Fill in the blanks below.
Find the slope of the line passing through the points (8,5) and (8,-4).

Using a linear function, we have that:

Given that, the percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.

Linear functions are those whose graph is a straight line. The standard form of the linear function is f(x)=y= mx + b. A linear function has one independent variable and one dependent variable.

Where, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0 and can also be interpreted as the initial value of the function.

The percentage in 1980 is considered as the initial amount, so b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by: m = (50.5 - 58.8)/15 = 0.5533.

Thus, the percentage in t years after 1980 is P(t) = 58.8 - 0.5533t.

Now, t + 1980, for which P(t) = 47.

So, P(t) = 58.8 - 0.5533t

47 = 58.8 - 0.5533t.

0.5533t = 11.8.

t = 11.8/0.5533

t = 21.3.

1980 + 21 = 2001, so the percentage will be 47% during the year 2001.

Now, 2005 is 25 years after 1980, so the percentage is P(25), given as follows: P(25) = 58.8 - 0.5533x25 = 44.97%.

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Answer:

f(5) = -1

Step-by-step explanation:

The points on the graph are (0,4), (1,3),(2,2), (3,1), (4,0), (5,-1).

The answers are in the form:

f(x) = y

That is, the number in the parenthesis is the x and the number by itself on the right is the y. The only one that is a point on the line is f(5) = -1, which is the point (5,-1)

Answer:

10 in base 3

Step-by-step explanation:

3 in base 10 =   10 in base 3

According to the information in the table, it can be inferred that the trend of the results is positive but does not have an exact linear fit (option B).

To calculate the average of the results we must add all the results and divide the result by the number of years as shown below.

Additionally, to identify if the trend is positive or negative, we must see if the results increase or decrease year after year. From the above, it is possible to infer that it is a positive trend.

On the other hand, it can be stated that it does not have an exact linear fit because the increase is not constant each year.

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Answer: [tex]144\pi[/tex] square feet

Step-by-step explanation:

[tex]A=\pi(0.00012 \times 10^{5})^{2}=\boxed{144\pi \text{ ft}^{2}}[/tex]

Answer:

Step-by-step explanation:

Solve -6 < 2x + 4 ≤ 16

To solve for x, we need to simplify the statement.

let's get rid of the 4 that is added to 2x.

do that by subtracting 4 on all sides (3 sides).

-6 - 4 < 2x + 4 - 4 ≤ 16-4

We get: -10 < 2x ≤ 12

Now, let's get rid of the 2 that gets multiplied to x.

do that by dividing all sides by 2.

-10 : 2 < 2x : 2 ≤ 12 : 2

We get: -5 < x ≤ 6

X = {-4,-3,-2,-1,0,1,2,3,4,5,6}

Hope I helped!

The proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9

The three sides of each of the rectangles should be proportional to each other

Triangle A : Triangle B

9 cm : 13.5 cm

= 9/13.5

14 cm : 21 cm

= 14 cm / 21 cm

6 cm : 9 cm

= 6 cm / 9 cm

Therefore, the proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9

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The number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is:

80 units needed 6 units per case. What are the number of cases and the number of additional units?

Total number of units  = 80 units

6 units per case

Number of case = 80/6 = 13.33 ≈ 13

Total units if the number of cases = 13

= 13×6

= 78

Additional units = 80 - 78 = 2 units

Thus, the number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.

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Answer :

10.5 miles

Given :

7 miles in 50 mins

Step-by-step explanation :

Calculate how many miles in 1 minute :

Divide both by 50 :

7/50 miles in 1 minute

To work out 75 minutes we multiply both by 75 :

75 × 7/50 =

10.5

Therefore our final answer is 10.5 miles

Hope this helped and have a good day

Answer:

10.676 mm

Step-by-step explanation:

The perimeter of a circle (circumference) formula is 2*(3.14)*r. Therefore since r is 1.7,  2*3.14*1.7 = 10.676 mm.

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The equation that models the curve of best fit for this data will be y = 1.4646·(1.818)ˣ.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

Consider the scatter plot.

Then the equation that models the curve of best fit for this data will be

At (1.2, 3), then we have

[tex]\rm 3 =ab^{1.2}[/tex] ..........1

At (4, 16), then we have

16 = ab⁴  ..........2

By solving the equations 1 and 2, we have

a = 1.4646 and b = 1.818

Then the equation will be

y = 1.4646·(1.818)ˣ

Then the graph is drawn.

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The reflected function is g(x) = √(-x).

And the correct option is the third one.

Remember that for a function f(x), a reflection across the y-axis gives:

g(x) = f(-x).

In this case, the original function was:

f(x) = √x

Then we have:

g(x) = √(-x).

So we can only evaluate this function in values of x such that:

x ≤ 0.

Then the correct option is:

"On a coordinate plane, a graph starts at (0, 0) and goes to the left through (negative 4, 2)."

As when we evalute g(x) in -4, we get:

g(-4) =  √(-(-4)) = √4 = 2

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Answer:

C

Step-by-step explanation:

The probability that both are red marbles is 0.2391

The given parameters are:

Red =12

Blue = 12

Total = 24

The probability of selecting the first red marble :

P(Red) = 12/24

Now, there are 11 red marbles and 23 marbles in all

The probability of selecting the second red marble :

P(Red) = 11/23

The required probability is:

P =  12/24 * 11/23

Evaluate

P = 0.2391

Hence, the probability that both are red marbles is 0.2391

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Answer:

i think, bond rating agencies giving CDOs very low ratings, discouraging investors to invest

Step-by-step explanation:

Answer:

its wrong answer and question

Were you not given a diagram?

The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.

Using sine rule, we find the length of AB and BC as shown in the image.

a/sin A = b/sin B = c/sin C

Angle C = 180 - (58 + 52) = 70⁰

1.3/(sin 70) = b/(sin 52)

b = (1.3sin 52) / (sin 70)

b = 1.09 mile

c = (1.3sin 58) / (sin 70)

c = 1.1732 miles

Bisect angle C, and use sine rule again to find the lengths of bisected line AB.

1.09/(sin 90) = x/[sin (90 - 58)]

1.09/(sin 90) = x/(sin 32)

x = (1.09 sin 32)/(sin 90)

x = 0.578 mile

Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile

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Answer:

4

Step-by-step explanation:

10xyz/40xyz

the xyz would cancel out

leaving 10/40.

10/40 would then simplify to 1/4 (divide by 10)

1/4

The reciprocal of 1/4 is 4

To check:

1/4 * 4 = 1

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9 ( divide through by 9 )

x + y = 1 ( subtract x from both sides )

y = 1 - x

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9

First, take 9x to the right side.

9y = 9 - 9x

9y = 9 ( 1 - x )

Divide both sides by 9.

y = 1 - x

The triangles are not similar as the ratios are different.

ΔXYZ

XY = 1.5, XZ = 1, ZY = 2

Δ QSR

QR =1, RS = 1.5, SQ = 0.5

Ratios:

XY/SQ = 1.5/0.5

XZ/QR = 1/1  

ZY/RS = 2/1.5

The answer is no because ratios are different

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Answer:

[tex]\huge\boxed{\sf 4x + 8}[/tex]

Step-by-step explanation:

= 4(x + 2)

Distribute

= 4x + 8

[tex]\rule[225]{225}{2}[/tex]

The expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

The most fundamental of curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. From a geometric perspective, it may be compared to a prism with a circle as its basis.

Given the volume of a cylinder is given by the formula V = 3.14r^2h, where r is the radius of the cylinder and h is the height and suppose a cylindrical cane has radius (x+8) and height (2x+3)

We have to find expression which represents the volume of the cane

So as per given,

r = x+8

h = 2x + 3

v = πr²h

v = π(x+8)²(2x+3)

v = π(x²+64+16x)(2x+3)

v = π(2x³+128x+32x²+3x²+192+48x)

v = π(2x³+35x²+176x+192)

v = π2x³+π35x²+π176x+π192

Hence the expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

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The truth set for each predicate are:

a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

b) d ∈ {  1, 2, 3, 6}

c) x ∈ { [-2, -1] U [1, 2]}

d) x ∈ {-2, -1, 1, 2}

We only need to find the sets of values such that the statements are true.

a)

We want to find vales of d, such that d is an integer, and 6/d is an integer.

Here the possible values of d will be:

d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

Which are all the factors of 6, so all these integers divide 6.

b) Same as before, but this time the domain is a positive integer, so now the truth set will be:

d ∈ {  1, 2, 3, 6}

c) We want to find real values of x such that:

1 ≤ x² ≤ 4

If we apply the square root to the 3 sides, we get two inequalities:

-√1 ≥ x ≥ -√4

√1 ≤ x ≤ √4

Simplifying:

-1  ≥ x ≥ -2

1  ≤ x ≤ 2

So the truth set is:

x ∈ { [-2, -1] U [1, 2]}

c) Same as before, but now we only have integer solutions, so the truth set is:

x ∈ {-2, -1, 1, 2}

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Answer:

The increasing number of students who are hooked on playing online mobile games (OMG) is alarming. As such, this study was realized to address the problem. This study assessed the gaming profile towards OMG and its relation to the academic performance of the engineering students of Eastern Visayas State University Tanauan Campus (EVSUTC). Specifically, the study investigated the correlation between student's number of hours spent on playing OMG (at school and home), commonly played OMG (at school and home), reasons for playing OMG and attitudes on playing OMG with academic performance utilizing Eta and Pearson r correlation analyses. A random sample of 134 student respondents were selected through purposive sampling of those who are playing OMG using their mobile phones. Descriptive correlational research design was utilized and a validated survey instrument was employed to gather the needed information. The findings revealed that majority of the students played mobile legends and spent mostly 2 hours playing OMG for a reason of boredom. The overall attitudes of the students on playing OMG were interpreted as Less Favorable (M=2.58, SD=1.13). Out of the independent variables being set in the study, the number of hours spent on playing OMG at home (r=-0.188, p=0.039) and commonly played OMG at school (r=0.203, p=0.045) were found significantly correlated with student's academic performance. Hence, the students' time spent on playing OMG at home and the type of games that students played at school have significant bearing to their academic performance. As such, delimiting student's usage of internet can be made to address the problem.

Answer: -21

Step-by-step explanation:

Let the number be x.

Then, this means 2(x+8)+5=x.

The domain of the graph is [-3, 2) and the range is (-4, 5]

From the given graph, we have the following highlights:

Open circles are represented with () while closed circles are represented with []

Hence, the domain of the graph is [-3, 2) and the range is (-4, 5]

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