Use the quadratic formula to find both solutions to the quadratic equation
given below.
4x² + 5x+1=0
A. X=-
-3-√√-7
8
□ B. x=-3-√7
8
C. x=
E. x=
-3+√√-7
8
D. x=-¹
+3+√7
8
F. x= -1

The value of the composite function [f(g(f(f(f(g(27))))))], when f(x) = log₃(x) and g(x) = 3ˣ is 1

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

Let f(x) = log base 3 of x and g(x) = 3^x.

Express the equations properly

So, we have the following representations

f(x) = log₃(x) and g(x) = 3ˣ

Calculating the composite function [f(g(f(f(f(g(27))))))], we have

[f(g(f(f(f(g(27))))))] = [f(g(f(f(f(3²⁷))))))]

Next, we have:

[f(g(f(f(f(g(27))))))] = [f(g(f(f(log₃(3²⁷))))))]

This gives

[f(g(f(f(f(g(27))))))] = [f(g(f(f(27))))))]

For f(27), we have

[f(g(f(f(f(g(27))))))] = [f(g(f(3)))))]

For f(3), we have

[f(g(f(f(f(g(27))))))] = [f(g(1))))]

Calculating g(1), we have

[f(g(f(f(f(g(27))))))] = f(3)

Lastly, we have

[f(g(f(f(f(g(27))))))] = log₃(3)

Evaluate

[f(g(f(f(f(g(27))))))] = 1

Hence, the solution is 1

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The answer is 90 times to expect picking an apple or banana.

If the fruit is chosen 300 times, then it would be a 1:3 ratio of apple or banana to the other fruits. This means that 100 times out of the 300 times, you would expect to pick an apple or banana.

Predicting the outcome using the experiment results because 300 times is a sizable number.

8+4 is either an apple or a banana in 40 times.

Therefore, the solution would be x in 300 times.

[tex]x = \frac{300}{40}[/tex] x12

x = 90

Therefore, the probability of picking an apple or banana is 90 times.

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Answer: 47

Step-by-step explanation:

4.72 / .1= 47

47

Answer:

01?

Step-by-step explanation:

I didn't see a picture so maybe just one

The initial saving of the Winston was $55952.48

Compound interest is when you receive interest on both your interest income and your savings.

According to the question given,

Let the initial savings amount be P

We know Compound interest =

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

Where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest is applied per year

t = number of time periods elapsed

Given,

A = $65000

t = 3 years

r = 5% = 0.05

n = 2 *12 = 24

So

65000 = P(1 + (0.05/24))^72

P =  $55952.48

Therefore the initial savings was  $55952.48

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Answer:

(1/3) (44.5)π cm3.

Step-by-step explanation:

The volume of the two scoops of ice cream combined with the ice cream inside the cone can be calculated as follows:

Volume of cone = (1/3) π (3/2)2h = (1/3) π (4.5)8 = (1/3) (35.5)π

Volume of scoop = (1/6) π d3 = (1/6) (3)π

Total volume = (1/3) (35.5)π + 2(1/6) (3)π = (1/3) (44.5)π cm3.

The graph of the inequality system is attached. The coordinate of a point in the solution set is (-1, 2).

In order to graph the system of inequalities graphically, consider the equation of each inequality.

y = x – 1

y = x - 4

Choosing a few values of x, plot the graph for each equation. Shade the area bounded by the line based on the inequality. If the inequality is less than, shade the area right to the line and if the inequality is greater than, shade the area left to the line. Hence, y < x – 1 is represented by red area and y > x – 4 is represented by blue area. The overlapping shaded area contains the coordinates that represent the solution of the inequality system. The coordinate of a point in the solution set is (-1, 2).

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The area of the isosceles triangle having two sides 12.5 cm and another 20cm is 75cm².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know that an isosceles triangle has two sides having the same length and the third one is different.

We also know that the area of an isosceles triangle is (1/2)×b×√(a² - b²/4),

where b is the value of the third side and a is the value of two similar sides.

Therefore, The area of the isosceles triangle having side lengths of two similar sides is 12.5 cm and the third side is 20 cm is,

= (1/2)×20×√((12.5)²- (20)²/4) cm²,

= 10×√(156.25 - 100) cm².

= 10×√(56.25) cm².

= 10×7.5 cm².

= 75 cm².

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We have inequality. So, we have to take a test point (0,0) and as the statement is true therefore Graph will shade towards the test point (0,0).

2(0)+3(0) ≤ 30 => 0≤ 30

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.

First we make inequality according to question.

In a family number of children 3

Charge for 1 child = $y per hour

Charge for 3 children = 3y

Charge for 1 Adult = $x per hour

Charge for 2 adults = 2x

If the family does not want to spend more than $30 an hour at health club.

2x+3y≤30

Where, x and y should be greater than 0.

x≥0 and y ≥0

Now we make the graph of this inequality.

First we take equality of equation and then find x and y table.

2x+3y=30

x        y

0        10

6        6

15      0

Here we have inequality. So, we have to take a test point (0,0)

2(0)+3(0) ≤ 30 => 0≤ 30

This statement is true. So, Graph will shade towards the test point (0,0)

Please see the attachment for graph:

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The probability that at least 12 buy their lunch =  0.887

Given that 73% of students buy their lunch.

⇒ p = 0.73

And q = 1-p

q =  0.27

sample size (the number of student selected) n = 19

We need to calculate the probability that at least 12 buy their lunch.

i.e., P(x ≥ 12)

We use binomial distribution formula, P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

P(X ≥ 12)

= P(X= 12) + P(X= 13) + P(X= 14) + P(X= 15) + P(X= 16) + P(X= 17) + P(X= 18) + P(X= 19) [tex]=~ ^{19}C_{12}(0.73)^{12}(0.27)^{7} + ^{19}C_{13}(0.73)^{13}(0.27)^{6}+ ^{19}C_{14}(0.73)^{14}(0.27)^{5} + ^{19}C_{15}(0.73)^{15}(0.27)^{4} + ^{19}C_{16}(0.73)^{16}(0.27)^{3} + ^{19}C_{12}(0.73)^{17}(0.27)^{2}+ ^{19}C_{12}(0.73)^{18}(0.27)^{1}+ ^{19}C_{12}(0.73)^{19}(0.27)^{0}[/tex]

= 0.1207 + 0.1757 + 0.2036 + 0.1835 + 0.1240 + 0.0592 + 0.0178 + 0.0025

= 0.887

The required proability is  0.887

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In the transaction, he will receive $374 more in sales of buttered popcorn than caramel popcorn.

An operation, often known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

Given, Derek owns a snack shop where he sells tins of buttered and caramel popcorn. The table shows the number of each type of popcorn sold over w weeks.

Popcorn Sales     Popcorn Cost ($)      Number Sold Over w Weeks

Buttered                   11                                        8w+9

Caramel                    11                                        6w−1

After 12 weeks of total buttered popcorn, he will make the sale

= $11 * (8*12 + 9)

= 11 * (96 + 9)

= $1,155

After 12 weeks of total caramel popcorn, he will make the sale

= $11 * (6*12 - 1)

= $11* (71)

=$781

In the sale, he will get more sales in buttered popcorn than sales in caramel popcorn by 1,155 - 781 = $374

Therefore, He will make $374 more in sales of buttered popcorn than caramel popcorn during the sale.

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The amount of mold after n days is 3 × (1.5)ⁿ⁻¹.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

At first, mold was 3 cm², then 4.5 cm², and it was increasing each day by 50%.

a₁ = 3

a₂ = 4.5

a₃ = 4.5 + (4.5 × 50%) = 6.75

.............

Here the common ratio, r = a₂/a₁ = a₃/a₂ = ..... = 1.5

n th term of a GP = a rⁿ⁻¹, where a is the first term and r is the common ratio.

Area of mold after n days = 3 × (1.5)ⁿ⁻¹

Hence the mold at any time can be calculated by the formula 3 × (1.5)ⁿ⁻¹.

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Answer: 60

Step-by-step explanation:

If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60

The final statement is: y=16

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The exponential function y=4×2ˣ

Therefore for x=2 we get

y=4×2²

y=16

Hence, The value of y at x equal to 2 is 16

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Trejo is correct, because if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

A relation between a set of inputs having one output each is called a function.

Given that;

Trejo says that if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

But, Hilary disagrees, She says you know the intercepts but that is all you know for sure.

Now,

We know that;

In a function, If if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

Thus, The Trejo is correct.

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The volume of the cone is 50π cubic units .

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.

A cone has a circular base.

A cone has no edges, one face, and one vertex.

The length of the line segment from a cone's apex to any point around the circle of the cone's base is known as the slant height of the cone.

A right circular cone is a cone with its apex perpendicular to the base of the cone and directly above it.

An oblique cone is one that doesn't have its apex precisely over the base's circle.

Radius of the cone = 5

Height of the cone is 6

Volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] = [tex]\frac{1}{3}\pi *5^{2}* 6 = 50\pi[/tex] cubic units.

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To find the nature of the roots of a given quadratic equation, use the quadratic formula, which is [tex]x= \frac{(-b±\sqrt{b^2-4ac} )}{2a}[/tex].

Substitute the values of a, b, and c from the given equation into the formula and solve for x. The nature of the roots can then be determined by examining the sign of the discriminant, b² - 4ac.

If the discriminant is positive, the quadratic equation will have two real roots; if the discriminant is zero, the quadratic equation will have one real root; and if the discriminant is negative, the quadratic equation will have two complex roots.

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The odds against exactly 5 cars passing over the bridge in that time are given as follows:

5.25:1.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.

The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:

0.16 : (1 - 0.16) = 0.16 : 0.84.

To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:

0:84 : 0.16.

As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:

5.25 : 1.

Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.

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Solving for W in the equation 4 = (2 + W) / 2 gives W = 6

Using the equation 4 = (2 + W) / 2, W is solved by making it the subject of the formula and this is means placing W alone at the left hand side of the equation'

This is achieved by the following procedure

clearing the fraction

4 = (2 + W) / 2,

8 = 2 + W

rearranging the equation

W + 2 = 8

subtracting 2 from both sides of the equation

W + 2 - 2 = 8 - 2

since 2 - 2 = 0 we have

W = 6

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Answer:

C. 50%

Step-by-step explanation:

Since 40 is half of 80, and 50% means half, and 42 out of 80 is close to half, then 42 out of 80 is close to 50%.

Answer: C. 50%

Answer:

b25

Step-by-step explanation:

beacuse that is a rain and reasonable he percentage

Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.

A straight line is made up of many points connected at each end. Any straight line's slope, m, is determined by the formula. The slope-intercept formulation of a linear equation is y = mx + b. The equation's variables are X and Y. The slope of the line (m) and the value of y when x is 0 are represented by the values m and b, respectively.

[tex]m = \frac{y2-y1}{x2 - x1}[/tex]

given

the graph is,(0,8) and (9,2)

The slope of the line is,

m = 1/2

Because it crosses the y-axis at the point where the intercept C is equal to 8,

The equation of the line will be :

⇒ y = mx + c

⇒ y = (1/2)x + (8)

⇒ y = x/2 + 8

Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.

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Answer: Ball A, B, C, F, E, D

Step-by-step explanation:

An object has the greatest amount of Gravitational Potential Energy when it is furthest from the ground.

This means that Ball A has the most gravitational potential energy. This is followed by Ball B and Ball C. Then, Ball F is farthest from the ground, followed by Ball E. Ball D has the least gravitational potential energy.

So, the order is as follows: Ball A, B, C, F, E, D

There are seven zeroes  located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).

Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.

Let P=1/(2^5.5^8)

Multiplying and dividing the numerator by 2^3

P= 2^3/(2^5.5^8.2^3)

P=8/(2^8.5^8)

P=8/10^8

P=0.00000008

The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.

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The length UY of the triangle is 90 units

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

This means that

UY = 2 * VX

Substitute the known values in the above equation, so, we have the following representation

13p - 1 = 2 * (20p - 95)

Evaluate the products

13p - 1 = 40p - 190

So, we have

40p - 13p = 190 - 1

So, we have

27p = 189

Divide by 27

p = 7

Substitute p = 7 in UY = 13p - 1

UY = 13 * 7 - 1

So, we have

UY = 90

Hence, the length is 90 units

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Answer:

Any value

Step-by-step explanation:

X is a variable, meaning it can be any number, and they are just using our variable, x, as a little mask to hide the exact value. In math, we will usually need to find x by solving different equations.

Examples:

x + 4 = 7

Know, x in this case is 3 because we just know 3 + 4 = 7, but x can be any value, and sometimes it gets more complicated than this. For example, we can have something like:

2x + 8 = 16

In this case, we need to have multiple steps to solve for x. First, we minus 8 from both sides:

2x = 8

Then we divide by 2:

x = 4

So, we know x = 4. In conclusion, x is a variable that is hiding a value, and you will need to either solve or substitute x. Meaning x can be any value.

Hope this Helped!

So Amy needs to use 2 pounds of Colombia beans and 32 pounds of Kenya beans to create her blend.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

We are aware that an inverse variation or indirect variation occurs when two values are coupled in a way that a rise in one generates a corresponding reduction in the other, and vice versa.

Let x be the number of pounds of Kenya beans and y be the number of pounds of Colombia beans. We know that:

x + y = 30 (since the blend is 30 pounds)

We also know that the blend sells for $8.50 per pound, so the total cost of the blend is:

8.50(x + y) = 8.50(30) = $255

We know that the cost of the Kenya beans is $9.00 per pound and the cost of the Colombia beans is $7.50 per pound, so the total cost of the Kenya beans is:

9.00x and the total cost of the Colombia beans is 7.50y

We can set up the following equation:

9x + 7.5y = 255

We have 2 equations and 2 variables, we can solve this system of equation by different methods, one of them is substitution:

x + y = 30

9x + 7.5y = 255

We can substitute the first equation into the second equation

9(x + y) + 7.5y = 255

9(30) + 7.5y = 255

270 + 7.5y = 255

7.5y = -15

y = -2

So Amy needs to use 2 pounds of Colombia beans. We can substitute that value into the first equation to find the amount of Kenya beans:

x + (-2) = 30

x = 32

So Amy needs to use 32 pounds of Kenya beans.

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Answer:

120x - 96y + 32

Step-by-step explanation:

12 (10x + 3 -8y)

We use the distributive property to solve

120x - 96y + 32

One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is

120x - 96y + 32

the probability that the card is either a queen or a diamond is: 4/13

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Number of cards, n(S) = 52

Let E = Event of getting a diamond

F = Event of getting a queen

(E ∩ F) = Event of getting a diamond of queen.

Then, n(E) = 13

n(F) = 4 ,

n (E ∩ F)=1

P(E) = 13/52 = 1/4

P (F) = 4/52 = 1/13

P (E ∩ F) = 1/52

(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)

P (E or F) = 1/4 + 1/13 - 1/52

P (E or F) = (13 + 4 - 1)/52

P (E or F) = 16/52

P (E or F) = 4/13

The required probability of getting either diamond or a queen is 4/13

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Answer:

alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25

Step-by-step explanation:

The order of the quantities in an inequality matters. Therefore, it is true.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.

Therefore, the order matters.

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