consider functions f and g defined by the graph and table

Answer:

Step-by-step explanation:

x=7/11

Answer: 2 real solutions

Step-by-step explanation:

The discriminant is [tex](-9)^2 -4(1)(3)=69[/tex].

Since the discriminant is positive, there are 2 real solutions.

The relation among unit rate, slope and constant rate of change of a proportional linear relationship is y = kx.

What is unit rate?

The rate of change is the ratio between the x and y (or input and output) values in a relationship. Another term for the rate of change for proportional relationships is the constant of proportionality. If the rate of change is yx, then so is the constant of proportionality.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

The slope is defined as y = mx +b

b =1, m=k

y =k x.

Here, k is constant rate of change.

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If a decimal number, x = 0.3 then 10x is 10 multiplying 0.3 the result is 3

A decimal is a number that is divided into two parts: a whole and a fraction.

Between integers and fractions, decimal numbers reflect the numerical value of whole

0.3 is x which is a decimal

10 multiplies 0.3 the result is 3

The process involve converting a fraction to a whole number as the result of multiplication changed the number system from decimal to a whole number

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Answer:

[tex]1+\sqrt{1190}[/tex] and [tex]\sqrt{1190}-11[/tex]

Step-by-step explanation:

Let the length in meters be [tex]l[/tex]. Then, the width is [tex]l-12[/tex].

[tex]l(l-12)=1189 \\ \\ l^2-12l=1189 \\ \\ l^2-2l-1189=0 \\ \\ l=\frac{2 +\sqrt{(-2)^2-4(1)(-1189)}}{2(1)} \text{ } (l>0) \\ \\ l=1+\sqrt{1190} \\ \\ \implies l-12=\sqrt{1190}-11[/tex]

The binomial distribution is a parametric probability distribution with two parameters, X and B. For a large number of trials, n, binomial probability tends to follow a continuous normal probability distribution.

The binomial distribution is a type of probability distribution that models the likelihood of one of two outcomes given a set of parameters. It sums up the number of trials when each trial has the same chance of achieving a single outcome.

Therefore,

The following is the definition of the Binomial distribution's probability mass function:

P (X = x) = (n x)p x(1p)n x, where x = 0, 1, 2, 3,..., n

Given,

Probability of defective, p = 0.03

Number of bulbs, n = 144

(i) The required probability is P(X = 5).

P(X = 5) = (1445) 0.035(1 − 0.03)144 − 5

= 144151 × (144 − 5) 1 × 0.035(1 − 0.03)144 − 5 ≈ 0.169

Within a carton of 144 bulbs, there is a 0.169 percent chance that 5 of them will be defective.

(ii) The required probability is P(X>2).

P(X>2) = 1 − P(X≤2)

= 1 − P(X = 0) − P(X = 1) − P(X = 2)

= 1 − 144101 × (144 − 0)10.030

Then simplifying,

(1 − 0.03)144 − 0 − 14411 × (144 − 1) 10.031 (1 − 0.03)144 − 1 − 14412 × (144 − 2)10.032 (1 − 0.03)144 − 2

= 1 − 0.01245 − 0.0554 − 0.1226

= 0.810

There is a 0.810 percent chance that there will be more than two faulty bulbs in a carton of 144 bulbs.

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Jon's semi-final jump compared with Anthony's was 3 inches lower. This was based on the heights given.

Given that Jon jumped 1 inches below the qualifying height, but his friend Anthony

made it to 2 inches above the qualifying height.

In this case, the difference in the jump will be gotten by subtracting the values. This will be illustrated as:

= Anthony's jump - Jon's jump

= 2 - (-1)

= 2 + 1

= 3

Therefore, Jon was 3 inches lower.

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Answer: 2%

Step-by-step explanation:

First, we know that the experimental value is 13.3, and the true value 13.6. After plugging in, we get |13.3 - 13.6| = -0.3 which is just 0.3 as it is the absolute value. Then, we divide it by 13.6 which brings us the equation 0.3/1.36 which rounds to 0.022. Continuing, we multiply it by 100 which gets our answer of 2.2. The nearest percent is 2, so our answer is 2 percent.

Answer:

The three numbers are -4, 0, and 1.

The sum of three numbers is -3: -4 + 0 + 1 = -3

If the second number is subtracted from the sum of the first and third numbers, the result is -3: (-4 + 1) - 0 = -3

If the third number is subtracted from the sum of the first and second numbers, the result is -5: (-4 + 0) - 1 = -5

Step-by-step explanation:

x --> first number

y --> second number

z --> third number

x + y + z = -3

(x + z) - y = -3

(x + y) - z = -5

x = -3 - y - z

(-3 - y - z + z) - y = -3

-3 - y - y = -3

-2y = 0

y = 0

(-3 - y - z + y) - z = -5

-3 - z - z = -5

-3 - 2z = -5

-2z = -2

z = 1

x = -3 - 0 - 1

x = -4

With a correlation coefficient of 0, A. I can’t be confident at all; this is about as close to a random guess as you can get.

A correlation coefficient measures the strength of the linear relationship between two variables.

Correlation coefficients usually range between -1 to 1, and they show how one variable moves in relation to another.

A positive correlation coefficient indicates that the two variables move uniformly in the same direction, while a negative correlation coefficient shows the opposite.

A zero correlation coefficient shows no linear relationship between the two variables.

Thus, if the correlation coefficient is 0, then Option A is correct.

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B.

The age of a person's systolic pressure is 130 mm Hg is 45.98 years.

P = 0.004[tex]y^{2}[/tex] - 0.01y + 122

substitute p = 130 mm

130 = 4/1000 [tex]y^{2}[/tex] - 1/100 y + 122

8 = 4[tex]y^{2}[/tex] - 10y / 1000

8000 = 4[tex]y^{2}[/tex] - 10 y

[tex]2y^{2} -5y -4000=0[/tex]

y = 45.98 years

Therefore the age of a person's systolic pressure is 130 mm Hg is 45.98 years.

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As per the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.

As given in the question,

Let us consider the cost of each pound of walnuts is equal to $x.

And cost of each pound of chocolate chips is equal to $y.

Now as per the given condition system of equation is given by,

4x + 8y = 25  __(1)

2x + 3y = 11   __-(2)

Multiply (2) by 2 and subtract it from (1) we get,

4x + 8y = 25

4x + 6y = 22

0x + 2y = 3

⇒y = $(3/2)

Substitute value of y in (1) to get the value of x,

4x + 8(3/2) = 25

⇒4x = 25-12

⇒x = $(13/4)

Therefore, for the given cost of pounds of walnuts and chocolate chips , the cost of each pound of walnuts and chocolate chips is equal to $(13/4) and $(3/2) respectively.

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The rate of the boat in still water is 45.5 km/hr and  the rate of the current is 100.5 km/hr.

A motorboat travels 74 km in 2 hours going upstream.

Rate = Distance/time

Rate = 74 /2

Rate = 36 km/hr

It travels 110 km going downstream

Rate = Distance/time = 110/2

Rate  = 55 km/hr

Equations:

Upstream: b-c = 36 km/hr

Downstrm: b+c = 55 km/hr

Add and solve for b

2b = 36 km/hr + 55 km/hr

2b = 91 km/hr

Divide both side by 2b

b = 91 km/hr /2

b = 45.5 km/hr (speed of the boat)

Solve for c

b+c = 55

45.5+ c = 55

c = 55 + 45.5

c = 100.5 km/hr (speed of the current)

Therefore  45.5 km/hr  and  100.5 km/hr are the speed.

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Answer:

10,172 women

Step-by-step explanation:

47093 / 50 = 941.86

So 941.86 lots of 50 women

941.86 x 10.8 = 10172.088 women

rounded to 10,172 women

( can't have part of a person

The  amount of money that she yas to pay at the end of 3 yesrs to clear her debt  is:  $16,140.

First step is to find the interest

Interest = ( Principal × Interest rate × time)

Interest = $12,000 × 11.5% × 3

Interest = $4,140

Now let find the amount she use to clear the debt

Amount = Principal + Interest

Amount = $12,000 + $4,140

Amount = $16,140

Therefore she will use $16,140 to clear the debt.

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{(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

When one magnitude depends on another, the relationship between them is known as a mathematical function. So long as they are uniquely and solely connected.

Every mathematical function is the relationship between an element of group A and an element of group B. Consequently, the following algebraic expression can be used to represent this function:

Therefore, the {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The complete question is given below,

Which relation describes a function? What makes it a function?

A) {(-2,3),(-2,5),(-6,7)} Each member of the range is unique.

B) {(2,3),(3,3),(3,4)} Each member of the domain and range is positive.

C) {(2,3),(3,3),(3,4)} Each member of the domain and range is a real number.

D) {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range.

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex]

then

[tex]\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }[/tex]

= [tex]3^{\frac{4}{9}-\frac{2}{9} }[/tex] ← first expression

= [tex]3^{\frac{2}{9} }[/tex] ← third expression

Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.

We know that the relation between distance, speed, and time is given by:

distance = speed * time

speed = distance / time

We are given;

A Mazda traveled 326 miles in 7 hours.

A Ford Explorer traveled 230 miles in 5 hours.

Let us find the rate or speed one by one:

For Mazda;

Distance = 326 miles

Time = 7 hours

Rate = distance / time = 326 / 7 mile per hour = 46.57 mile per hour

For Ford Explorer;

Distance = 230 miles

Time = 5 hours

Rate = distance / time = 230 / 5 mile per hour = 46 mile per hour

We can analyze that Mazda was traveling faster than Ford Explorer.

Thus, Mazda was traveling faster than Ford Explorer by 0.57 miles per hour.

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Answer:

0.075%

Step-by-step explanation:

Answer:

1.57500 US$

Step-by-step explanation:

You equation looked like this:

$1.50; + 5% so guugle thought something else it should be:

$1.50 + 5% without the " ; "

The ammount of 5% = 0.075

Since your adding the 5% or 0.075 it would be =

1.50 + 0.075 = 1.57500

y'all get it now?

Answer:

4/3 or 1.333333

Step-by-step explanation:

Answer:

1st = 2 sin (x)

2nd = cos^2 (x)

3rd = sin^2 (x)

Considering the uniform distribution, we have that:

a) The density curve is given by the image at the end of the answer.

b) The percentage of time in which an enemy will appear between 0.5 minutes and 2 minutes after the timer starts is of 60%.

c) The 20th percentile for the distribution is of 0.75 minutes.

The uniform probability distribution is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

In this problem, the bounds are given as follows:

a = 0.25, b = 2.75.

The height of the density curve is of:

f(x) = 1/(b - a).

Hence:

f(x) = 1/(2.75 - 0.25) = 0.4.

As shown by the image given at the end of the answer.

The probability that a measure is between two values is given by:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Hence, for item b:

P(0.5 < X < 2) = (2 - 0.5)/(2.75 - 0.25) = 0.6 = 60%.

The 20th percentile is the value of X for which:

X = a + 0.2(b - a).

Hence:

X = 0.25 + 0.2(2.75 - 0.25) = 0.75 minutes.

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The solutions of the inequality are given by:

x > -3

Here we have the following inequality:

-(4x - 5) + 16x > -31

To solve this, we need to isolate the variable x in one of the sides of the inequality, so let's do that.

-(4x - 5) + 16x > -31

-4x + 5 + 16x > -31

(-4 + 16)*x + 5 > -31

12x + 5 > -31

12x > -31 - 5

12x> -36

x > -36/12

x > -3

So all the values of x that are larger than -3 are solutions of the inequality.

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Answer: They have to climb 11,535 ft.

Step-by-step explanation:

To solve this equation, we need to do this equation:

29,035 ft - 17,500 ft.

29,035 ft - 17,500 ft = 11,535 ft.

The equation to represent this scenario is y = 43*(3)ˣ  , the correct option is (a) .

In the question ,

it is given that ,

Number of pennies that Kyle starts the fundraiser =  43 pennies

goal is to triple the number of pennies each day .

let  "x" to represent the number of days .

let the total number of pennies be "y" .

this situation is represented by an exponential increase ,

that can be represented as

y = 3ˣ * 43

y = 43*3ˣ

Therefore , The equation to represent this scenario is y = y = 43*3ˣ  .

The given question is incomplete , the complete question is

Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal. Use x to represent the number of days and y to represent the total number of pennies .

Select the Equation that represents the this scenario ?

(a) y = 43(3)ˣ

(b) y = 3(43)ˣ

(c) y = [(43)(3)]ˣ

(d) y = 43(x)³

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Answer:

Step-by-step explanation:

Take the square root of both sides

[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{25}[/tex]

x=±5

Answer: It could be (3, -3) (3,3) or (-3,-3)

Step-by-step explanation:

they are all 3 away.