(x) = f(-x)

Here we know that:

f(x) = (1/2)*(3)^x

Then, replacing that in the equation for g(x), we get:

g(x) =  f(-x) = (1/2)*(3)^(-x)

g(x) =  (1/2)*(3)^(-x)

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Answer:

  x-intercept: (4, 0)

  y-intercept: (0, 3)

Step-by-step explanation:

The intercepts of the equation can be found by setting each variable to zero and solving for the other. The graph will be a line through the intercept points.

Setting x=0 and solving for y, we have ...

  4y -12 = 0   ⇒   y = 12/4 = 3

Setting y=0 and solving for x, we have ...

  3x -12 = 0   ⇒   x = 12/3 = 4

The intercepts are ...

  x-intercept: (4, 0)

  y-intercept: (0, 3)

The line will go through these intercept points.

Check the picture below.

so the composite is really a trapezoid and two triangles, let's get their area and sum them all up.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a = 2\\ b = 5\\ h = 7 \end{cases}\implies A=\cfrac{7(2+5)}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{yellow~trapezoid}{\cfrac{7(2+5)}{2}}~~ + ~~\stackrel{blue~triangle}{\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{5})}~~ + ~~\stackrel{orange~triangle}{\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{2})}} \\\\\\ 24.5~~ + ~~7.5~~ + ~~10\implies \text{\LARGE 42}[/tex]

Answer:

6%

Step-by-step explanation:

Got it right on the test.

Answer: 13

Step-by-step explanation:

4x+3y=-5 solve x :    

4x = -3y + -5           | -3y

1x = -0.75y + -1.25  | : 4

-3x + 7y = 13 solve x :

-3x + 7y = 13              | -7y

-3x = -7y = 13             | : (-3)

Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333

-0, 75y - 1,25 = 2,333y - 4, 333 solve y:

-0, 75y - 1,25 = 2,333y -4, 333    | -2,333y

-3, 083y - 1,25 = -4,333               | + 1, 25

-3. 083y = -3,088                         | : (-3, 083)

y = 1

Plug y = 1 into the equation 4x + 3y = -5 :

4x + 3 · 1           | Multiply 3 with 1

4x + 3 = -5        | -3

4x = -8              | : 4

x = -2

So the solution is:

y = 1, x = -2

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Based on the given parameters in the question, the value of the probability of A and D is 0.30

The given parameters from the tree diagram are:

The probability P(A and D) is calculated using the following probability formula

P(A and D) = P(A) × P(D)

Substitute the known values in the above equation

P(A and D) = 0.5 × 0.6

Evaluate the product of 0.5 and 0.6

P(A and D) = 0.30

Hence, the value of the probability of A and D is 0.30 based on the given parameters in the question

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Based on the given diagram (see attachment), the statement which is missing in the proof is: D. m∠7 ≅ m∠5.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

From the given diagram (see attachment), we can logically deduce that line m is parallel to line n (m || n) and a transversal line intersects both of them.

Based on these reasons, we can prove the following statements:

In conclusion, we can logically deduce that the statement which is missing in the proof is m∠7 ≅ m∠5.

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Answer:

here you go

Step-by-step explanation:

Answer:

Based on the mean of the sample and the proportion who read below grade level, the probability that a second sample would have a proportion greater than 0.54 is 0.9772.

The probability that the second sample would be selected with a proportion greater than 0.54 can be found as:

P (x > 0.54) = P ( z > (0.54 - 0.30) / 0.12))

Solving gives:

P (x > 0.54) = P (z > 2)

P (x > 0.54) = 0.9772

In conclusion, the probability that the second sample would be selected with a proportion greater than 0.54 is 0.9772.

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if any number or variable is outside a parenthesis it will go to all the number rin the parenthesis.

in this case -y is outside the parenthesis so it will got to both the sides :

-y(-6y-3) = -6y x y - 3 x y

= -6y² -3y//

Answer:

the coordinates of equations

1.4x+y=-7

for x =0

f(0,y)=4(0)+y=-7

y=-7

for y=0

f(x,0)=4x+0=-7

4x=-7

x=-7/4

2.x-y=2

for x=0

f(0,y)=0-y=2

-y=2

y=-2

for y=0

f(x,0)=x-0=2

x=2

graph all of the equations coordinates or you can look the image

so the answers are : {-3,-1}

CMIIW

The most reasonable unit to measure the time spent at school on an average school day is in hours.

In anything we are going to measure, we have to pay special attention to the unit. When doing this, we want to keep the absolute value of the measure, that is, the number small, hence the do this conversion of units may be used.

For example, it is easier and more practical to say one day instead of 87,840 seconds. The same logic is applied to this problem, in which the most reasonable unit to measure the time spent at school on an average school day is in hours, as it keeps the numerical measure smaller than it would be in minutes or seconds.

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Answer: [tex]\Large\boxed{3.52~;~66.88}[/tex]

Step-by-step explanation:

Given information

One number is 19 times the other

The smaller number is less than 5

Sum = 70.4

Set variables

Let x be the smaller number

Let 19x be the larger number

Set equation according to the given information

Smaller number + Larger number = Sum

x + 19x = 70.4

Simplify by addition

20x = 70.4

Divide 20 on both sides

20x / 20 = 70.4 / 20

[tex]\Large\boxed{x=3.52}[/tex]

Substitute values into the variables to find the larger number

Larger number = 19x

                         = 19 (3.52)

                         [tex]\Large\boxed{=66.88}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

smaller number 3.52

greater number 66.88

Step-by-step explanation:

Let x and y be two numbers ,where x < 5 and x ≤ y.

x + y = 70.4

y = 19x

By replacing y by 19x in the first equation we get :

x + 19x = 70.4

Then

20x = 70.4

Then

x = 70.4÷20

  = 3.52

y = 19x

Then

y = 19 × 3.52  (just replace x by 3.52)

  = 66.88

Step-by-step explanation:

1.

the expected sample mean is always the general mean : 168.5 pounds.

2.

the SD of a sample is the general SD / sqrt(sample size).

in our case

the sample SD = 68/sqrt(150) = 5.55217675...

3.

if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :

z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68

but we have here the question about the probability of the mean value of a whole sample of 150 women.

so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :

z = (x - mean)/(SD × sqrt(sample size)) =

= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =

= -0.010206207 ≈ -0.01

that gives us in the z-table the p-value 0.49601

this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.

4.

similar to 3.

the z value we are looking for

z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =

= 0.007804747... ≈ 0.01

that gives us the p-value 0.50399.

that would be the probability of a sample mean of 175 or below.

to get above 175 we need to get the other side of the bell-curve :

1 - 0.50399 = 0.49601

so, this case has about the same probability as 3.

5.

as 3), just with the sqrt(200) instead of the sqrt(150).

z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01

so, the probability is still about the same as in 3) :

0.49601

6.

as 4) just with sqrt(200).

z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01

so, the probability is still about the same as for 4) :

0.49601

The answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

What is probability ?

Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.

1)

We know that the expected mean of a sample is always equal to general mean.

As per the question, mean weight is 168.5 pounds.

This implies :

The expected mean for a sample of 150 women is :

= 168.5 pounds

2)

The standard deviation (SD) of the mean for a sample of 150 women is :

= 68 / (√150)

= 5.55

3)

The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :

z = ( x - mean) / ( SD × (√sample size))

= (160 - 168.5) / (68 × √150)

= 0.01

If we use the z table then the probability will be :

= 0.49601

4)

Similarly as part 3 :

z = (175 - 168.5) / (68 × √150)

z  = 0.01 (approximately)

The probability of 150 women having a sample mean below 175 pounds will be :

= 0.50399

And the probability of 150 women having a sample mean above 175 pounds will be :

= 1 - 0.50399

= 0.49601

5)

Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.

i.e.,

z = (160 - 168.5) / (68 × √200)

z = 0.01 ( approximately)

and probability will be :

= 0.49601

6)

Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.

z = (175 - 168.5) / (68 × √200)

z = 0.01

And probability equal to :

= 0.49601

Therefore , the answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

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Answer:

2827 m²

Step-by-step explanation:

The equation for volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Using this equation and the given volume of the sphere, we can find the radius of the sphere.

[tex]V=\frac{4}{3}\pi r^3[/tex]

[tex]4500\pi = \frac{4}{3}\pi r^3[/tex]

Divide both sides by π

[tex]4500=\frac{4}{3}(r^3)[/tex]

Multiply both sides by 3

[tex]13500=4( r^3)[/tex]

Divide both sides by 4

[tex]3375=r^3[/tex]

Take the cube root of both sides

[tex]r=15[/tex]

Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.

The equation for surface area of a sphere is [tex]4\pi r^2[/tex]. Substituting the value we found for the radius into the equation, we find:

[tex]SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2[/tex]

The surface area of the sphere, rounded to the nearest square meter, is 2827 m².

[tex]v(x) = wlh \\ 2x {}^{3} + {x}^{2} - 16 x- 15 =(2x + 5)(x - 3)h \\ h = \frac{2x {}^{3} + x {}^{2} - 16x - 15 }{2x {}^{2} - x - 15 } \\ using \: long \: divison \\ h = x + 1[/tex]

Reason:

The angles x and 71 are opposite the congruent sides. We call these the base angles. The base angles are congruent for any isosceles triangle. Therefore, x = 71.

It might help to rotate the triangle so that the angles x and 71 are flat along the ground (rather than tilted).

Answer:

k ≈ 50.77

Step-by-step explanation:

using the cosine ratio in the right triangle

cos19° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{48}{k}[/tex] ( multiply both sides by k )

k × cos19° = 48 ( divide both sides by cos19° )

k = [tex]\frac{48}{cos19}[/tex] ≈ 50.77 ( to 2 dec. places )

Hi :)

            We'll use sohcahtoa to solve this problem

[tex]\Large\boxed{\begin{tabular}{c|1} \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~\div \text{hyp}\\\sf{Cah} & Adj \div \text{hyp}\\\sf{Toa} & Opp \div \text{adj} \end{tabular}}[/tex]

Looking at our triangle, we can clearly see that we have :

Set up the ratio

[tex]\longrightarrow\darkblue\sf{cos(19)=\dfrac{48}{k}}[/tex]

solve for k

[tex]\longrightarrow\darkblue\sf{k\cos(19)=48}[/tex] > multiply both sides by k to clear the fraction

[tex]\longrightarrow\darkblue\sf{k=\dfrac{48}{\cos(19)}}[/tex]  > divide both sides by cos (19)

[tex]\star\longrightarrow\darkblue\sf{k\approx50.77}\star[/tex]

[tex]\tt{Learn~More ; Work\ Harder}[/tex]

:)

Step-by-step explanation:

68% of all values are within 1 SD (110 ± 15).

95% of all values are within 2SD (110 ± 2×15 = 30)

99.7% of all values are within 3 SD (110 ± 3×15 = 45)

a)

95 is 110 - 15, so exactly 1 SD apart from the mean value.

68% or 0.68 is the probability of all values between 95 and 125.

so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 95 is

0.34 + 0.5 = 0.84

b)

125 is 110 + 15, so exactly 1 SD apart from the mean value.

so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 125 is

0.5 - 0.34 = 0.16

The child is 59.4 inches tall, assuming the length from the coach's shoulder to his head cap is approximately 10 inches.

Height refers to the vertical distance between the top and bottom of something.

Height measures the length of some objects or persons vertically to determine whether it is high or low, according to some ascertained criteria.

Baseball coach's height = 70 inches

Coach's shoulder to head = 10.6 inches

Height of the child standing slightly below the coach's shoulder = 59.4 inches (70 - 10.6)

Thus, the child standing slightly below the coach's shoulder is 59.4 inches tall.

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Assume that the height of the coach from his shoulder to the head is 10.6 inches.

Mathematically speaking, the Riemann sum of the linear function is represented by A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}, whose representation is represent by the graph in the lower left corner of the picture.

Graphically speaking, Riemann sums with right endpoints represent a sum of rectangular areas with equal width with excess area for positive y-values and truncated area for negative y-values generated with respect to the x-axis. Mathematically speaking, this case of Riemann sums is described by the following expression:

A ≈ [(b - a) / n] · ∑ f[a + i · [(b - a) / n]], for i ∈ {1, 2, ..., n}

Where:

a - Lower limit

b - Upper limit

n - Number of rectangles

i - Index of a rectangle

If we know that f(x) = 2 · x - 1, a = - 6, b = 4 and n = 5, then the Riemann sum with right endpoints of the area below the curve is:

A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}

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Answer:

B) 9:35

Step-by-step explanation:

the travel time we get by dividing the distance by the speed

distance / distance/time = time

so,

60 / 80 = 6/8 = 3/4 = 0.75 hours or 45 minutes.

since she arrived 20 minutes late, that means at 10:20 am, she left home 45 - 20 = 25 minutes before 10:00am.

and that is 9:35 am.