=
O QUADRATIC FUNCTIONS AND EQUATIONS
Solving a quadratic equation using the square root prope
V
2
Solve 3w +9=90, where w is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
W
w = 0
No
solution

The number of Americans experience hearing loss sufficient to affect communication is: 1 in 4.

According to the National Institute on Deafness and Other Communication Disorders (NIDCD).

Approximately 1 in 4 adults in the United States aged 65 and older have hearing loss that is sufficient to affect communication.

This is based on data from a survey conducted by the NIDCD and the National Health Interview Survey.

NIDCD (National Institute on Deafness and Other Communication Disorders).

In the United States, 1 in 4 persons 65 and older suffer hearing loss severe enough to impair conversation.

This is based on information from surveys done by the National Health Interview Survey and the NIDCD.

The number of Americans who experience hearing loss sufficient to affect communication is: 1 in 4.

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The solution is, 5.4 × 10⁻³ is the number in scientific notation.

Given:

The signal from a certain satellite takes approximately 0.0054 seconds to reach earth.

we will write the number in a scientific notation

The scientific notation is the number that is between 1 and 9 multiplied by 10 raised to an exponent

So, the given number will be:

0.0054

=54/10000

=54/10 * 1/1000

=5.4 × 10⁻³

Hence, The solution is, 5.4 × 10⁻³ is the number in scientific notation.

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Answer: Look below:

Step-by-step explanation:

when n = 1:

a1 = 4 x 3^(1-1) = 4 x 3^0 = 4 x 1 = 4

so a1 = 4

similarly working:

a2 = 4 x 3^1 = 12

a3 = 36

a4 = 108

a5 = 324
a6 = 972

The surface area of the given pyramid is 203 in²

From the question, we are to calculate the surface area of the given square pyramid

From the given information, the base of the pyramid is 7 in

and

The slant height of the pyramid is 11 in

The surface area of a pyramid can be calculated by using the formula

A = a² + 2al

Where A is the area of the pyramid

a is the side base

and l is the slant height

From the given information,

a = 7 in

and

l = 11 in

Thus,

Surface area = 7² + 2(7)(11)

Surface area = 49 + 154

Surface area = 203 in²

Hence,

The surface area is 203 in²

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The length of the string required to fly the kite at a height of 75 meters from the ground is 86.6 meters.

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the height of the kite (75 m), and the hypotenuse is the length of the string that we need to find. We can set up an equation using the sine function:

sin(60 degrees) = opposite/hypotenuse

sin(60 degrees) = 75/hypotenuse

We can simplify the equation using the value of the sine of 60 degrees, which is √3/2.

√3/2 = 75/hypotenuse

To solve for the length of the string, we can cross-multiply and simplify:

hypotenuse = 75/(√3/2)

hypotenuse = (75*2)/√3

hypotenuse = 150/√3

hypotenuse = (150/√3) * (√3/√3) (to rationalize the denominator)

hypotenuse = (150√3)/3

hypotenuse = 50√3 meters = 86.6 meters.

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Complete Question:

A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60 ∘ to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take √ 3 =1.732].

The length of NI is 8.5 cm.

The area of a kite can be found using the formula: Area = (d1 * d2)/2, where d1 and d2 are the lengths of the diagonals.

Substituting the given values, we get:

Area = (12 * 15)/2

Area = 90 square cm

Therefore, the area of the kite is 90 square cm.

In a parallelogram, opposite angles are equal. So, we have:

Angle A = Angle C (opposite angles)

Angle B = Angle D (opposite angles)

Also, sum of adjacent angles in a parallelogram is 180 degrees. So, we have:

Angle A + Angle B = 180 degrees

(x+30) + (3x-90) = 180

4x - 60 = 180

4x = 240

x = 60

Therefore, Angle A = x + 30 = 90 degrees, and Angle B = 3x - 90 = 90 degrees.

Let the shorter base of the trapezoid be x. Then, the longer base is x+6 (as given in the problem).

The median of a trapezoid is the average of the two bases. So, we have:

Median = (x + x + 6)/2 = 19

2x + 6 = 38

2x = 32

x = 16

Therefore, the shorter base of the trapezoid is 16 m and the longer base is 22 m.

In an isosceles trapezoid, opposite angles are supplementary. So, we have:

Angle C + Angle L = 180 degrees

4x + 3 + 5x - 15 = 180

9x - 12 = 180

9x = 192

x = 21.33

Therefore, the value of x is 21.33.

In a trapezoid, the median is the average of the two bases. So, we have:

AB = 18 (given)

Median = (SP + NI)/2

But SP = NI (opposite sides of a trapezoid are equal)

So, Median = 2SP/2 = SP

Therefore, SP = Median = 19/2 = 9.5 cm

Also, AB = SP + NI

18 = 9.5 + NI

NI = 8.5 cm

Hence concluded that the length of NI is 8.5 cm.

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Answer:

parallelogram and rectangle

Step-by-step explanation:
the shape can’t be a rhombus or a square, because all sides of it are not the same length. it’s a parallelogram, because all 4 sides are parallel to each other, and it’s a rectangle, because it’s a parallelogram and all of its sides aren’t equal.

we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.

To construct a 95% confidence interval for the proportion of people with brown hair in the U.S., we can use the following formula:

[tex]Confidence Interval = p± z \sqrt{\frac{p(1-p)}{n} }[/tex]

where p is the proportion of people with brown hair in our sample, z is the critical value for a 95% confidence level (which is 1.96), and n is the sample size.

In this case, our sample proportion is , and our sample size is 100. Plugging these values into the formula, we get:

[tex]Confidence Interval = 0.63  ± 1.96\sqrt{\frac{0.63(1-0.63)}{100} }[/tex]

Simplifying the expression inside the square root, we get:

[tex]Confidence Interval= 0.63 ± 0.098[/tex]

Therefore, the 95% confidence interval for the proportion of people with brown hair in the U.S. is:

[tex]\frac{63}{100}  = 0.63[/tex](0.532, 0.728)

This means that we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.

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11. The area difference between them is 96 square units (192 - 96).

12. The trough stands 4 feet tall.

11. The area of Figure A is 96 square units (12 x 8) and the area of Figure B is 192 square units (16 x 12). The difference in their areas is 96 square units (192 - 96).

12. Let the height of the trough be h. The volume of the trough is given by the formula:

Volume = base area x height

Substituting the given values:

96 = 24h

Dividing both sides by 24:

h = 4

Therefore, the trough is 4 feet tall.

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The equivalent expression for 6r in terms of s is 20s, which we obtain by substituting the value of r from the given equation and simplifying.

The given equation, r = (10/3)s, shows that there is a proportional relationship between the variables r and s. This means that when one variable changes, the other variable changes in direct proportion to it. In other words, if we increase r by a certain factor, s will increase by the same factor, and vice versa.

To find an expression that is equivalent to 6r, we can substitute the value of r from the given equation and simplify.

r = (10/3)s (given equation)

6r = 6(10/3)s (substitute 6r for r in the equation)

6r = 20s (simplify by multiplying 6 and 10/3)

Therefore, the expression that is equivalent to 6r in terms of s is 20s. This means that if we know the value of s, we can use this expression to find the value of 6r in a proportional relationship. For example, if s = 2, then 6r = 20s = 20(2) = 40.

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Answer:

Yes it is an exponential function

Step-by-step explanation:

The given equation can be written in the form y = abˣ , and:

a and b are constants (a = 2, b = 15)

a ≠ 0

b > 0

b ≠ 1

As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.

given

Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:

F(x) = 8x 3 sin (y)

[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]

where the derivative of y with respect to x is denoted by y'.

We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].

Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:

[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]

f'(1) = -24 + 0

f'(1) = -24

As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

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A good way to solve for lines and segments will be to know the equations and properties of the shapes that we are provided with.

To get the answers for the lines and segment, you can begin by applying the following steps:

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Answer:

0 and 1

Step-by-step explanation:

hope this helps ;)

Therefore, the probability of getting a prime number on one die and a composite number on the other die when rolling two dice simultaneously is 1/6 or approximately 0.1667.

Probability theory is a branch of mathematics that deals with the study of random events and the analysis of their outcomes. It is widely used in statistics, science, engineering, finance, and many other fields to model and predict the behavior of complex systems.

Here,

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled simultaneously. We need to count the number of outcomes where one die shows a prime number and the other die shows a composite number.

Prime numbers in the sample space are 2, 3, and 5. Composite numbers are 4, 6, and any number greater than 1 that is not prime.

So, there are three possible outcomes where one die shows a prime number and the other die shows a 4 or 6:

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

Therefore, there are a total of 6 possible outcomes where one die shows a prime number and the other die shows a composite number.

The probability of getting one prime number and one composite number on the two dice is:

P = number of favorable outcomes / total number of possible outcomes

P = 6 / 36

P = 1/6

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The factored form of the trinomial 9b² + 13b + 4 is ( 9b + 4 )( b + 1 ).

Given the trinomial in the question:

9b² + 13b + 4

To factor the trinomial 9b² + 13b + 4, we need to find two binomials whose product equals 9b² + 13b + 4.

We can start by looking for two numbers that multiply to 9 × 4 = 36 and add up to 13. Those numbers are 9 and 4.

Now we need to use these numbers to factor the trinomial.

9b² + 4b  + 9b + 4

Factor out the greatest common factor from each group

9b² + 9b  + 4b + 4

9b( b + 1 ) + 4( b + 1 )

( 9b + 4 )( b + 1 )

Therefore, the factored form is ( 9b + 4 )( b + 1 ).

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Kira will be paid $120 in interest in the first two years.

Simple interest is expressed as;

I = P × r × t

Where I is the interest, P is the principal amount, r is the interest rate per year, and t is the time in years.

Given that:

Substituting the given values, we get:

I = P × r × t

I = 2000 × 0.03 × 2

I = $120

Therefore, the interest in the first two years is $120.

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The values for p and q in the equation (x² - 6x + 9 = 49) transformed into (x - p)² = q are p = 3 and q = 40, so the answer is option A: -3 and 40.

An equation is a mathematical statement that shows that two expressions are equal. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find unknown values of variables.

In the given question,

To transform the equation x² - 6x + 9 = 49 into the equation (x - p)² = q, we can first subtract 49 from both sides to get:

x² - 6x - 40 = 0

Next, we complete the square by adding (6/2)² = 9 to both sides:

x² - 6x + 9 - 40 + 9 = 0 + 9

(x - 3)² - 22 = 0

Now we can see that p = 3 and q = 22.

Therefore, the answer is D) 3 and 49.

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After conversion, B) 5 mL is 0.005 L milliliters

The quantity given = 0.005 L

Using a unit conversion, the same property is stated in a different unit of measurement. Minutes can be used to measure time instead of hours, and feet, kilometres, or any other measurement method can be used to measure distance in place of miles.

To convert from litres to millilitres, it is required to multiply the quantity by 1000. This is because there are 1000 millilitres in one litre.

Therefore, converting the given value-

= 0.005 L x 1000 mL/L

= 5

Thus, the resultant value after conversion is 5mL

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Answer: c

Step-by-step explanation:

Answer:

Θ ≈ 21.62°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{19}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{7}{19}[/tex] ) ≈ 21.62° ( to the nearest hundredth )

Null hypothesis: Bags are filled correctly at 441 grams. Alternative hypothesis: Bags are overfilled (mean weight > 441 grams).

The null hypothesis (H0) is that the bags are filled correctly at the 441 gram setting, meaning the mean weight of the bags is 441 grams. The alternative hypothesis (Ha) is that the bags are overfilled, meaning the mean weight of the bags is greater than 441 grams. Thus, the hypotheses can be written as:

H0: μ = 441

Ha: μ > 441

To test these hypotheses, we can use a one-sample t-test with a significance level of 0.02. We will compare the sample mean weight of a random sample of bags to the population mean of 441 grams, using the t-test statistic and the corresponding p-value. If the p-value is less than 0.02, we can reject the null hypothesis and conclude that the bags are overfilled

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The quarterly dividend payment per share based on the question above will be: $0.02.

The close price for the week will be: $5.45.

For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:

Close price = Total cost / Number of shares

                    = $2,790.40 / 512

                    = $5.45

To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:

Annual dividend per share = Total annual dividend / Number of shares

                                              = $40.96 / 512

                                                = $0.08

From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:

Quarterly dividend per share = Annual dividend per share / 4

                                                  = $0.08 / 4

                                                   = $0.02

Hence the quarterly dividend payment per share will be: $0.02.

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See text below

Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)

EARNINGS

52-WEEK

TICK

VOL.

WEEK'S

LATEST

THIS NEXT DIV

High Low

Name

Sym.

100s

Yld.

P/E Last Chg.

Year

Year

Year

Amt

8.50

3.20

Targa Resources

TRGP

412574 1.8

PO

dd

+0.41

0.25

0.18

0.12

The equation of the line which is as graphed in the task content is; Choice D; 5x - 3y = 3.

By observation, two points on the given line are; (0, -1) and (3, 4).

On this note, the slope of the line can be determined as the rate of change in y to change in x as follows;

slope, m = (4 - (-1)) / (3-0)

Slope, m = 5 / 3.

Using the point-slope form equation; using the slope, m = 5/3 and point (3, 4).

y - 4 = 5/3 (x - 3)

3y - 12 = 5x - 15

Therefore, 5x - 3y = 3.

Ultimately, the equation of the line is; Choice D; 5x - 3y = 3.

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Answer:

natural radioactive decay, examples: postassium and carbon. Three ways to classify their physical properties mineralogical composition, grain size, and texture

Step-by-step explanation: