Let f be the function given by f(x)=∣∣x2−2∣∣(x+0.4)(x2−2)(x+0.4). On which of the following open intervals is f continuous?

The answer is 5

Step-by-step explanation:

-3=z-8

put +8 underneath -8. Then cross it out.

Put +8 underneath -3. -3+8=5

The answer is 5.

I hope this helped you!

The estimates  for [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{10}{21}[/tex]

The actual answer of [tex]6\frac{1}{9}. 1\frac{5}{7}[/tex] is [tex]10\frac{30}{63}[/tex]

The estimated answer of the fraction can be done as follows:

[tex]6\frac{1}{9}. 1\frac{5}{7}[/tex]

Hence,

[tex]6\frac{1}{9} = \frac{55}{9}[/tex]

[tex]1\frac{5}{7} = \frac{12}{7}[/tex]

Therefore, the actual answer of the fractions is as follows:

[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = 10\frac{30}{63}[/tex]

Hence, the estimated answer of the fractions can be calculated as follows

[tex]\frac{55}{9}.\frac{12}{7} = \frac{660}{63} = \frac{220}{21} = 10\frac{10}{21}[/tex]

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Answer:

8 - 3 = 5

5 divided by 2 = 2.5

i = 2.5

3 x 2.5 = 7.5

4 + 7.5 = 11.5

11.5 divided by 9 = 1.277

z = 1.277

Hope this helps!

AlphaFay

Buying 12 pack is better as it is cheaper than 4 pack.

A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units.

Given Data

Protein bars come in a 4 pack box or a 12 pack box

4 pack costs 7.68 and the 12 pack costs 22.32

In 4 pack

4 pack = 7.68

1 pack = 1.92

In 12 pack,

12 pack =  22.32

1 pack = 1.86

4 pack > 12 pack

Buying 12 pack is better as it is cheaper than 4 pack.

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Answer: [tex](-16, -6) \cup (-2, 8)[/tex]

Step-by-step explanation:

[tex]||x+4|-7| < 5\\\\-5 < |x+4|-7 < 5\\\\2 < |x+4| < 12\\\\1. -2 < x+4 < 2 \implies -6 < x < -2\\\\2. -12 < x+4 < 12 \implies -16 < x < 8\\\\\therefore (-16, -6) \cup (-2, 8)[/tex]

Mrs. Parkow's 5-digit mystery number is 73248.

Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousands in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousands place.

A general 5-digit number can be written as:

a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.

a is the ten thousands digit

b is the thousands digit

c is the hundreds digit

d is the tens digit

e is the units digit.

Let 8 be at one's place that is e

Now, it is given that 8 is in a place that is 10 times less than the place of the 4.

This implies 4 is at the ten's place that is d.

Next, it is given that 3 is in a place that is 100 times greater than the place of the 4.

That is 100×10 = 1000 place

So, 3 is at the place of b.

The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.

The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 place.

Thus, 7 is at the place of a.

Thus, we obtain

a= 7

b= 3

c= 2

d= 4

e= 8

Therefore, the 5-digit mystery number is 73248.

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Answer:

Explanation:

Here, we want to estimate the rabbit population after 5 years

From the question, there was an approximate increase in the rabbit population by 150 (from 150 to 300) in a space of 2 years

Let us have an exponential relationship for this:

Let us get the value of t

P is the current population at 300

I is the initial

a is ?

t is the number of years which is 2

Mathematically, we have it that:

Now, for the 5 years tenor, we substitute 5 for t

We have that as:

From the option, we have an approximate value of 800 rabbits

The 90% confidence interval for the mean score, μ, of all students taking the test is; CI = (28.36, 30.64)

The formula for confidence interval is;

CI = x' ± z(s/√n)

where;

CI = Confidence Interval

x' is sample mean

z is critical value at confidence level

s is standard deviation

n is sample size

We are given;

n = 59

x' = 29.5

s = 5.2

z at CL 0f 90% = 1.645

Thus;

CI = 29.5 ± 1.645(5.2/√59)

CI = 29.5 ± 1.136

CI = (28.36, 30.64)

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Calls greater than 400 would be more economical in plan 1 than plan 2 and the inequality is 29 < 17 + 0.03x

The given parameters are:

Plan 1

Plan 2

Let the number of months be x.

So, we have the following equation

Plan 1: 29

Plan 2: 17 + 0.03x

For plan 1 to be more economical plan than plan 2, then we have the following inequality

Plan 1 < Plan 2

This is represented as

29 < 17 + 0.03x

Subtract 0.03x from both sides of the inequality

So, we have

0.03x > 12

Divide both sides by 0.03

x > 400

In (a), we have

x > 400

This means that the number of calls for the plan 1 to be more economical than plan 2, then the number of calls must be greater than 400

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Answer:

-1

Step-by-step explanation:

Correct option is A)

Given,

f(x)=5x−1

To find: f(0)

Put x=0 in the given eqation.

Therefore, we get

f(0)=5(0)−1

=0−1

=−1

A. The graph is shifted up 2 units

Answer:

[tex]\textsf{A.} \quad f(x)=\dfrac{1}{x-4}[/tex]

Step-by-step explanation:

An asymptote is a line that the curve gets infinitely close to, but never touches.

A vertical asymptote occurs when the denominator of a rational function is zero.

From inspection of the given graph, there is a vertical asymptote at [tex]x=4[/tex] .  

Therefore, the denominator of the rational function must equal zero when [tex]x=4[/tex] .

Therefore, the only solution where the denominator is zero when [tex]x=4[/tex] is:

[tex]\boxed{f(x)=\dfrac{1}{x-4}}[/tex]

The circumference of a circle whose radius is 15 inches measures 94.2 inches.

For a circle of radius R, the circumference is given by the formula:

C = 2*pi*R

Where pi is 3.14

In this case, we know that the radius is 15 inches, then we can write:

R = 15 in

Replacing that in the circumference formula we get:

C = 2*3.14*15 in = 94.2 inches.

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The simplified representation of the complex number expression is

23 + 37i

a + bi, where a and b are real numbers, can be used to represent any complex number.

The complex number expression is (6-4i)(1+5i)-(3-i)

now let us simplify,

or, (6-4i)(1+5i)-(3-i)

or, 6 + 30i - 4i -20i² -3 + i

or, 6 + 36i + 20 - 3 + i (we know that i² = -1)

or, 23 + 37i

Therefore the simplified complex expression is 23 + 37i

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To get the percentile

Step 1: Write the formula

For the 38th percentile

This means that the 38th percentile is between the 5th and 6th number

P38 = 41.64This means that approximately 38% of the data lie below 43, when the data are ranked

For the 60th percentile,

6089

60

A. The relationship between number of towers and number of customers is proportional.

B. 12 customers.

A proportional relationship between two variables, x and y, is a relationship whereby the ratio y/x is the same all through the table of values.

Thus, the value of y/x is constant, and is referred to as the unit rate or constant of proportionality, k.

Part A:

Given the table of values, we have:

Constant of proportionality (k) = y/x = 252/5.25 = 300/6.25 = 348/7.25 = 444/9.25 = 48.

Therefore, it is a proportional relationship because it has a constant of proportionality, k = 48.

Part B:

Substitute k = 48 into y = kx (proportional relationship)

y = 48x.

The equation for the relationship is, y = 48x. Substitute y = 576 into the equation to find the value of x, number of customers:

576 = 48x

Divide both sides by 48

576/48 = 48x/48 [division property of equality]

12 = x

x = 12

The number of customers is 12.

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The cost of one hotdog based on the given situation is $5

The correct answer option is Option C

let

Family A:

3h + 5w = 20

Family B:

6h + 3w = 33

Solve the two equations simultaneously:

3h + 5w = 20

6h + 3w = 33

Multiply (1) by 2

6h + 10w = 40

6h + 3w = 33

Substract the equations to eliminate h

10w - 3w = 40 - 33

7w = 7

divide both sides by 7

w = 7/7

w = 1

Substitute w = 1 into

3h + 5w = 20

3h + 5(1) = 20

3h + 5 = 20

3h = 20 - 5

3h = 15

divide both sides by 3

h = 15/3

h = 5

So therefore, the cost of one hotdog and one bottle water is $5 and $1 respectively.

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Answer: the answer is 5 dollars

Step-by-step explanation:

Option (c)

Given:

The measure of pantry shelf is 3 yard by 3/7 yrds.

The objective is to find the area of the pantry shelf.

The area of shelf can be calculated as,

Hence, option (c) is the correct answer.

So C receives py/(x+y)(p+q) share of money out of the total money

The ratio of money shared between A and B = x:y

Sum of the ratios is x+y

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.

B' share of money = y/(x+y)

The ratio of money between C & D = p:q

Sum of the ratio = p+q

B's share of the money is further divided among C & D in the ratio of p:q therefore:

C's share of money = y/(x+y)*p/(p+q)

= py/(x+y)(p+q)

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A method of notation in which digits are divided into groups of three by commas is known as the standard form of a number.

When a number has three digits, these groups are termed periods?

The periods are separated by commas.

Large numbers have three spots between each group of digits. Periods are the names of the groups.

The periods are typically separated by commas.

number follows 100000 and 100001

nonetheless, does not include decimals, negative integers, or fractions. Let's first express the quantity in numerical form, so 100,000 represents 100,000. The next whole number after 100,000 is the one obtained by adding 1 to the previous amount. As a result, 100000 + 1 Equals 100001, the following whole number.

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viven

t = time

function

what is the probability that the machine will not need repairs within 12

rocedure

The probability would be 0.0016

The sum of complementary angles = 90°

The angle shown is a right angle

Therefore:

k + 54.3 = 90

k = 90 - 54.3

k = 35.7°

Answer:

The line is parallel to y + x =3

=> y = -x+3

the slope = -1

passes (-12, 0)

the equation would be :

y-0 = -1(x+12)

y = -x -12 Y=-x+12

Turn into mx+b form.

Y=-x+3

Plug in (-12,0)

0=-12+b

b=12

y=-x+12

It is negative X, because the slope has to be the same since it is paralle

Step-by-step explanation:

The equation of the line that passes through the points (0, 3) and (2, - 1) in point-slope form is y - 3 = - 2 · x, that is equivalent to y = - 2 · x + 3 (m = - 2, b = 3).

According to Euclidean geometry, a line can be constructed by knowing the location of two distinct points on a plane. Then, we can determin the slope of the line from the two points. First, determine the slope of the line by using the secant line formula:

m = (- 1 - 3) / (2 - 0)

m = - 4 / 2

m = - 2

Second, substitute all the variables in the equation of the line in point-slope form:

y - 3 = - 2 · x (Point-slope form)

y = - 2 · x + 3 (Slope-intercept form)

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Given:

1.1.1 The equation of the reflection of g(x) in the x-axis is of the form:

The rule for the reflection in the x-axis:

Applying the rule:

Hence, g'(x) = 4-3x

1.1.2 The equation of the reflection of h(x) in the y-axis.

The rule for reflection in the y-axis:

Applying the rule:

Hence, h('x) = 2/-x

1.1.3 The values of k for which :

Re-arranging:

Using the rule that for an equation to have non-real roots, the discriminant (D) must be less than zero.

Simplifying we have:

Hence, the values of k for which the equation has non-real roots is that k must be less than -8

1.1.4 The average gradient of f(x) between x=-4 and x=0:

First, we need to find the value of f(x) at x=-4.

Next, we must find the value of f(x) at x=0:

Using the average gradient formula:

Hence, the average gradient is -12

Answer:

[tex]y=2x^2+4x[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & -3 & -2 & -1 & 0\\\cline{1-5} f(x) & 6 & 0 & -2 & 0\\\cline{1-5}\end{array}[/tex]

The x-intercepts of a quadratic function are when f(x) = 0.

Therefore, the x-intercepts are:  x = -2 and x = 0.

Intercept form of a quadratic equation

[tex]y=a(x-p)(x-q)[/tex]  

where:

Substitute the found x-intercepts and one of the points from the table into the formula and solve for a:

[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies6&=a(-3-(-2))(-3-0)\\6&=a(-1)(-3)\\6&=3a\\a&=\dfrac{6}{3}\\\implies a&=2\end{aligned}[/tex]

Substitute the x-intercepts and the found value of a into the formula:

[tex]\implies y=2(x+2)(x-0)[/tex]

Expand to standard form:

[tex]\implies y=2(x+2)(x-0)[/tex]

[tex]\implies y=2x(x+2)[/tex]

[tex]\implies y=2x^2+4x[/tex]

SOLUTION

Recall that a quadratic equation is of the form

The possible number of zeros of a quadratic function is 2The zeroes of a quadratic function could be real or complex

Therefore a quadratic function can have zero real roots

or 1 real root or 2 real roots.

Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.

bank A

Dollars ($)     Kroner

80                  408

100                 510

120                 612

Since $ 80 = 408 Kroner

=>       $ 1    = 408 / 80 = 5.1 Kroner   . . . . . . conversion rate of $ to Kroner)

=>   $ 1700 = 1700 x 5.1 = 8670 Kroner

Hence Mia will get 8670 Kroner in exchange for $ 1700

The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).

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The graph for the function (y = -(1/4)x + 3) is given in the attached image. See the explanation below.

Step 1 Find (x,y) pairs
Step 2: plot the points

Step 3 Draw the line on the graph.

Let's look at Step 1.

Using the graph as an example, our first pair of x,y is (0, 3)

This is obtained by substituting 0 in the equation y = -(1/4)x + 3

⇒ y = -(1/4)0 + 3

y = 0 +3

y = 3, where x = 0

If we repeat this process with x = 1, x = 2, x = 3, we will get the corresponding y for case.

Step 2: Plotting the x,y pairs will give us points on the graph.

Step 3: connecting the dots will give us the same line in the graph that is attached.

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