Find the derivative of each function. Then,
determine whether the function has any local
extrema.

Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie. The required critical value is 1.31.

Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie; for example, if the null hypothesis is true, the critical value is surpassed with probability alpha.

The value of α can be written as,

α = 1 - 0.81 = 0.19

[tex]z_{\frac{\alpha}{2}} = \dfrac{0.19}{2}= 0.095[/tex]

Now, using the z-table the value of z will be,

z = 1.31

Hence, the required critical value is 1.31.

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The percentage discount allowed by the wholesaler is 1%

25 naira = 25 × 100

= 2500 Kobo

Percentage discount allowed = 25 / 2500 × 100

= 0.01 × 100

= 1%

Therefore, the percentage discount allowed is 1%

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The linear inequality depicted by the graph is: [tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

A linear function is modeled by:

y = mx + b

In which:

For this line, when x = 0, y = 0.2, hence the y-intercept is of b = 0.2. When x = 3, y = 2.2, hence the slope is given as follows:

[tex]m = \frac{2.2 - 0.2}{3 - 0} = \frac{2}{3}[/tex]

Hence the equation of the line is:

[tex]y = \frac{2}{3}x + 0.2[/tex]

[tex]y = \frac{2}{3}x + \frac{1}{5}[/tex]

The inequality is the values below(less) than the line, also including it, as it is not dashed, hence:

[tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

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Step-by-step explanation:

formula to get the volume of a cylindrical shape =πr²h

π=3.14 , r=diameter /2=19/2= 9.5, h= 40

: πr²h= 3.14 ×9.5²×40

3.14×90.25×40

=11,335.4

=11,335

The solution to the system of inequalities given is: [tex]\frac{4}{3} \leq y \leq 4[/tex]

The solution is the set of values that respect all conditions of the system.

The first condition is:

[tex]3y - 13 \geq -9[/tex]

[tex]3y \geq 4[/tex]

[tex]y \geq \frac{4}{3}[/tex]

The second condition is:

[tex]3y - 13 \leq -1[/tex]

[tex]3y \leq 12[/tex]

[tex]y \leq \frac{12}{3}[/tex]

[tex]y \leq 4[/tex]

The intersection of the conditions, which is the solution to the inequality, is:

[tex]\frac{4}{3} \leq y \leq 4[/tex]

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That is the answer for the 3 questions

The slope m = -6 and y-intercept = ( 0, 5 ).

The graph is a dash line, shaded area above the boundary line since y is greater than -6x + 5.

Given that;

y > -6x + 5

We use the slope intercept form y = mx + b to determine the slope (m) and the y-intercept (b).

y > -6x + 5

y = mx + b

We can see that;

m = -6 and b = 5

Hence, slope = -6 and y-intercept = ( 0, 5 ).

The graph is a dash line, shaded area above the boundary line since y is greater than -6x + 5.

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Answer:

[tex]\huge\boxed{\sf x = 6 \ \ \ OR \ \ \ x = -1/6}[/tex]

Step-by-step explanation:

Let the number be x

[tex]\displaystyle x - \frac{1}{x} =\frac{35}{6} \\\\Subtract \frac{35}{6} \ to \ both \ sides\\\\x - \frac{1}{x} -\frac{35}{6} = 0\\\\Multiply \ 6x \ to \ both \ sides\\\\x \times 6x - \frac{1}{x} \times 6x -\frac{35}{6} \times 6x = 0 \times 6x\\\\6x^2-6-35x=0\\\\6x^2-35x - 6 = 0[/tex]

Applying mid term break formula

[tex]6x^2-36x+x-6=0\\\\Take \ common\\\\6x(x-6)+1(x-6)=0\\\\Take \ (x-6) \ common\\\\(x-6)(6x+1)=0[/tex]

Either:

x - 6 = 0     OR    6x + 1 = 0

x = 6          OR      6x = -1

x = 6          OR       x = -1/6

Answer:

the value of x will be

x= (10x15)/25=6

Answer:

17.32

Step-by-step explanation:

since there is a 5 in the thousandths, we round the 1 in the hundredths up and get 17.32

The height of the ramp of Raúl is calculated as; 8ft

Both big and small triangles are similar triangles because all three of their corresponding angles are congruent.

Now, to get the height we will use the concept of similar triangles to get;

h/2 = 12/3

Cross multiply to get;

h = 24/3

h = 8 ft

Thus, the height of the ramp of Raúl is 8ft.

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The 2018 actual overhead cost rate is $6.55

Compute the actual overhead cost rate for 2018?

Note that the requirement is to determine the actual overhead cost rate per machine hour in the year 2018, which considers the actual manufacturing overhead incurred and the actual machine hours used.

In essence, the actual overhead cost rate is the actual manufacturing overhead cost divided by the actual machine hours

actual overhead cost rate=$360,000/55,000

actual overhead cost rate=$6.55

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The number line first represents the solution to the inequality x/-1 > -6 option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The complete question is:

Which of the following number lines represents the solution set of x/-1 > -6?

For the number lines shown in the attached picture, please refer to the picture.

We have an inequality:

x/-1 > -6

x < 6  

x ∈ (-∞, 6)

Thus, the number line first represents the solution to the inequality x/-1 > -6 option first is correct.

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Answer:

32+q=x

Step-by-step explanation:

32(jakes) + q (molly) = x(total)

Answer:

32+Q= total number of quarters.

Step-by-step explanation:

The two triangles are similar by the AA Similarity theorem.

The height of the tree can be calculated by figuring out the ratio between the distance between the mirror to her feet and the distance from the mirror to the tree

From Law of Reflection, we know that the angle of incidence and the angle of reflection are equal to each other.

Now, triangles can be proved similar by the AA, SAS, or SSS theorems. However, in this question, the triangles as seen in the attached image can be proved similar by the AA similarity theorem.

This is because both triangles have one congruent angle in common.

Sarah and the tree are standing straight and perpendicular to the ground and as such, the angles formed by Sarah and the tree are right angles.

The above tells us that the two triangles have two angles in common, making them similar triangles by the AA (Angle Angle) similarity theorem.

Since the triangles are similar, it means that the ratios of the sides of the triangles will be the same. Thus,  if Sarah knows the distance from the mirror to her feet and the distance from the mirror to the tree, she can create the ratio between the two triangles.

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Answer:

a) 9×2=18

b)16×2=32

c)14×9=126

d)20×10=200

e)10×3=30

The whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

Let x be the speed of a whale in calm water

and y be the speed of the current

In 7 hours the whale swims against the current and travels 140 miles:

7(x - y) = 140

x - y = 140/7

x - y = 20 ...........(1)

In 3.5 hours the whale swims the same distance with the current:

3.5(x + y) = 140

x + y = 140/3.5

x + y = 40 ...........(2)

Adding (1) and (2), we get the value of x:

x - y = 20  + ...........(1)

x + y = 40 ...........(2)

-----------------

2x = 60

x = 60/2

x = 30

Using this value for "x" in either (1) or (2) we can solve for "y":

x - y = 20 ...........(1)

substitute for "x"

30 - y = 20

10 = y

Therefore, the whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

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This transformation requires us to shift 1 unit left and 4 units down.

Explanation:

Dalvin drives 190 miles in 5 hours. His speed is 190/5 = 38 mph.

From here we would say the following

distance = rate*time

distance = (38 mph)*(8 hrs)

distance = 304 miles

Hello!

The weight is 4,338 pounds and 2.169 tons.

Answer: 2 tons and 338 pounds

Step-by-step explanation:

1 ton is 2000 pounds

4338 has 2 tons and 338 pounds

Answer:

6 projects

Step-by-step explanation:

Original ribbon length = 24 yards

After 10 yards given to sister, Mia is left with 24-10 = 14 yards of ribbon

Each project requires 2 1/4 yards of ribbon.

2 1/4 is 9/4 yards as an improper fraction (2 * 4 + 1 is the numerator and the denominator is unchanged)

We now have to figure out how many times 9/4 yards goes into 14 yards.

For this,

14 ÷ 9/4.
To do this, flip the numerator and denominator of the fraction and multiply

14 ÷ 9/4 = 14 × 4/9 = 56/9 . We ignore any remainder.

9 goes into 56 6 times with remainder of 2 (ignore remainder)
In other words the greatest number of projects = 6

Slope formula: [tex]\frac{y1-y2}{x1-x2}[/tex]

To find the slope:

[tex]\frac{1-0}{0-(-7)} =\frac{1}{7}[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

Good morning/evening!

The table we have is,

[tex]\Large\boxed{\begin{tabular}{c | 1} x & y \\ \cline {1-2} -7 & 0 \\ 0 & 1 \end{tabular}}}[/tex]

This is enough information. Using this we CAN find the slope of the line.

We will utilise the formula,

[tex]\Large\boldsymbol{\sf{m=\dfrac{\triangle y}{\triangle x}}}[/tex]

The change in y is 1, and the change in x is 7.

∵, the slope is [tex]\boxed{\rm{1/7}}[/tex]

done !!

[tex]\orange\hspace{300pt}\above3[/tex]

Answer:

[tex] \frac{35}{33} [/tex]

Step-by-step explanation:

[tex] \frac{8}{11} - ( - \frac{1}{3} ) \\ = \frac{8}{11} + \frac{1}{3} \\ = \frac{8 \times 3}{11 \times 3} + \frac{1 \times 11}{3 \times 11} \\ = \frac{24}{33} + \frac{11}{33} \\ = \frac{35}{33} [/tex]

Things to note :

Subtracting a negative value will be equals to adding.

To add/subtract 2 fractions together, the denominator must be the same.

Answer:

1860 yards

Step-by-step explanation:

The iterative rule for each sequence in the table will be to use the slope-intercept form of the equation of a line y=mx+b.

In this situation, x is the week, and y is the amount paid. Basically, you need to find the slope, represented by m, which is the amount the amount paid increases by each week, and the y-intercept, b, which is the "amount paid" at week 0.

The x-coordinate is the week, and the y coordinate is the amount paid. Because the weeks are incrementing by 1, x2-x1=1.

After that, to complete the rule, you need to find the y-intercept. If the amount paid is 200 on week 1, and the amount paid increases by 50 each week.

Another way to think about it is by plugging your points into the incomplete rule. Let b represent the y-intercept. Plug in the values for week 1 and solve for b.

The calculations to convince your friend that both your rules work are:

m=(y2-y1)/(x2-x1)

(x1,y1)=(1,200)

(x2,y2)=(2,250)

m=(250-200)/(2-1)

=50/1 =50

y=50x+b

200=50(1)+b

200=50+b

b=200-50

b=150

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Step-by-step explanation:

the slope of a line is the factor of x, when the equating looks like

y = ...

so,

x - 3y = 3

x = 3y + 3

3y = x - 3

y = 1/3 x - 1

so, the original slope is 1/3.

a parallel line has the same slope.

having a specific point we can use the point-slope form as equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

y - -3 = 1/3(x - 2)

y + 3 = 1/3(x - 2)

simplified that is

y + 3 = 1/3 x - 2/3

y = 1/3 x - 2/3 - 3 = 1/3 x - 2/3 - 9/3 = 1/3 x - 11/3 =

= 1/3 × (x - 11)

Answer:

[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]

Step-by-step explanation:

We are given the line x-3y=3.

We want to write the equation of the line that is parallel to this line, and that passes through (2, -3).

Parallel lines have the same slope.

Therefore, let's find the slope of x-3y=3.

The line is currently written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients.

In order to find the slope of this line, we can convert it into slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

To do that, we need to isolate y on one side; this is the same as solving the equation for y.

x - 3y = 3

Start by subtracting x from both sides

-3y = -x + 3

Now divide both sides by -3

[tex]y = \frac{1}{3} x - 1[/tex]

The slope of the line is 1/3, as 1/3 is the coefficient in front of x.

It is also the slope of our new line.

Since the question doesn't specify which format for the equation of the line, we can use any form. However, let's put the equation of the new line into slope-intercept form.

So, substitute 1/3 as m in y=mx+b.

[tex]y = \frac{1}{3} x + b[/tex]

Now we need to find b.

As the equation passes through the point (2, -3), we can use its values to help solve for b.

Substitute 2 as x and -3 as y.

[tex]-3 = \frac{1}{3} (2) + b[/tex]

Multiply.

[tex]-3 = \frac{2}{3} + b[/tex]

Subtract 2/3 from both sides (we can write this as an improper fraction).

[tex]-\frac{11}{3} = b[/tex]

Substitute -11/3 as b in the equation.

[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]

We will spend altogether $1400.

We know that the process of combining two or more items is known as an addition. Addends are the sums of the numbers that are added. The addition sign (+), which is positioned in between the addends, is present. The outcome of adding the addends is referred to as the sum.

Given that

Food = $594.09

Clothes = $204.33

Trips = $100.40

Transport = $310.05

Extras = $189.74

Now we have to round each price to a hundred dollars.

Food = $600

Clothes = $200

Trips = $100

Transport = $300

Extras = $200

Now the sum = 600 + 200 + 100 + 300 + 200 = 1400

Therefore, we will spend altogether $1400.

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The slope-intercept form is y=mx+b

m=slope=-5

y-int/b = 300

so, y = -5x+300 is the equation of the line