Factor the binomial using its GCF: 10x-15x^4

f(x) = 2^x

f(5) = 2^5

f(5) = 32

Answer:

1/20

Step-by-step explanation:

To calculate how many potential combinations of genre and duration, we multiply the number of options in each category.

5 genres * 4 durations = 20 combinations

So for each film placed, there is a 1 in 20 chance that it will be a specific combination.

The probability that the next movie added is an action movie that is longer than 120 minutes is 1/20.

To calculate the probability that the next movie added is an action movie that is longer than 120 minutes, we need to make some assumptions, as the exact numbers of each category are not provided.

If we assume that movies are equally distributed among the different genres and durations, and there are 5 genres and 3 durations, we can conduct a probability calculation.

To calculate the probability that the next movie is an action movie longer than 120 minutes:

Calculate the probability of choosing an action movie, with 5 genres,

the probability is 1/5.

Calculate the probability of the movie being longer than 120 minutes, with 4 durations,

the probability is 1/4.

Multiply these two probabilities to get the combined probability

1/5 × 1/4 = 1/20 or 5%

Answer:

The scores for period 1 had the highest median.

Step-by-step explanation:

The median is the middle score.

Thus if the class had the highest median, it would mean that more scores are higher, that there are more high scores, than the other classes.

Answer:

[tex]\large\boxed{-\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=0\ \text{and}\ x=4.\\(look\ at\ the\ picture)\\\\f(0)=5,\ f(4)=0\\\\\text{Substitute:}\\\\\dfrac{f(4)-f(0)}{4-0}=\dfrac{0-5}{4}=-\dfrac{5}{4}[/tex]

To find the average rate of change of the function from x = 0 to x = 4, subtract the y-coordinate at x = 0 from the y-coordinate at x = 4, then divide by 4. The exact answer depends on the specific values provided by the graph of the function.

The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a). For the given problem, we are asked to find the average rate of change from x = 0 to x = 4. However, the specific values of f(0) and f(4) on the graph are not provided. Generally, to find the average rate of change in this case, you will need to subtract the y-coordinate at x = 0 (f(0)) from the y-coordinate at x =   4 (f(4)), then divide by the difference in x-values (4 - 0). Without the exact values from the graph, a specific numerical answer can't be provided.

https://brainly.com/question/33629701

#SPJ2

Answer:

$ 31050

Step-by-step explanation:

Step 1 : Write the formula for calculating simple interest.

Simple Interest = P x R x T

                                100

P: Principal Amount-The loan taken (30,000)

R: Interest rate at which the loan is give (6)

T: Time period of the loan in years-there are 12 months in 1 year. There are 7 months from May till June (7/12)

Step 2: Substitute values in the formula

Simple Interest = 30,000 x 6 x 7/12

                                       100

Simple Interest = $1050

Step 3: Calculate the amount due at maturity

At the maturity or the end of the time period given, the original or principal amount of the loan has to be repaid along with the simple interest.

Amount at maturity = Principal Amount + Simple Interet

Amount at maturity = 30,000 + 1050

Amount at maturity = $31050

!!

Answer:

a line that might best estimate the data and be used for predicting values.

Choice B is correct

Step-by-step explanation:

A line of fit might be defined as;

a line that might best estimate the data and be used for predicting values.

This line connects most of the data points thus minimizing the squared residuals of the regression.

I hope this helps...

Answer:

A line of fit might be defined as:

b)  a line that might best estimate the data and be used for predicting values.

Step-by-step explanation:

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

Line of best fit is actually a good approximation of data and is used to predict values on the graph.

Answer:

[tex]8(x+10)[/tex]

Step-by-step explanation:

we have the expression

[tex](8x+80)[/tex]

we know that

[tex](8x+80)=(8x+8(10))[/tex]

Factor the number 8

[tex](8x+8(10))=8(x+10)[/tex]

therefore

The expression factored is [tex]8(x+10)[/tex]

The factorization of the given expression is given as:

                                 [tex]8(x+10)[/tex]

To factor a algebraic equation means to represent it as the multiplication of the simple expressions.

( i.e. if the expression has a common multiple in each of the terms then we take  it out and represent the rest of the expression in brackets.

Also, we can express a algebraic equation by the multiplication of the factors of the expression )

We are given a expression as:

[tex]8x+80[/tex] which represents  the total amount in the account after 8 months.

and x represents the amount saved each month.

Since both the terms i.e. 8x and 80 have a common multiple as: 8

Hence, we take it out of the expression and write the resulting expression as follows:

[tex]8x+80=8(x+10)[/tex]

Step-by-step explanation:

Volume of a pyramid is:

V = ⅓ AH

where A is the area of the base and H is the height of the pyramid.

The base is a triangle.  Area of a triangle is:

A = ½ bh

where b is the base length and h is the height.

A = ½ (4)(1.5)

A = 3

V = ⅓ (3)(9)

V = 9

The volume is 9 in³.

The volume of the triangular pyramid with a triangular base is 9 cubic inches.

The volume of the triangular pyramid with a height h and base area B is

Volume = 1/3 × B × h cubic units

The area of a triangle is 1/2 × b × h sq. units

where b - base and h - height the triangle.

It is given that a triangular pyramid has a triangular base with

base length b = 4 inches

height of the triangle h = 1.5 inches and

height of the pyramid = 9 inches

So, the volume of the pyramid = 1/3 × B × h

Where base area B = 1/2 × b × h

⇒ B = 1/2 × 4 × 1.5

       = 3.0 sq. inches

And the volume = 1/3 × 3.0 × 9

                             = 9 cubic inches.

Therefore, the volume of the given triangular pyramid is 9 cubic inches.

Learn more about the volume of the triangular pyramid here:

https://brainly.com/question/16377998

#SPJ2

Answer:

Step-by-step explanation:

A double-blind study is a study where neither participants nor experimenters know which subjects are receiving the treatment.

This method is really useful to minimize possible biased conclusions about the experiment.

Therefore, the right answer is C, the situation described refers to a double-blind study.

A double-blind study is an experimental design in which both the subjects and experimenters are unaware of the treatment or control group assignments, thereby reducing bias and increasing the reliability of the study's findings.Therefore, the correct answer is option C.

An experiment where neither the subjects nor the experimenters know which subjects are in the treatment or control group is best described as a double-blind study.

This type of research design is crucial to prevent biases from affecting the outcome of clinical trials or other medical studies. In a double-blind study, both the participants and researchers are 'blind' to the assignments, thereby reducing the risk of placebo effects or experimenter bias influencing the results.

Experiments in the field of medicine often use this design to test the efficacy of new drugs, treatments, or interventions in the most unbiased way possible.

A control group that receives a placebo is essential in these experiments to compare the actual efficacy of the experimental treatment against no treatment or a standard treatment.

Answer:

Limitation

Step-by-step explanation:

Answer:

126.

Step-by-step explanation:

Using long division:

        1 2 6

       ---------

36 ) 4536

       36

       ---

         93

          72

          ---

          216

          216

           ----

Answer:

126

Step-by-step explanation:

you divide 4536 and 36 and you get 126 as your quotient

Answer:

m= -2/3 or -0.6

Step-by-step explanation:

6m-1= -5+1

6m= -4/-6

m= - 2/3 or -0.6  

Answer:

m = -2/3

Step-by-step explanation:

-5 = 6m-1

Rewrite

6m - 1 = -5

Add 1 to both sides

6m = -4

Divide both sides by 6

m = -4/6

Simplifying

m = -2/3

Answer:

1) If 3 is an odd number, then 3 times 3 is an even number.

False because multiplying odd number by an odd number also gives an odd number.

2) If 6 is less than 7, then 4 is greater than 7.

False because 4 is smaller than 6. As 6 is smaller than 7 then 4 must also be smaller.

3) Six is divisible by 3, and 10 is a multiple of 2.

True. 6/3 = 2 and 2 x 5 = 10. Both the conditions are true so it is also true.

4) The average of the data is greater than the largest value in the data, or it’s less than the largest value in the data.

True.

We have two conditions in this statement and an 'or' between them. One of the conditions is true that is "average is less than the largest value in the data". So the statement as a whole is true.

5) The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.

True.

6) If an equilateral triangle has equal angles, then all its angles will measure 45°.

False.

A triangle has 3 angles whose sum = 180 degrees.

For equilateral triangle each angle will measure 180/3= 60 degrees.

Answer:  2 following statements are true

The first true statement:

Six is divisible by 3, and 10 is a multiple of 2.

We know this because 6 is divisible by 3, and again proven by when we  divide 10 by 5 we get 2, so 10 is a multiple of 2.

The second true statement:

The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.

Step-by-step explanation:

Step-by-step explanation:

7(x + 6) = 42

distributive property:  a(b + c) = ab + ac

(7)(x) + (7)(6) = 42

7x + 42 = 42

subtraction property of equality  (subtract 42 from both sides)

7x + 42 - 42 = 42 - 42

7x = 0

division property of equality   (divide both sides by 7)

7x : 7 = 0 : 7

x = 0

Answer:

1. Distributive property: a(b + c) = a.b + a.c

2. Property of subtraction of equality

3. Property of division of equality

Step-by-step explanation:

The given equation is 7x + 42 = 42

7(x+6)=42    [Distributive property: a(b + c) = a.b + a.c]

7x+42=42   [Property of subtraction of equality]

Subtract 42 from both sides.

7x + 42 - 42 = 42 - 42

7x=0  

Property of division of equality

Divide both sides by 7.

x=0

Answer:

43.98 cm

Step-by-step explanation:

Circumference is π x diameter

Diameter is 2 x radius

276.32/π = 87.955 (3dp)

87.955/2 = 43.978 (3dp)

43.98cm = radius

Answer:

66 cm

Step-by-step explanation:

Let's define the circumference first.

It is the boundary of any curved geometric figure specially circle.

We are given the diameter of the circle in the diagram

The diameter is:

d = 21 cm

to find the circumference, we have to find the radius of the circle first.

As radius is half of diameter

d = r/2

= 21/2

= 10.5 cm

The formula for circumference is:

[tex]C = 2\pi r\\Putting\ the\ values\\C = 2 * \frac{22}{7}*10.5\\ C = \frac{462}{7}\\ C= 66\ cm[/tex]

The circumference is 66 cm ..

Answer:

The circumference of the circle is 66 cm

[tex]\bf 9x^2+2=10x\implies 9x^2-10x+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-10}x\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}~~\checkmark\\ negative&\textit{no solution} \end{cases} \\\\\\ (-10)^2-4(9)(2)\implies 100-72\implies 28[/tex]

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(y2-y1) ^ 2 + (x2-x1) ^ 2}[/tex]

We find the distance AB:

[tex]A: (3,4)\\B: (- 5, -2)[/tex]

[tex]AB = \sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\AB = \sqrt {(- 5-3) ^ 2 + (- 2-4) ^ 2}\\AB = \sqrt {(- 8) ^ 2 + (- 6) ^ 2}\\AB = \sqrt {64 + 36}\\AB = \sqrt {100}\\AB = 10[/tex]

We have the BC distance:

[tex]B: (- 5, -2)\\C: (5, -2)[/tex]

[tex]BC = \sqrt {(5 - (- 5)) ^ 2 + (- 2 - (- 2)) ^ 2}\\BC = \sqrt {(5 + 5) ^ 2 + (- 2 + 2) ^ 2}\\BC = \sqrt {(10) ^ 2 + (0) ^ 2}\\BC = \sqrt {100}\\BC = 10[/tex]

We find the CA distance:

[tex]C: (5, -2)\\A: (3,4)[/tex]

[tex]CA = \sqrt {(3-5) ^ 2 + (4 - (- 2)) ^ 2}CA = \sqrt {(- 2) ^ 2 + (4 + 2) ^ 2}\\CA = \sqrt {4 + 36}\\CA = \sqrt {40}\\CA = \sqrt {4 * 10}\\CA = 2 \sqrt {10}[/tex]

Thus, the perimeter is given by:

[tex]10 + 10 + 2 \sqrt {10} = 20 + 2 \sqrt {10}[/tex]

ANswer:

[tex]20 + 2 \sqrt {10}[/tex]

Answer:

44506

Step-by-step explanation:

458687+5800=51487

51487-6981=44506

Answer:

Step-by-step explanation:

We can find the vertex either by completing the square or taking advantage of the simple formula x = -b / (2a), which provides the x-coordinate of the vertex.

Here a = 2, b = -20 and c = 100.  Then the x-coordinate of the vertex is at

x = -(-20) / (2*2), or x = 5.

Next, evaluate y = 2x^2 - 20x + 100 to find the y-coordinate of the vertex.  It is y(5) = 2(5^2) - 20(5) + 100, or y(5) = 50 - 100 + 100, or 50.  y = 50.

The vertex is at (5, 50).  This states that the stock reaches its minimum value, $50 per share), after 5 months.  From that time on, the stock appreciates (increases) in value.

Answer:

B) symmetric

Step-by-step explanation:

We will find the sample space for rolling two dices first

Here first value in ordered pair represents yellow die and second represents blue die

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

The subtraction gives us:

0 , -1 , -2, -3, -4, -5, 1, 0, -1, -2, -3, -4, 2, 1, 0, -1, -2, -3, 3, 2, 1, 0, -1, -2, 4, 3, 2, 1, 0, -2, 5, 4, 3, 2, 1, 0

So the distribution will be as follows:

X      5       4       3       2        1        0        -1       -2      -3       -4      -5

P(X)  1/36  2/36  3/36 4/36  5/36  6/36  5/36  4/36  3/36  2/36  1/36

By observing the probabilities, we can conclude that the distribution will be symmetric

Hence, Option B is correct ..

Answer:

its B symmetric

Step-by-step explanation:

got it right on ed

Answer:

{0,-8}

Step-by-step explanation:

Factor!

3x(x+8)=0

3x=0  or x+8=0

x=0    or x=-8

Answer:

x=0    x =-8

Step-by-step explanation:

3x^2+24x=0

Factour out a 3x

3x(x+8) =0

Using the zero product property

3x =0   x+8 =0

x=0     x+8-8 =0-8

x=0    x =-8

Answer:

[tex]\large\boxed{y=-(2)^x+3}[/tex]

Step-by-step explanation:

[tex]\text{A function y = a(b)}^x\ \text{has a range:}\\\\y<0\ \text{for}\ a<0\\\\y>0\ \text{for}\ a>0\\\\f(x)+n-\text{shift a graph}\ n\ \text{units up}\\f(x)-n-\text{shift a graph}\ n\ \text{units down}\\f(x+n)-\text{shift a graph}\ n\ \text{units to the left}\\f(x-n)-\text{shift a graph}\ n\ \text{units to the right}\\\\\text{We have the range}\ y<3.\ \text{Therefore}\ a<0\ \text{and}\ n=3.[/tex]

The function with a range of y < 3 among the given options is y=-(2)x +3, because it decreases by 2 for each increase in x, starting from y=3.

The function which has a range of y < 3 is y=-(2)x +3. This is an example of a linear function where the slope is negative and the y-intercept is 3. This means that the y-values (the range) will always be less than 3. This is because the value of y will decrease by 2 for every increase in x, starting from y=3. For the other functions, the range of y-values is not consistently less than 3.

https://brainly.com/question/29145252

#SPJ2

Answer:

80 times 13.58 =1086400

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(-2) = 3*abs(x - 2) + 1

f(-2) = 3*abs(-2-2) + 1

f(-2) = 3* abs(-4) + 1

f(-2) = 3 * 4 + 1

f(-2) = 13

===========

f(1) = 3*abs(1 - 2) + 1

f(1) = 3*abs(-1) + 1

f(1) = 3*1 + 1

f(1) = 4

Answer:  [tex]y=\frac{1}{30}x+1[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

You need to find slope of the line with the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Pick to  points of the given line. You can choose the point (60,3) and the point (30,2).

Then, substituting into the formula:

 [tex]m=\frac{2-3}{30-60}=\frac{1}{30}[/tex]

You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:

[tex]b=1[/tex]

Substituting the slope and the y-intercept found into  [tex]y=mx+b[/tex], you get the equation of this line:

 [tex]y=\frac{1}{30}x+1[/tex]

Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.

Answer:

No, the answer is actually a) 962

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

b=12 , a=6[tex]6 \sqrt{3}[/tex] , c=6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

based on the graph you are showing, you can use  "SOH CAH TOA"

for right triangles, then you use "CAH" for get b:

[tex]Cos(60)=\frac{6}{b}\\b*Cos(60)=6\\b*\frac{1}{2}=6\\ b=6*2\\b=12\\\\[/tex]

you do the same for a, but in this case you use sin, not cos:

[tex]sin(60)=\frac{a}{b} \\b*sin(60)=a\\\\12*\sqrt{3}/2=a\\ 6\sqrt{3}=a\\[/tex]

and with your b value, you can get c, but now you use Cos with the 45 angle:

[tex]b*cos(45)=c\\12*\sqrt{2}/2=c\\ 6\sqrt{2}=c[/tex]

remember SOH CAH TOA means, Sin(x)=opposite/Hypotenuse, Cos(x)=adjacent/hypotenuse, and tan(x)=Opposite/adjacent.

Answer:

(- 1, 0), (9, 0)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (4, 75), so

y = a(x - 4)² + 75

To find a substitute (0, 27) into the equation

27 = a(- 4)² + 75 , that is

27 = 16a + 75 ( subtract 75 from both sides )

16a = - 48 ( divide both sides by 16 )

a = - 3, thus

y = - 3(x - 4)² + 75 ← equation in vertex form

To obtain the x- intercepts let y = 0

- 3(x - 4)² + 75 = 0 ( subtract 75 from both sides )

- 3(x - 4)² = - 75 ( divide both sides by - 3 )

(x - 4)² = 25 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{25}[/tex] = ± 5

Add 4 to both sides

x = 4 ± 5, hence

x = 4 - 5 = - 1 or x = 4 + 5 = 9

Substitute these values into the equation for corresponding values of y

x = - 1 : y = - 3(- 5)² + 75 = - 75 + 75 = 0 → (- 1, 0)

x = 9 : y = - 3(5)² + 75 = = 75 + 75 = 0 → (9, 0)

The x- intercepts are (- 1, 0), (9, 0)

Answer:

The x intercepts are (-1, 0) and (9, 0).

Step-by-step explanation:

We can write the equation in vertex form:

y = a(x - b)^2 + c

Here b = 4 and c = 75 so we have

y = a(x - 4)^2 + 75 where a is a constant to be found.

The y-intercept is (0,27) so

27 = a(0 - 4)^2 + 75

16a = 27 - 75

a = -48/16 = -3

So to find the x-intercepts we solve the equation:

-3(x - 4)^2 + 75 = 0

(x - 4)^2 = -75 / -3 = 25

x - 4 = +/- √25

x =   5+ 4 = 9 , -5 + 4 = -1.