What is the value of x if 15 = 5x +45?

Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

Answer:

Her elevation went down too quickly, if she is going down 300 ft per hour at a constant rate, at 1 hour, she should be at 2700 feet. It should take her about 10 hours to get down the mountain.

11) The pre-image, R at the point (-2, 3) on the grid shown produces an image following the reflection across the line y = 2·x - 3 as follows;

I. The line \(\overline{RR'}\) which is obtained from the image R' following a reflection across the line y = 2·x - 3, is perpendicular to the line y = 2·x - 3, because the points R and R' are vertically opposite each other, therefore, the slope is the negative inverse of the slope of y = 2·x - 3, which is -0.5

II. Please find attached the graph made using MS Excel showing the points R and R'

A reflection transformation is one in which a point is reflected across a line such that the distances of the image and the pre-image from the line are the same and the line acts like a mirror producing an image of the object.

The coordinates of point R = (-2, 3)

The equation of the line of reflection is; y = 2·x - 3

The coordinates of the image of a point, (x₁, y₁) reflected across a line, a·x + b·y + c = 0, is found as follows;

The image of is found using the formula;

\(\dfrac{x - x_1}{a} =\dfrac{y-y_1}{b} = -\dfrac{2\cdot (a\cdot x_1+b\cdot y_1+c)}{a^2+b^2}\)

The equation, y = 2·x - 3, can be expressed in the form a·x + b·y + c = 0, as follows;

y = 2·x - 3

0 = 2·x - 3 - y

Therefore;

a = 2, b = -1, and c = -3

(x₁, y₁) = (-2, 3)

\(\dfrac{x - (-2)}{2} = -\dfrac{2\times (2\times (-2)- 3-3)}{2^2+(-1)^2}=4\)

\(\dfrac{x +2}{2} = 4\)
x = 2× 4 - 2 = 6

x = 6

\(\dfrac{y-3}{-1} = 4\)

y = 4 ×(-1) + 3 = -1

The coordinates of the image, (x, y) = (6, -1)

The slope of the line is -(1/2)

The equation of the perpendicular line is therefore;

(y - 3) = -0.5·(x - (-2)) = -0.5·x - 1

y = -0.5·x - 1 + 3 =  -0.5·x + 2

Equation of the perpendicular line through R; y = -0.5·x + 2

The intersection point is therefore;

-0.5·x + 2 = 2·x - 3

2.5·x = 5

x = 5 ÷ 2.5 = 2

y = 2×2 - 3 = 1

y = 1

The point is therefore, (2, 1)

The difference in the x-values = 2 - 2 = 4

The difference in the y-value = 1 - 3 = -2

Therefore, 4 is added to the x-value of the point (2, 1) and 2 is subtracted to get the image as follows;

(x, y) = (2 + 4, 1 - 2) = (6, -1)

The slope of \(\overline{RR'}\) = (3 - (-1))/(-2 - 6) = -0.5

b. Graphically, the equation of the line \(\overline{RR'}\) can be used to find the point R', by adding the horizontal distance and subtracting the vertical distance of the point R from the the point of intersection of the two lines.

Please find attached the graph showing R and the image R' created with MS Excel.

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Answer:

h(x)=2x-1

Step-by-step explanation:

The Given function is

f(x) =2*(0.35)* x

→y=0.7* x→Pre image

The line passes through first and third quadrant.

it is equation of straight line passing through origin and slope =0.7.

When this line is reflected over y axis , the equation of new line will be

→y= - 0.7 x⇒image

Slope of image will be = -0.7

The Image passes through Second and fourth Quadrant.

The correct expression is 6x + 50 = 4x + 100

A sentence with variable and numbers connected by one or more operations is called an expression.

Given that, John has $50 and his sister has $100. John is saving $6 per week and his sister is saving $4 per week.

Amount John have = 6x+50

Amount his sister have = 4x+100

Therefore, establishing the equation, the equations will be equal, since the amount both have is equal, therefore, for equating the expression will find the value x which is the number of week.

6x + 50 = 4x + 100

6x-4x = 100-50

2x = 50

x = 50/2

x = 25

Therefore, they will have equal amounts in 25 weeks.

Hence, the equation for them having the same amount is 6x + 50 = 4x + 100.

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Answer:

Error: +3x should be -3x

x should equal 3

Step-by-step explanation:

In this problem, you have to pay attention how values are transferred from one side to the other. This includes paying attention t the signs.

In 3x + 4 = 8x - 11, you want to try an keep all the values positive

      3x   +   4   =   8x  -   11

    - 3x                - 3x

                  4   =   5x  -   11

                 +11               +11      <--This part of the equation was correct.

                  15  =  5x

                  /5       /5   <--This part of the equation should result in dividing by 5

                  3   =  x

Hope this helps!

125 cubes with an edge length of 1/5 inch are needed to build a cube with an edge length of 1 inch.

A cube is a 3-dimensional solid shape with six square faces that are all congruent, and with all edges of equal length.

The volume of a cube is calculated by cubing the length of one of its edges.

To find the number of cubes with an edge length of 1/5 inch that are needed to build a cube with an edge length of 1 inch, we need to calculate the ratio of the volumes of the two cubes.

The volume of the larger cube with an edge length of 1 inch is:

V_large = (1 inch)^3 = 1 cubic inch

The volume of the smaller cube with an edge length of 1/5 inch is:

V_small = (1/5 inch)^3 = 1/125 cubic inches

To find the number of small cubes, we need to divide the volume of the larger cube by the volume of the smaller cube:

Number of small cubes = V_large / V_small = 1 cubic inch / (1/125 cubic inches) = 125

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Answer:

665tggy66yh345666ygvv

The width of the rectangle is 9 meter.

Now, According to the question:

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.

Now, Solving the problem:

Perimeter of rectangle is 50 meter sq.

Length of the rectangle(L) is 16 meter.

We have to find the width (W) of the rectangle.

We know that,

Perimeter of rectangle is = 2 (L + W)

50 = 2(16 + W)

50 = 32 + 2W

2W = 50 - 32

2W = 18

W = 18/2

W = 9

Hence, The width of the rectangle is 9 meter.

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Answer:

\(-5\leq x\leq 3\)

Step-by-step explanation:

The reason is that if you count each line on the graph you see that it starts at -5 and ends at 3.

(Hint: each line on the graph is incrementing by 1)

Hope this helps! :)

Please mark as brainiest if this worked or ask me a question if you do not understand :)

The unit vector in the same direction will be equal to  (6 i/5.1 - 3 j/5.1).

A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity.

A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.

As per the given data in the question,

The unit vector is calculated as:

\(\vec u_a=\frac{\vec a}{||\vec a||}\)

\(\vec a= x \vec i+y \vec j\)

Now, calculate the magnitude of the vector,

\(\vec a\) = √(x² + y²)

\(|\vec a|\) = √6² - 3²

= √36 - 9

= 5.1

So, the unit vector will be,

\(\vec u_a\) = (6 i - 3 j)/5.1

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Answer:

The answer would be c

Step-by-step explanation:

i choosed c because u have da negative sign in front of 4 and 2 and positive numbers with 1 and 2

Answer:

b

Step-by-step explanation:

I think this means to find the mid-point(?) of the line which by doing that you take both x-values and you add them and then divide by two, and then you take both y-values and add them and then divide by two. So you have: (1+-4)=-3, (-3/2)=-1.5

-1.5=x

(2+-2)=0, (0/2)=0

0=y

(-1.5, 0)

Answer: The answer is 20

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(Equation:\)

\(\rm{3^2 + 1\times 2}\)

\(Simplifying:\)

\(\rm{3^2 + 1\times 2}\)

\(\rm{= 3\times 3+ 1\times 2}\)

\(\rm{= 9 + 1\times2}\)

\(\rm{= 9 + 2}\)

\(\rm{= 11}\)

\(Therefore, your\ answer\ should\ be:\)

\(\huge\boxed{\frak{11}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The third one

This graph is the only one that shows the correct slops with the correct y intercepts (-3 and 3)

use desmos it help lot                                                                    

Answer:2

Step-by-step explanation:

The median of the probability distribution given in the table is 1.

Given that X, the value of a spin and the corresponding probability distribution.

X     :   0     1     2     5     10

P(X) :  0.4  0.2  0.2  0.1  0.1

CF   : 0.4   0.6  0.8  0.9  1

So the sum of the cumulative frequency = 1

We have to find the value where the half of the cumulative frequency lies in.

1/2 = 0.5

0.5 lies in between 0.4 and 0.6.

The value of the spin that corresponds to 0.6 is 1.

So the median of the distribution is 1.

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hola quien habla español bueno ya no Adios :)

Answer:

C.(B and D

Step-by-step explanation:

A professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6.

First, let's define some variables to represent the probabilities of making a hole for a professional golfer and an amateur golfer:

Let p be the probability that a professional golfer makes a hole with the new club.

Let q be the probability that an amateur golfer makes a hole with the new club.

According to the company's claims, we know that:

p = 1.2q (since the professional golfer makes a hole 120% of the time, which is 1.2 times the probability of the amateur golfer making a hole)

Next, we need to determine the probability of each golfer making a hole during one round of golf, which consists of 18 holes. Let's assume that each hole is independent of the others, meaning that the outcome of one hole does not affect the outcome of another. In that case, the probability of making at least one hole in a round can be calculated using the complement rule:

The probability that a professional golfer makes at least one hole in a round is 1 minus the probability that the golfer misses every hole: \(1 - (1-p)^{18} .\)

The probability that an amateur golfer makes at least one hole in a round is\(1 - (1-q)^{18} .\)

Now, let's use these probabilities to calculate the expected number of holes each golfer will make in 5 rounds of golf:

The expected number of holes made by a professional golfer in 5 rounds is 5 times the expected number of holes made in one round, which is \((1 - (1-p)^{18} )\times18.\)

The expected number of holes made by an amateur golfer in 5 rounds is 5 times the expected number of holes made in one round, which is \((1 - (1-q)^{18} )\times18.\)

We can simplify these expressions using the relationship between p and q:

The expected number of holes made by a professional golfer in 5 rounds is \(518(1 - (1-1.2q)^{18} ).\)

The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-q)^{18} ).\)

We can now evaluate these expressions using the values of p and q:

\(p = 1.2q, so q = p/1.2\)

Substituting this into the expressions above, we get:

The expected number of holes made by a professional golfer in 5 rounds is\(518(1 - (1-1.2(p/1.2))^{18} ) = 518(1 - (1-p)^{18} ).\)

The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-p/1.2)^{18} ).\)

Finally, we can evaluate these expressions using the given probabilities:

The expected number of holes made by a professional golfer in 5 rounds is\(518(1 - (1-1.2q)^{18} ) = 518(1 - (1-1.2(0.1))^{18} ) = 40.7.\)

The expected number of holes made by an amateur golfer in 5 rounds is \(518(1 - (1-q)^{18} ) = 518(1 - (1-0.1/1.2)^{18} ) = 1.6.\)

So according to these calculations, we would expect a professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6

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Answer:

Step-by-step explanation:

domain = x

range = y

when the domain is -1

y = 2(-1) - 3

y = -2 - 3

y = -5

range is -5

When the domain is 0

y = 2(0) - 3

y = 0 - 3

y = -3

range is -3

when the domain is 5

y = 2(5) - 3

y = 10 - 3

y = 7

range is 7

The range is { -5, -3, 7 }

Answer:

12.7

Step-by-step explanation:

The Correct answer is 27

Odd number are the numbers that are not multiple 2 and cannot be divided into two parts equally.

For examples: 3 , 5 , 7, 9,11 . . . . .

According to the question,

If the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3.

Sequence of the number is 1, 5, 4, 7, 3, 7, 9, 2

where  1 , 5 , 7 , 7 ,9 are odd numbers

The third odd number is 7 which is greater than 6

according to question we have to multiple 9 by 3

= 9 × 3

= 27

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Answer:

No

Step-by-step explanation:

Equivalent ratios are created by multiplying/ dividing the parts by the same value.

3 : 4 ( multiply both parts by 4 )

= 12 : 16 not 9 : 16

Answer:

b

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

One foot would have 3 1/3 pieces (because 3 * 1/3 = 1) so that means 5 would have 15 pieces (because 3 * 5 = 15)

The probability model for this situation is a discrete probability model because we are dealing with a finite number of markers in the box.

1. The probability model is based on the three different colors of markers in the box: red, blue, and yellow.
2. There are a total of 16 markers in the box, with 5 red markers, 6 blue markers, and 5 yellow markers.
3. The probability of selecting a marker of a certain color can be calculated by dividing the number of markers of that color by the total number of markers in the box.
4. For example, the probability of selecting a red marker is 5/16, the probability of selecting a blue marker is 6/16, and the probability of selecting a yellow marker is 5/16.
5. Since the probability model is based on a finite number of markers, it is a discrete probability model.
6. The probability of selecting any one marker is independent of the probability of selecting any other marker, assuming that the markers are well-mixed and that the selection process is random.

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Answer:

128 in^2

Step-by-step explanation:

L * W

16 * 8 = 128 in^2

An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.

In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.

For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p = 10.

Ha: p < 10.

In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.

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Answer:  \(5n + 10d \ge 100\)

===============================================

Explanation:

5n represents the value of all the nickels, where n is the number of nickels. Let's say he had 8 nickels. This would mean 5n = 5*8 = 40 cents is from just the nickels.

The 10d represents the value of all the dimes. For example, if he had d = 2 dimes, then he has 20 cents from those dimes because 10d = 10*2 = 20.

Combining the two expressions leads to 5n+10d as the total value of both types of coins. This total value is in cents. We want this value to be 100 cents or more. This is why we set 5n+10d to be greater than or equal to 100. That's how we arrive to \(5n+10d \ge 100\)

Optionally we can divide each term by 5 to get \(n + 2d \ge 20\) ,but I'll put the other inequality as the answer because it seems more descriptive in my opinion. Keeping 5n shows each nickel is 5 cents, and 10d shows each dime is 10 cents. Something like n+2d loses a bit of its descriptive nature.

The inequality for the given situation is 5n+10d≥100.

Given that, Matthew has n nickels and d dimes. He has a minimum of $1 worth of coins altogether.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

We know that,

A nickel is worth 5 cents. A dime is worth 10 cents. A dollar is worth 100 cents.

Now, the inequality 5n+10d≥100

Therefore, the inequality for the given situation is 5n+10d≥100.

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Answer: A

Step-by-step explanation:

Unit means per 1, there are 4 units. 2.12 divided by 4 is 0.53

Answer:

y=100t+1200, where t is years since 2013 and

Step-by-step explanation:

We only have two points from which to form an equation.  Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0).  Let's make the x axis the year and y the student population.

Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013.  "t is the number of years after 2013."  (0,1200) becomes is the data point for 2013.  The school's population will be the y-axis.

(0,1200)   [primary school had 1200 students enrolled in 2013], and

(3,1500)   [1500 students in 2016]

---

First calculate m, the slope.  Slope is the Rise/Run between the two points (the change in y over the change in x)

Going from (2013,1200) to (2016,1500) we find that:

  Rise  (in y) = (1500 - 1200) = 300 students

  Run  (on x) = (2016 - 2013) =     3 years

The Rise/Run, or slope, m, is 300/3 or 100:  m = 100

Lets put that into our equation format:

y = 100x + b

X will be the time, in years.  The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:

y = 100t +b, where t is years after 2013.

(The 100 tells us that the student population increases by 100 per year)

We now need b, the y-intercept.  One can either graph this and look for the value of y when x=0, of simply input either of the data points.  This looks easy enough to input a point and solve for b:

Remember that t is the (year - 2013)

y = 100t +b   Solve for (2013,1200)

 t = 2013 - 2013 = 0

1200 = 100*(0) + b

b = 1200

Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).

The equation becomes y = 100t + 1200

See the attached graph.