PLEASE help. Will give brainliest.

\(x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}\)

Answer:

1. False

2. True

3. True

4. True

Step-by-step explanation:

A rational number is a number that can be written as a fraction of two integers. An irrational number can not be written as a fraction of two integers.

(Remember that an integer and a whole number are the same).

This means that...

All whole numbers/integers are rational.

3 is true for reasons mentioned above.

4 is just asking the same as 3.

Answer:

From the picture attached,

There are two parallel lines intersected by three transverse lines.

m∠2 = 98°, m∠3 = 23°, m∠8 = 70°

a). Since ∠1 and ∠2 are linear pairs,

=

  m∠1 + m∠2 = 180°

  m∠1 + 98° = 180°

  m∠1 = 180 - 98

  m∠1 = 82°

b). m∠4 = m∠7 [Corresponding angles]

m∠7 = 180° - (m∠2 + m∠3) [Property of a triangle]  

= 180 - (98 + 23)

= 180 - 121  

= 59°

m∠4 = m∠7 = 59°

c). m∠5 = 180° - (m∠3 + m∠4)

= 180° - (23° + 59°)

= 180° - 82°

= 98°

d). m∠6 = 180° - (m∠7 + m∠8)

= 180° - (59° + 70°)

= 180 - 129

= 51°  

e). m∠7 = 59° [Calculated in part b]

f). m∠9 = 180° - (m∠4 + m∠8) [Property of a triangle]

= 180° - (59 + 70)°

= 180 - 129

= 51°

g). m∠10 = 180° - m∠9

= 180 - 51

= 129°

Answer:

B. 40 ≤ e ≤ 100

Step-by-step explanation:

In a function, the domain values are the independent variables, and are always plotted on the x-axis, while the range values the dependent variables, which are always plotted on the y-axis on a graph.

From the graph given, it shows that f is a function of e. Which is, \( e(f) \).

Therefore, the range of the function would be: B. 40 ≤ e ≤ 100

Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

To determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.

If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.

Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.

However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.

Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

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Answer:

  12 mL of 46% solution

Step-by-step explanation:

Let q represent the volume of 46% solution needed in the mix. Then the total amount of hydrogen peroxide in the solution is ...

  0.46q +0.36(30 -q) = 0.40(30)

  0.10q +10.8 = 12.0

  0.10q = 1.2

  q = 12 . . . . . . mL of 46% solution needed

He must mix 12 mL of 46% solution to make the desired result.

__

... and 18 mL of 36% solution

The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.

To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.

The total number of students who have not found a job would be 1500 - 1380 = 120.

To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:

The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.

Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.

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Answer:

326

Step-by-step explanation:

The value of the given expression is 326.

Given:

The given expression 2 hundreds + 12 tens + 6 ones.

To find:

The value of the given expression.

Explanation:

The numeric form of given expression is:

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

Therefore, the value of the given expression is 326.

Step-by-step explanation:  

C

The symmetric equations of the line passing through a point and parallel to a vector are -(x - 4) = y + 1/4 = -(z - 9)/2. The line intersects the xy-, xz-, and yz-planes at (5, -9/4, 0), (15/4, 0, 23/2), and (0, -17/4, 11/2), respectively.

To find the symmetric equations of the line, we first need to find the direction vector of the line. Since the line is parallel to the vector <4, -1, 9>, any scalar multiple of this vector will be a direction vector of the line. So, let's choose the parameter t and write the vector equation of the line:

r = <4, -1, 9> + t<-1, 4, -2>

Expanding this vector equation component-wise, we get:

x = 4 - t

y = -1 + 4t

z = 9 - 2t

These equations can be rearranged to get the symmetric equations of the line:

-(x - 4) = y + 1/4 = -(z - 9)/2

To find the points in which the line intersects the coordinate planes, we substitute the corresponding variables with 0 in the equations for the line.

For the xy-plane, we set z = 0 and solve for x and y:

-(x - 4) = y + 1/4 = -(-9)/2

x = 5, y = -9/4

So, the line intersects the xy-plane at the point (5, -9/4, 0).

For the xz-plane, we set y = 0 and solve for x and z:

-(x - 4) = 0 + 1/4 = -(z - 9)/2

x = 15/4, z = 23/2

So, the line intersects the xz-plane at the point (15/4, 0, 23/2).

For the yz-plane, we set x = 0 and solve for y and z:

-(-4) = y + 1/4 = -(z - 9)/2

y = -17/4, z = 11/2

So, the line intersects the yz-plane at the point (0, -17/4, 11/2).

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The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)

\(= (x^2 + x - 12)(x - 5)\)

\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)

\(= x^3 - 4x^2 - 17x + 60\).

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Answer:C

Step-by-step explanation:

Answer:

x = 5 - 2a

Step by step explanation:

2x + 4a = 10

So, 2x = 10 - 4a

=> x = (10 - 4a)/2

=> x = 5 - 2a

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Thank you.

The number of bacteria after 8 hours is approximately 2,713.

Let's apply the exponential growth formula:

N = N0 * e(rt),

N is the number of bacteria at a particular period. N0 is the initial bacterial population, e is the mathematical constant (about equal to 2.71828), r is the growth rate, and t is the amount of time that has passed.

The information provided in the problem can be used to determine the growth rate:

N1 = N0 * e(r*2)

N2 = N0 * e(r*4)

To get eliminate N0, divide the second equation by the first equation:

N2/N1 = e(r4) / e(r2)

385/135 = e(r4) / e(r2)

If we condense this expression, we get:

e(r*2) = 385/135

e(r*2) = 2.8519

When we take the natural logarithm of both sides, we get:

r*2 = ln(2.8519)

r = ln(2.8519)/2

r = 0.5457 (rounded to 4 decimal places)

The number of bacteria after 8 hours can now be determined using the exponential growth algorithm once more:

N = N0 * e(rt)

N = 135 * e(0.5457*8)

N = 2,713 (rounded to the nearest whole number)

Therefore, the number of bacteria after 8 hours is approximately 2,713.

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1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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Answer:#

i'm guessing 47.12

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer: 1/2B

Step-by-step explanation: Because there are 3 odd numbers, meaning that you will have 3/6 which is also 1/2.

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This question is of a topic called subset that is a part of set theory.

statement 1 is true. statement 2 is true. statement 3 is false, statement 4 is true.

I assume the questioner has the basic understanding of set theory and what subsets are.

Statement 1st "{1,2,3,4,5} ⊄ {1,2,4}" is true because here not every element of set {1,2,3,4,5} is an element of set {1,2,4}.

Statement 2nd "{11, 13, 15} ⊂ { 11, 12, 13, 14, 15, 16, ... }"  that is set {11, 13, 15} is a proper subset of set { 11, 12, 13, 14, 15, 16, ... } is true since every element of set {11, 13, 15} belongs to set { 11, 12, 13, 14, 15, 16, ... } also set

{11, 13, 15} is not equal to set  { 11, 12, 13, 14, 15, 16, ... }.

statement 3rd "∅ ⊈ {d, f, g, n}" is false since ∅ = null set is the subset of every set.

statement 4th "{21, 22, 23, 26, 29} ⊆ {21, 22, 23, 26, 29}" is true both sets have same elements therefore are subsets of each other and hence both are also equal to each other.

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Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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The representations of the inequality is  an open circle is at 1 and a bold line starts at 1 and is pointing to the right.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Since our answer is x > 1.  An open circle will be at 1 and a bold line starts at 1 and is pointing to the right (>). Check the attached image.

Note: You only shade up if you have ≤ (less than or equal) or ≥ (greater than or equal).

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In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Step-by-step explanation:

(-8,-10) (-10,-12) (-12,-14)

just plug them into the formula and see that it works.

Answer:

(a)Degree 3

(b) \(f(x)=x^{3}+2 x^{2}-7 x+3\)

Step-by-step explanation:

(a)Given the function represented by the set of points: {(-3,15)(-2,17), (-1,11), (0,3),(1,-1), (2,5),(3,27)}.

To determine the degree of the polynomial of the function, we plot the function on a graph.

From the graph, the function has 2 turning points.

The maximum number of turning points of a polynomial function is always one less than the degree of the function.

Therefore, the polynomial has a degree of 3 .

(b)A cubic function is one in the form  where d is the y-intercept.

A cubic function is one in the form \(f(x)=a x^{3}+b x^{2}+c x+d\) where d is the y-intercept.

Therefore, our polynomial is of the form:

\(\begin{array}{l}f(x)=a x^{3}+b x^{2}+c x+3 \\\text {At }(-3,15), 15=a(-3)^{3}+b(-3)^{2}+c(-3)+3 \implies -27 a+9 b-3 c=12 \\\text {At }(-2,17), 17=a(-2)^{3}+b(-2)^{2}+c(-2)+3 \Longrightarrow -8 a+4 b-2 c=14 \\\text {At }(-1,11), 11=a(-1)^{3}+b(-1)^{2}+c(-1)+3 \Longrightarrow -a+b-c=8\end{array}\)

Solving the three resulting equations simultaneously (using a calculator), we obtain:

a=1, b=2, c=-7

Therefore, the equation for this function is:

\(f(x)=x^{3}+2 x^{2}-7 x+3\)

Answer:

3.6666666.... and continuing

or 3.7 if you want to round

Step-by-step explanation:

To find the mean, I added all the numbers up:

4+3+1+ 6+ 1+7 = 22

Then I divided that by how many numbers there are total (6).

22/6= 3.66666.. or 3.6 with a bar symbol on top of the 6.

Thus, the answer is 3.666666...