If 4x + 12 = 76, then x =

The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.

The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.

Mathematically, the null and alternative hypotheses can be expressed as follows:

H0: σ = 0.04

Ha: σ ≠ 0.04

where σ represents the standard deviation of the number of accidents per day.

The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.

The equation of the straight line is 2x+5y=340.

The x-intercept point of that line is (170,0).

A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.

As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).

Now, use the two-point form of the equation of a line.

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

(y-64)/(x-(-10))=(54-64)/(15-(-10))

(y-64)/(x-10)=-10/25

25(y-64)=-10(x-10)

5(y-64)=-2(x-10)

5y-320=-2x+20

2x+5y=340

Therefore, the required equation of the line is 2x+5y=340.

To find the x-intercept, substitute y=0 into the equation of the line.

2x+5×0=340

2x=340

x=170

Therefore, the x-intercept point is (170,0).

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Answer:

10x = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

Step-by-step explanation:

Distributive property of multiplication says every element within every pair of elements is added and multiplied to each other. So the value of 10 times that of 5 is 50.

Answer:

Step-by-step explanation:

We can start by finding how much money Carlos spent on clothes. To do this, we simply multiply the original amount of $400 by 40%:

Clothes = $400 * 40% = $400 * 0.40 = $160

Next, we find how much money Carlos has left after spending on clothes. To do this, we subtract the amount spent on clothes from the original amount:

Remaining Money = $400 - $160 = $240

Finally, we find how much money Carlos spent on video games. To do this, we multiply the remaining money by 50%:

Video Games = $240 * 50% = $240 * 0.50 = $120

So, in total, Carlos spent $160 on clothes and $120 on video games, for a total of $160 + $120 = $280.

And Carlos has $400 - $280 = $120 left.

After spending 40% of the $400 on clothes, Carlos has $400 x (100 - 40) / 100 = $240 left.

Next, he spent 50% of the remaining $240 on video games, which is $240 x 50 / 100 = $120.

Therefore, Carlos spent a total of $400 - $240 = $160.

Finally, Carlos has $240 - $120 = $120 left.

The proof of congruence by SAS, then 2 corresponding sides and the corresponding included angles of both triangles are equal.

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

[tex]m\angle A = m\angle B[/tex]is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

The SAS postulate , Two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.

In the triangle, the angles mCAD and mACB are congruent.

m∠CAD ≅ m∠ACB

Since m∠CAD and m∠ACB are congruent, AD and BC must also be congruent.

As a result, the SAS Congruence postulate is proven.

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The measure of the side AE would be 70 units.

We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

In the given triangle B, D, F are the midpoints of the triangle.

AC=50, CE=60,

BD=35

Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).

⇒ BD ≅ FE= 1/2 AE

AE = 70 units

Then, the length of line segment AE = 70 units

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Answer:

Step-by-step explanation:

4.

first, you broke the 2 eggs, and then cooked the eggs. after cooking them, you ate the two eggs that you cracked and cooked.

The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;

[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]

[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7

[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE

A piecewise function is a function that has rules or definition based on the interval of reference of the function.

The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;

The points on the line of the graph are;

(1, 1), and (3, 3)

The slope of the graph as x tends to 2⁺ is therefore;

Slope = (3 - 1)/(3 - 1) = 1

The equation of the line is therefore;

y - 1 = x - 1

y = f(x) =  x

Therefore;

f(x) - 4 = x - 4

f(x + 3) = x + 3

[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]

The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;

f(f(x) + 4) = f(x + 4) = x + 4

[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;

[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;

The equation of the function at x = 2 is; y = f(x) = x

f(2 + h) = 2 + h

f(2) = 2

Therefore;

[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h

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Answer:

The solution of the equation is B. 4

Step-by-step explanation:

√x + 2 = x

√x = x - 2

(√x)² = (x-2)²

x = (x-2) (x-2)

x = x² - 4x + 4

x moves to the right

0 = x² - 4x - x + 4

0 = x² - 5x + 4

0 = (x-1) and (x-4)

x-1 = 0 x-4 = 0

x = 1 (not) x = 4

So, the solution to the equation is B. 4

The equation of the line is (y - 1/12) = -4/3(x - 7/5).

What is the slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be depicted by

tan θ = Δy/Δx

So, the slope of a line is tan.

The given equation of a line is:

3x-4y=7

-4y = -3x + 7

y = 3/4 x - 7/4

The slope of the line is 3/4.

The slope of the line perpendicular to the given line is - 1/m = - 4/3

The point-slope of a line is y - y₁ = m(x - x₁).

The given point is (7/5,1/12)

The equation of the line is

(y - 1/12) = -4/3(x - 7/5)

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The 5th , 6th and 7th term of the arithmetic sequence is 1 , 13/16 and 10/16 respectively

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the first term of the AP be a₁ = 1 3/4

Let the second term of the AP be a₂ = 1 9/16

So , the common difference of AP d = a₂ - a₁

On simplifying the equation , we get

The common difference d = 1 9/16 - 1 3/4 = ( 25/16 - 7/4 )

The common difference d = - ( 3/16 )

And , the nth term of the AP is a + (n - 1) d

So , the 5th term of the AP = ( 1 3/4 ) + ( 4 ) ( -3/16 )

On simplifying the equation , we get

The 5th term of the AP = ( 7/4 ) + ( -3/4 )

The 5th term of the AP = 4/4 = 1

Therefore , the value of A = 1

And , the 6th term of the AP = ( 1 3/4 ) + ( 5 ) ( -3/16 )

On simplifying the equation , we get

The 6th term of the AP = ( 7/4 ) + ( -15/16 )

The 6th term of the AP = 13/16

Therefore , the value of B = 13/16

And , the 7th term of the AP = ( 1 3/4 ) + ( 6 ) ( -3/16 )

On simplifying the equation , we get

The 7th term of the AP = ( 7/4 ) + ( -18/16 )

The 7th term of the AP = 10/16

Therefore , the value of C = 10/16

Hence , the arithmetic progression is solved

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Step-by-step explanation:

Your picture looks blurry however I think the graph passes through the points (0,0)(-1,0) and (3,0) so the equation becomes

[tex](x +1)(x - 3)x[/tex]

[tex] {x}^{3} - 2x {}^{2} - 3x + c[/tex]

Where C is the y intercept.

Since C is 0, our equation becomes

[tex] {x}^{3} - 2 {x}^{2} - 3x[/tex]

Answer:

The solution to the equation 20 = m ÷ -5 is m = -100

To see this, we can multiply both sides of the equation by -5 to isolate the variable m:

20 × -5 = m ÷ -5 × -5

Expanding the right side of the equation:

20 × -5 = m × 1

Combining like terms:

-100 = m

And the solution is:

m = -100

Verification:

To verify the solution, we can plug in the value of m back into the original equation and see if it is true:

20 = -100 ÷ -5

Expanding -100 ÷ -5:

20 = 20

Since 20 = 20 is a true statement, we have verified that the solution m = -100 is correct.

The interest for the first quarter would be $ 15

The value of the CD when it matures is $ 2, 030. 11

The interest is said to compound quarterly which means that the periodic interest rate per quarter is:

= 3 % / 4

= 0. 75 % per quarter

The interest in the first quarter :

= 0. 75 % x 2, 000

= $ 15

The value of the CD at maturity is:

= 2, 000 x ( 1 + 0. 75% ) ²

= $ 2, 030. 11

Note : 2 periods because 6 months is 2 quarters.

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The statement that describes the point of intersection on the graph is  Calvin will plant lily bulbs and iris bulbs. Option C

The point of intersection on the graph represents the values of x and y where both conditions are satisfied.

In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.

So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".

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Answer:

this hard

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

c) 6

Step-by-step explanation:

in a 45-45-90 degree triangle the hypotenuse is [tex]\sqrt{2}[/tex] times more than the length of the other sides

3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] is the same as 3(2) or 6

The length of the hypotenuse of the triangle is,

⇒ h = 6

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Base of triangle = 3√2

Length of triangle = 3√2

Now, We can formulate;

⇒ h² = (3√2)² + (3√2)²

⇒ h² = 18 + 18

⇒ h² = 36

⇒ h = 6

Thus, The length of the hypotenuse of the triangle is,

⇒ h = 6

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The area of the shaded portion is [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex].

From the given data,

The equilateral triangle with sides 6.

Equilateral triangle: The amount of space an equilateral triangle takes up in a two-dimensional plane is its area. A triangle is said to be equilateral if all of its sides are equal and all of its interior angles measure 60 degrees. As a result, the area of an equilateral triangle can be determined if its side length is known.

In this problem

area of equilateral triangle=[tex]6^{2}*\sqrt{3}/4[/tex]----->[tex]\frac{9}{\sqrt{3} }[/tex] units²

The internal angles of an equilateral triangle are equal to 60 degrees

The area of a circle=pi*r²

for a circle with radius r=3 units

See the attached figure to better understand the problem

The area of the figure ABC is equal to the area of the circle divided by 6

Area figure ABC=[tex]9* \frac{\pi}{6}[/tex]=[tex]\frac{3}{2} *\pi[/tex]units²

the area of the shaded portion is equal to

⇒[tex]9*\sqrt{3} units^{2} -3*(\frac{3}{2} )*\pi[/tex] = [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex]

[tex]=9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex]

Therefore, the area of the shaded portion is [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex].

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Answer:

7.5dollars

Step-by-step explanation:

25%/100×$30

On solving the provided question, we can say that from the graphs The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.

Prior to technological advancement, the opportunity cost of treating HIV/AIDS rises as the world deviates from its PPF. The potential cost of treating more HIV/AIDS cases falls as a result of technological advancements since less other commodities and services must be sacrificed in order to treat more HIV/AIDS patients. Alternatively, the world might treat more HIV/AIDS patients right now by forgoing the same number of other commodities and services.

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The correct question is -

More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect​ mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and​ now, a cure could be in sight.

​Source: The Guardian​, November​ 30, 2018

Make a graph of the production possibilities frontier with​ HIV/AIDS cases treated on the x​-axis and other goods and services on the y​-axis before and after the advance in technology.

Question content area bottom left

Part 1

The opportunity cost of treating​ HIV/AIDS cases increases as more​ HIV/AIDS cases are treated.

Draw a curve that shows the production possibilities for the world economy that produces​ HIV/AIDS treatments and other goods and services. Label the curve PPF0.

Then draw the PPF that shows the effect of an advance in technology on​ HIV/AIDS treatments. Label the curve PPF1.

The polygon DEFG is translated 3 units left to get F'(1, 6)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size.

Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). The polygon is translated 3 units left to get F'(1, 6)

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Joe was given  $329 for an overnight trip because he drove a distance of 220 miles

How to solve Word Problems ?

Five Easy Steps to Solving Word Problems (WASSP)

Given Data

Amount rep receive = $175

Added amount per mile driven = $0.70

Reimbursed/Total  = $329

The Mathematical relation for this scenario is

Total amount = Amount Receive+ 0.7*Distance driven

let the distance driven be x

Substituting our given data into the relation we have

329= 175+ 0.7*x

329-175 = 0.7x

154 = 0.7x

divide both sides by 0.7

x = 154/0.7

x = 220miles

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By calculating , The value of x we get is  5 as a final resultant.

What is trapezoid ?

A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.

Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that

180=110+17x-15

70=17x-15

85=17x

x=5

Therefore, By calculating , The value of x we get is 5 as a final resultant.

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Answer:

A. (f+g)(x)=-2x^2-2x+8

Step-by-step explanation:

You combine like terms by adding

The solution for x in the triangle is x = 51.98 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Using trigonometric ratio:

sin 38° = 32/x  (Sine = opposite/hypotenuse)

x = 32/sin 38°

x = 51.98 units

Therefore, the solution is x = 51.98 units

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Answer:

P = 72.5 * e^(0.025t)

Step-by-step explanation:

Here's a step by step solution with all the details and calculus involved.

(a) Express P as a function in the form P = Poat.

Since the population is growing continuously at a rate of 2.5% per year, we can use the formula for continuous growth:

P = Po * e^(rt)

where Po is the initial population (72.5 million), r is the continuous growth rate (0.025), and t is the time elapsed in years since 2004.

The continuous growth rate, r, is related to the annual growth rate, g, by:

r = g / 100

So, the continuous growth rate is 0.025.

Substituting the values into the formula for continuous growth, we get:

P = 72.5 * e^(0.025t)

This is the expression for the population as a function of time in the form P = Poat.

(b) Express P as an exponential function using base e.

The exponential function using base e is already in the desired form. So, we can simply write:

P = 72.5 * e^(0.025t)

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Step-by-step explanation:

a normal distribution with mean m and standard deviation d gives us a few regular pieces of information.

for example, we know that 68.2% of all events are within the interval

m ± d

and 95.4% of all events are in the interval

m ± 2d

and 99.7% of all events are in the interval

m ± 3d

that means only 0.3% of all events are outside the interval

m ± 3d = 10.2 ± 3×0.12 = 10.2 ± 0.36

now, when a bag is filled with 9.8 ounces, it is 0.4 off the mean (10.2).

that means it is outside the 10.2 ± 0.36 interval and inside the 0.3% "exception" range.

you have to see it also that way : 0.3% means 3 out of 1000 bags are in that range.

so, yes, it is considered unusual.

A) The rate of change in this situation is -$100 per week.

B) She will have $300 left in her account after five weeks.

The total surface area of cylinder formed is   924 cm²              

We are given a rectangular sheet of paper of dimensions 44 cm* 14 cm is rolled along its length

So, height of formed cylinder = Length of rectangular sheet = 14 cm

Circumference of base of cylinder = Breadth = 44 cm

Circumference of circle = 2πr

So,

2 × (22/7) × r =44

r = (44×7)/(22×2)

Radius of cylinder is 7 cm

Height = 14 cm

Total surface area of cylinder = 2πr(h+r)

                                                =    2  × 22/7 × 7 (14 +7 )                                      

                                                =     924 cm²                  

Hence the total surface area of cylinder formed is   924 cm²  .  

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