an automobile manufacturer claims that their jeep has a 34.9 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this jeep. after testing 16 jeeps they found a mean mpg of 34.6 with a standard deviation of 2.0. is there sufficient evidence at the 0.025 level that the jeeps underperform the manufacturer's mpg rating? assume the population distribution is approximately normal. step 1 of 5 : state the null and alternative hypotheses.

Answer:

96m2

Step-by-step explanation:

First we have to find the perimeter of parallelogram

Now,

Breadth(b)=10m

Height(h)=6m

Perimeter of paralleogram(p)=b×h

=10×6

=60m

Then,

Breadth(b)=12m

Height(h)=6m

Perimeter of triangle(p)=1×b×h

2

= 1 ×6×12

2

=36m2

Now,

Perimeter of above figure= Perimeter of paralleogram+perimeter of triangle

= 60+36

. =96m2

Answer:

none of the statements are true

Step-by-step explanation:

given the final statement in the solution is

5 = 0 ← not possible

this indicates the system has no solution.

then none of the previous statements are true

Answer:

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

If you add a parallel line through the point Q, then angle TQR will be divided by two angles.

One of them is congruent to ∠STQ and another one is congruent to ∠PRQ as alternate interior angles.

Therefore:

On solving the provided question, we can say that  the unique point equidistant from points in tetrahedron are PQ/AQ = 3/8

A polyhedron with four triangular faces, six straight edges, and four vertex corners is known as a tetrahedron in geometry, also known as a triangle pyramid. The only regular convex polyhedron with fewer than five faces is the tetrahedron, which is also the simplest of them all. Tetrahedra make up the pyramid at the bottom of the triangle. It is a tetrahedron if it has four faces that are triangular in shape. Regular tetrahedrons are those that have isosceles triangles for their faces and equilateral triangles for their bases. with four sides, a polyhedron

here,

the unique point equidistant from points

PQ/AQ = 3/8

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Hope it helps.

If you have any query, feel free to ask.

Answer:

G.1/4

Step-by-step explanation:

The probability of getting two heads when two fair coins are tossed is 1/4 or 0.25. This is because for each coin there are two possible outcomes, heads or tails, and the probability of getting heads is 1/2. Therefore, the probability of getting two heads when both coins are tossed is (1/2) * (1/2) = 1/4. So the correct answer is G. 1/4

Answer: The Area of Shaded Region is 576  [tex]cm^{2}[/tex] and the perimeter is 24 (2 + [tex]\pi[/tex]) cm

Step-by-step explanation: Given, the length of the line segment BC is 24 cm.

     First, The area of the Semi Circle AD : We know that area of a circle is [tex]\pi[/tex][tex]r^{2}[/tex]  where r=radius of the circle. Since the shape ABCD is a sqaure, BC=AD=24cm. We can see from the figure that AD is the diameter for the semi circle AD. And diameter = 2 x Radius. Therefore radius of the semi circle is 12cm.

Therefore, area of the first Semi circle AD will be :

⇒ [tex]\pi \frac{r}{2}cm ^{2}[/tex]

⇒([tex]\pi[/tex]*12*12)/2

⇒72[tex]\pi[/tex] [tex]cm^{2}[/tex]

Now, perimeter of semi circle AD : We know perimeter of a Semi circle is [tex]\pi[/tex]r + length of the base.

Therefore, perimeter of Semi circle AD is :

⇒[tex]\pi[/tex]*12 + 24 cm

⇒12 (2 + [tex]\pi[/tex])

Now, Area of the Shape ABCD, As we can see from the figure, The area will be Area of square ABCD - Area of the semi circle BC. Therefore,

Area of Square = [tex]side^{2}[/tex]

⇒24 x 24 [tex]cm^{2}[/tex]

Area of semi circle BC :

⇒(12 x 12 x [tex]\pi[/tex])/2 [tex]cm^{2}[/tex]

∴ Area of shape ABCD = [(24 x 24) - (12 x 12 x [tex]\pi[/tex])/2] [tex]cm^{2}[/tex]

⇒576 - 72[tex]\pi cm^{2}[/tex]

Now, Perimeter of Shape ABCD :

We can see from figure, the perimeter will be Sum of 3 sides of the square and the circumference of the semi circle BC.

Therefore,

⇒72 + 12[tex]\pi[/tex] cm

Now, Finally The Area of the shaded region :

⇒ Area of Shape ABCD + Area of Semi circle AD

⇒[576 - 72[tex]\pi cm^{2}[/tex]] + [72[tex]\pi[/tex] [tex]cm^{2}[/tex]]

⇒576 [tex]cm^{2}[/tex]

Perimeter of the shaded region :

⇒ Sum of 2 sides of the square ABCD + 2 Times the Circumference of the semi circle

⇒[24 + 24] + [2 x 12[tex]\pi[/tex]]cm

⇒ 24 (2 + [tex]\pi[/tex]) cm, Final Answer  

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So, on solving the provided question we can say that by probability we have [tex]256.014[/tex]= sample mean for 80th percentile

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

[tex]P(x < 240)[/tex]

Transform to z score =  (sample mean - population mean)/(standard deviation(std)[tex]/sample size^0.5)[/tex]

[tex]P(z < (240-250)/(50/49^0.5)[/tex]

[tex]P(z < -1.4) = 0.0808[/tex]

z-score corresponding to 80th percentile is 0.842

0.842 = (sample mean -[tex]250)/(50/49^0.5)[/tex]

[tex]6.014[/tex] = sample mean - [tex]250[/tex]

[tex]256.014[/tex]= sample mean for 80th percentile

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a) The unit rate of change of d with respect to t is equal to 1.6

b) the graph of the line in the attached figure.

Given: A proportionate relationship between d and t with the characteristic that a rise in t of 5 units causes a rise in d of 8 units.

To locate: A rise of 5 units in t causes a rise of 8 units in d, according to the line's unit rate of change with respect to t.

=> Slope  =   Δd/Δt   = 8/5 = 1.6

the proportional relationship between d  and t

=> d ∝ t

=> d = 1.6t

t           d=1.6t

0          0

1           1.6

2           3.2

3           4.8

Plot the points and draw a line passing through points.

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Paying a bill amount through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

1. Paying a bill amount through the mail without check is a convenient and secure way of making payments.

2. It allows for payment to be made without having to visit a physical location to do so.

3. It also allows for payment to be made without having to use a credit or debit card.

4. Therefore, an advantage of paying a bill through the mail without check is that it is convenient and secure.

Paying a bill through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

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The approximate number of years for which the species is extinct is 7.7 years.

Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.

Here,
The population of a species is modeled by the equation,
p(t) = -t⁴ + 56t² + 240,

Where t is the number of years.

The approximate number of years until the species is extinct, is given by determining the zero of the equation,
-t⁴ + 56t² + 240 = 0

So, zeros is given as,
t = 2i, -2i, 2√15, -2√15

Now,
We only consider the positive real value of t,
t = 2√15
t = 7.7 years

Thus, the approximate number of years for which the species is extinct is 7.7 years.

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The statement that when algebraic or numerical fractions are added or subtracted, the result is a single fraction is True.

For addition or subtraction of algebraic or numerical fractions, the denominator has to be the same for all terms in the equation.

For common denominator,

Suppose 2 numerical fractions are being added which have a common denominator: 3/5 + 1/5

The resultant fraction will be 4/5, which is a single fraction

For algebraic fractions, considering the denominators are common, such as 3x/5 + 4x/5 = 7x/5

The result is also a single fraction.

For different denominators,

Suppose 2 numerical fractions are being subtracted which have different denominators such as, 5/9 – 3/7

In this case, the least common multiple for the denominators are calculated: 9*7= 63, and the opposite numerators are multiplied to the opposite denominators

Therefore, (5*7 – 3*9)/63 = (35 – 27)/63 = 8/63, which gives us a single fraction.

The process is same for algebraic fractions, for example,

4x/7 – 3x/5 = (4x*5 – 3x*7)/35 = (20x – 21x)/35 = -x/35, which is also a single fraction.

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The probability that the flight would be delayed when it is not raining is 12.46%.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

To determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:

Probability that it will not rain = 1 - probability that it will rain

X = 1 - 0.11

X = 0.89

Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed

X = 0.89 x 0.14

X = 0.1246

0.1246 x 100 = 12.46

Therefore, the probability that the flight would be delayed when it is not raining is 12.46%.

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The four types of roots are: square roots, cube roots, fourth roots and nth roots, where n is any positive integer greater than 1.

The four types of roots are square roots, cube roots, fourth roots and nth roots. Square roots are the inverse of a number multiplied by itself. For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25. Cube roots are the inverse of a number multiplied by itself twice. For example, the cube root of 27 is 3, because 3 multiplied by 3 multiplied by 3 equals 27. Fourth roots are the inverse of a number multiplied by itself three times. For example, the fourth root of 256 is 4, because 4 multiplied by 4 multiplied by 4 multiplied by 4 equals 256. Nth roots are the inverse of a number multiplied by itself n times. N is any positive integer greater than 1. For example, the fifth root of 243 is 3, because 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 equals 243.

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Answer:

1.2

Step-by-step explanation:

[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex]  Cross multiply and solve for v

13v = 15  Divide both sides by 13

[tex]\frac{13v}{13}[/tex] = [tex]\frac{15}{13}[/tex]

v = 1.2 rounded to the nearest tenth

Why  this works

[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex]  we can clear the fraction by multiplying both sides of the equal sign by (5·13)

[tex]\frac{(5x13)}{1}[/tex] · [tex]\frac{v}{5}[/tex] = [tex]\frac{(5x13)}{1}[/tex] ·[tex]\frac{3}{13}[/tex]  On the left of the equal sign the 5's cancel out and the on the right of the equal sign the 13's cancel out.

13v = 5(3)

13v = 15

Answer:

5/8 is greater than 5/7. 5/8 is 0.625, while 5/7 is 0.714.

Step-by-step explanation:

5/8 is greater than 5/7. 5/8 is 0.625, while 5/7 is 0.714.

Answer:

5/7

A fraction is a fragment of a whole number, used to define parts of a whole.  The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

If we think about 5/7, we can relate this to a circle split into 7 parts, with 5 shaded in.

You can do the same for 5/8. Think of a circle with 8 parts, and 5 shaded in.

A way to figure out which is bigger is to find a common denominator between the two.

A common denominator is two fractions with the same denominator (Hence the name). Solving for a common denominator can be done with cross multiplication.

5/7 = 40/56

5/8 = 35/56

We can visibly see, that 40/56 (5/7) is bigger, therefore making 5/7 the greater fraction.

Using the triangle sum theorem, the value of x = 37.

The triangle sum theorem states that the sum of the three angles of a triangle is always 180 degrees.

The sum of the angles in a triangle is always 180 degrees, so we can use the triangle sum theorem to find the value of x.

So we can set up the following equation:

80 + 75 + (x - 12) = 180

80 + 75 + x - 12 = 180

Combine like terms:

x + 143 = 180

x = 180 - 143

x = 37

Solving for x, the value of x = 37

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Answer:

60°

Step-by-step explanation:

To find the angle of the terminal side through a point P on the unit circle, we can use the coordinates of the point. The angle is given by the inverse tangent (atan) of the y-coordinate divided by the x-coordinate.

The point P is given as (√15/5, √10/5)

Using the arctan function we have:

theta = arctan(√10/5/√15/5) = arctan(√2/√3)=atan(√2/√3) = pi/3

The angle theta is in radians, to convert it to degree we multiply it by 180/pi

Theta = (pi/3) * (180/pi) = 60. Therefore, the angle of the terminal side through the point P is 60°.

The values of a and b are 1 and 12 respectively.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Different Types of Equations

Linear Equation.

Radical Equation.

Exponential Equation.

Rational Equation

In the given question:-

y = ax² + bx

dy/dx=2ax+b

If x=3 and dy/dx=18

the solution becomes

18=6a+b

If x=5 and dy/dx=22

The solution becomes

22=10a+b

Solving the equation we get a=1 and b=12

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The scientist that made histogram of the data of amount of rainfall he collected each day for a year to study rainfall has performed descriptive statistics.

Descriptive statistics involves organizing, summarizing, and presenting data in a way that makes it easy to understand. Histograms are a common tool used in descriptive statistics. They are used to visualize the distribution of a dataset, by showing the frequency of data points within different ranges or bins. In this case, the scientist has organized the data by showing the frequency of days with different amounts of rainfall over the course of a year.

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Step-by-step explanation:

Step 1.) Plug in the numbers to each variable

(2(-25) -13) ÷ (-8.25)15

Step 2.) Solve in Parenthesis

(-50-13) ÷ -123.75

= -63÷-123.75

Step 3: Reduce/Solve

=28/55 (Fraction)

or

=0.51 (Decimal Rounded to nearest 10th)

Answer: The one below the top.

Step-by-step explanation: In order to tell if it is a function or not, you need to do the vertical line test. By examining the graph you can see that majority of the graphs has two points in the same x-axis. The only one that pasts the test is the graph below the top one.

Answer: The second one is because there can't be two y's in a straight line of a function and all of the other graphs have two y's in a line.

Step-by-step explanation:

40m  is the sound concentrated after reflection from the back wall of the niche.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

with radius 2.60m , the cylindrical wall is a highly efficient mirror  for sound , with focal length

     f = R/2 = 2.60/2 = 1.30

in  a vertical plane the sound disperses as usual butthat radiated in a horizontal plane is concentrated in a soundimage at a distance q from the back of niche ,

so 1/p+1/q = 1/f

 so 1/1.70 +1/q = 1/1.3

  1/q = 1/1.3 - 1/1.70

 q = 40m

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June has 27 coins, made up of quarters and dimes. in total, the coins are worth $4.20. Therefore, there are 10 quarters and 17 dimes she have.

Dime Coin:

A cent is a dime in US parlance, one tenth of the US dollar, and is officially called a "one cent". The name was first authorized by the Money Act of 1792.

The 10-cent coin is the smallest in diameter and the thinnest US coin in circulation, measuring 17.91 mm (0.705 inches) and 1.35 mm (0.053 inches) in diameter thickness. The obverse of the current cent features a profile of President Franklin D. Roosevelt, while the reverse depicts, from left to right, an olive branch, a torch, and an oak branch.

Quarter Coin:

The quarter (short for quarter dollar) is a United States coin denominated in 25 cents (quarter dollar). The obverse of the coin depicts George Washington in profile, and since 1998 the design of the reverse has changed frequently. In continuous production from 1796 to 1831. 955 inches (24.26 mm), 0.069 inches (1.75 mm) thick. The current version consists of two layers of cupronickel (75% copper, 25% nickel) plated on a pure copper core. The overall composition of the coin is 8.33% nickel and 91.67% copper, as the cupronickel layer accounts for 1/3 of the total weight. Its weight is 0.1823 troy ounces or 0.2000 regular Dupo ounces (5,670 grams).

We can consider that:

Let d = the number of dimes

Let q = the number of quarters

Now,

   d + q = 27                        -------------------------- (1)

⇒ d = 27 - q                      

⇒ 0.10d + 0.25q = 4.20                -------------------------- (2)    

Multiply both sides of this equation by 100 to get rid of the decimal points.

10d + 25q = 420

⇒ 10(27- q) + 25q = 420

⇒ 270 - 10q + 25q = 420

⇒ 15q = 150

⇒ q = 10

Now, Putting the value of q = 10 in equation (1) :

   d + 10 = 27

⇒ d = 27 - 10

⇒ d = 17

Therefore, there are 10 quarters and 17 dimes she have.

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The ratio of the lengths of the parallel sides of the trapezoid CD/AB = 13

A trapezoid is a quadrilateral that has a pair of parallel sides.

The median line of a trapezoid is the line joining the midpoint of the non parallel sides of a trapezoid

The parallel sides of the trapezoid are; AB and CD

The area of trapezoid ABMN = 8

Area of trapezoid NMCD = 20

The ratio of the lengths of the parallel sides, CD/AB is found as follows;

The length of the median, MN = (1/2) × (AB + CD)

Area of a trapezoid = (The sum of the length of the parallel sides) × (The distance between the parallel sides) ÷ 2

Area of the trapezoid ABCD = [ABMN]  + [NMCD]

[ABCD] = 8 + 20 = 28

Area of trapezoid [ABCD] = NM × h = 28

The height of trapezoid ABNM = h/2

Height of trapezoid NMCD = h/2

[ABNM] = ((AB + NM)/2) × (h/2)

[ABNM]  = ((AB × h + NM × h)/4) =  ((AB × h +28)/4) = 8

(AB × h + 28) = 4 × 8 = 32

AB × h = 32 - 28 = 4

AB × h = 4

[NMCD] = (NM + CD)/2 × (h/2)

[NMCD] = (NM × h + CD × h)/4 =  (28 + CD × h)/4 = 20

CD × h = 20 × 4 - 28 = 52

CD × h = 59

(CD × h)/(AB × h) = 52/4 = 13

CD/AB = 13

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According to the algebraic fundamental theorem, a polynomial equation of degree n has exactly n roots, be they real or imaginary.

Any polynomial of degree n has n roots, which is the fundamental theorem of algebra. Any polynomial has at least one solution, according to this statement. The theorem only reveals how many roots there are, not what the roots of a polynomial are. The theorem merely specifies how many roots there are in a polynomial; understanding what the roots are required knowledge of elementary mathematics. Additionally, it helps with the solution of polynomial equations [tex]x^2-9=0[/tex]. Use the definition of the algebraic fundamental theorem to determine the number of roots in the equation [tex]x^2-9=0[/tex].

Now, Solving above equation

[tex]x^2-9=0[/tex]

[tex](x-3)*(x+3)=0\\x=3,-3[/tex]

As here degree of equation is 2 and root of equation are also 2.

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Answer:

1) Nikhil 16 years & Mae 4 years

Step-by-step explanation:

x = 4y {equation 1}

Hence, x - 4y = 0 { equation 2}

x = 8 + 2y {equation 3}

Then, x - 2y = 8 { equation 4}

{equation 4-2}

x -x -2y - ( - 4y) = 8 -0

-2y +4y = 8

2y = 8

2 2

y = 4

By substituting { equation 1}

x = 4y

x = 4 × 4

= 16//

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Answer: A. p + 3 = 49

B. p = 46

Step-by-step explanation:

A. represents the equation that represents the word problem. In this case, the original number of paintbrushes Kaitlyn had is represented by (p) and Claire gives her 3 more paintbrushes, the total number of paintbrushes she has is 49.

B. represents the original number of paintbrushes Kaitlyn had. To find this, we can simply solve the equation from part A for (p) by isolating it on one side of the equation.

Therefore, Kaitlyn originally had 46 paintbrushes.

The shaded region corresponding to all values of x and y that satisfy these requirements is shown the graph

Suppose the considered function whose graph is to be made is

f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f(x)

are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Therefore, the graph is given with shaded region

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Answer:

1 foot 6 inches

Step-by-step explanation:

divide the length value by 12. Hope this helps.