The gas mileage of a hybrid car is 3.03(the 3 in the hundreds place has a repeating sign) times the gas mileage of a regular car. The regular car averages $24 miles per gallon. Find the gas mileage of the hybrid car. Round your answer to the nearest tenth. The gas mileage of the hybrid car is miles per gallon.

Answer:

D

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Step-by-step explanation:

This is a circle with center, h,k = 3,2 and radius = 2

   circle equation is   ( x-h)^2 + (y-k)^2 = r^2

so:

(x-3)^2 + (y-2)^2 = 4

Answer:

A hypothesis is "is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.". And an experiment is "is defined as to try out something new or to test a theory. An example of experiment is when you try out a new hair style. An example of experiment is when you use test tubes and chemicals in a lab to complete a project and to try to better understand chemical reactions.".

Answer: D

Step-by-step explanation:

Fits the definition

Answer: B

Step-by-step explanation:

The next point where the gap is would be B but you're looking for the point that comes after (8,4)  it would be C

Answer:

a. A western diet is associated with higher blood pressure.

b. Eating a western diet increases blood pressure.

Step-by-step explanation:

Given that :

Three groups of 21 participants participated in an observational study.

         A

The raw vegan diet group  who sedentary and had been eating a low-calorie, low-protein vegan diet composed primarily of unprocessed and uncooked plant-derived foods for at least 2 years.

          B

The subjects in the endurance runners group who ran an average of 48 miles per week for an average of 21 years.

         C

The subjects in the western diet group consisted of sedentary and non-obese subjects who ate a typical western diet (characterized by high intakes of red meat, sugary treats, high-fat foods, and refined grains).

From the observational study; we can observe that the raw vegan diet group will improve the heart health, they possess high fiber content necessary for healing. They don't quite have any issues related to higher blood pressure.

The Endurance runners groups who ran for an average of 48 miles per week for an average of 21 years will have a better heart health and a reduction in the risk associated with higher blood pressure or other health related diseases.

But the western diet group  who ate a typical western diet (characterized by high intakes of red meat, sugary treats, high-fat foods, and refined grains) will have a variety of health complications all types of the foods being consumed. For example, high intake of red meat and sugary treats and high-fat food can result an individual to having diabetes. Because these food mention contains high  saturated fat which raises  the blood cholesterol . As a result high level of these cholesterols in the body can cause several heart complications and other health related diseases.

So from the aforementioned , we can concluded that :

option A and B were appropriate summary for the students statements.

The new coordinates after translating 2 units right and 1 unit down are D'(-3,0), H'(-2,4) and S'(1,1) respectively.

Given, triangle DHS has the coordinates D(-5, 1), H(-4, 5) and S(-1, 2). Now, we have to find the coordinates of D'H'S' if DHS is translated 2 units right and 1 unit down.

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

To translate the point P(x,y), 'a' units right and 'b' units down, use P′(x+a,y-b).

Now, let's proceed to solve the question according to above listed points accordingly.

D(-5, 1), H(-4, 5) and S(-1, 2), these coordinates are translated 2 units right and 1 unit down. So, we will simply add 2 to the x-coordinate of the points and will subtract 1 from the y-coordinate.

Let's translate D, H and S accordingly into D', H' and S'.

D(-5,1)⇒ D(-5+2, 1-1)⇒ D'(-3,0)

H(-4,5)⇒ H(-4+2, 5-1)⇒ H'(-2,4)

S(-1,2)⇒ S(-1+2, 2-1)⇒ S'(1,1)

Therefore, the new coordinates after translation are D'(-3,0), H'(-2,4) and S'(1,1) respectively.

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Answer:

The null hypothesis is \(H_0: p = 0.51\).

The alternate hypothesis is \(H_1: p \neq 0.51\).

The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.

Step-by-step explanation:

A local police chief claims that about 51% of all drug related arrests are ever prosecuted

At the null hypothesis, we test if the proportion is of 51%, that is:

\(H_0: p = 0.51\)

At the alternate hypothesis, we test if the proportion is different from 51%, that is:

\(H_1: p \neq 0.51\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.51 is tested at the null hypothesis:

This means that \(\mu = 0.51, \sigma = \sqrt{0.51*0.49}\)

A sample of 900 arrests shows that 47% of the arrests were prosecuted.

This means that \(n = 900, X = 0.47\)

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.47 - 0.51}{\frac{\sqrt{0.51*0.49}}{\sqrt{900}}}\)

\(z = -2.4\)

P-value of the test:

Probability that the sample proportion differs from 0.51 by at least 0.04, which is P(|z|>2.4), which is 2 multiplied by the p-value of Z = -2.4.

Looking at the z-table, the Z = -2.4 has a p-value of 0.0082.

2*0.0082 = 0.0164.

The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.

Answer: 3,600

Step-by-step explanation:

1 kg. = 1000 g.

3.6 X 1000 = 3,600

Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

The two similar triangles in this problem are given by:

C. QRS and TUV

Similar triangles share these two features:

Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:

3/6 = 2.4/4.8 = 1.8/3.6.

Hence option C is correct.

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The length of the missing leg given the hypotenuse is 13 cm and the other leg is 5 cm would be 12 cm.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

a² + b² = c² (Pythagoras theorem)

where, c is the hypotenuse (longest length) of a triangle.

And a and b are the two other side of the triangle excluding the longest one.

Let x be the length of the missing leg of the given right triangle.

x² + 5² = 13²

x² = 13² - 5²

x² = 169 - 25

x² = 144

x = √144

x = 12

Hence,  the length of the missing leg given the hypotenuse is 13 cm and the other leg is 5 cm would be 12 cm.

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Given:

(3,5) is one solution which is given.

Required:

To get another solution.

Explanation:

We have given one solution which is equal to (3,5)

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

From the question, we have the following parameters that can be used in our computation:

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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Answer:

Step-by-step explanation:

the direction of inequality does not change

when you

the direction of inequality does change

when you

let's solve:

\(step - 1 : define\)

\(4x + 6 < 2x + 1\)

\(step - 2 : solve \: for \: x\)

To multiply a number by 10, you just need to add o at the end place of this number

Examples:

2 x 10 = 20

55 x 10 = 550

102 x 10 = 1020

Now we can solve the question 10 x 67

Just put a zero at the last place, then

67 x 10 = 670

Answer:

2

Step-by-step explanation:

1+1=

(((2!!!x3)/0.1)/6x10^4)-(((500000/5)+2.39)/w)x10391304347x((dx10^-4)+0.175838)/200000–0.159585 or 2

Step-by-step explanation:

-5m+_3m+19m=-8m+19m=11m

==========================================================

Explanation:

Define the events

The given probabilities are

The notation "P(F given H)" refers to conditional probability. If we know the person ordered a burger, then it changes the P(F) from 0.50 to 0.80; hence the events H and F are dependent.

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

We want to find the value of P(H and F), which is the same as P(F and H)

We can use the conditional probability formula

P(F given H) = P(F and H)/P(H)

P(H)*P(F given H) = P(F and H)

P(F and H) = P(H)*P(F given H)

P(F and H) = 0.60*0.80

P(F and H) = 0.48

There's a 48% chance someone orders a burger and fries.

By another pair of sides along with pair of angles we can prove that two triangles are congruent by ASA congruence postulate.

What is ASA Congruence Postulate?

A set of triangles can be proven to be congruent using the angle-side-angle rule.

According to the ASA rule, two triangles are congruent if their two included sides and two angles are the same as those of another triangle.

Using the ASA Congruence Postulate and by considering the following image,

∠ B = ∠ Q, ∠ C = ∠ R and sides between ∠B and ∠C , ∠Q and ∠ R are equal to each other.

i.e. BC= QR.

Hence, Δ ABC ≅ Δ PQR.

Therefore, By another pair of sides along with pair of angles we can prove that two triangles are congruent by ASA congruence postulate.

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Answer:

14. x=20

15. 11.36 repeating

16. 47

Step-by-step explanation:

let me know if you need help with any others

The Central tendency is typically located to the right of the tallest bar.

In a skewed left distribution, the central tendency is typically located to the right of the tallest bar. Skewed left distributions, also known as negatively skewed distributions, are characterized by a tail that extends towards the left side of the distribution.

The central tendency refers to the measure that represents the center or average of a distribution. It provides information about the typical or central value around which the data points tend to cluster. Common measures of central tendency include the mean, median, and mode.

In a skewed left distribution, the mean is usually influenced by the long tail on the left side of the distribution. This tail pulls the mean towards lower values, resulting in a lower mean compared to the median. Therefore, the mean will typically be located to the left of the tallest bar in a skewed left distribution.

On the other hand, the median is less affected by the skewness of the distribution and is relatively robust to extreme values. It represents the value that separates the lower 50% of the data from the upper 50%. In a skewed left distribution, the median will be located closer to the tallest bar or even slightly to the right of it.

The mode, which represents the most frequently occurring value in a distribution, may or may not be influenced by the skewness depending on the shape of the distribution. It can be located anywhere along the distribution, and its position is not necessarily tied to the location of the tallest bar.

To summarize, in a skewed left distribution, the central tendency is typically located to the right of the tallest bar. The median is usually closer to the tallest bar or slightly to the right, while the mean is influenced by the skewness and tends to be located to the left of the tallest bar.

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For this problem, we are given a compound image and we need to calculate the area of the triangle, the shaded region, and the circle.

Let's draw the problem, so we can better understand the problem:

We need to first calculate the area of the large triangle, which is done below:

Now we need to determine the area of circle, which is given below:

Now we need to determine the shaded area, which is the subtraction between the triangle's area and the circle's. We have:

The area of the triangle is 540 square km, the area of the circle is 113.04 square km and the area of the shaded area is 426.96 square km.

Answer:

8.97 x 10^6

Step-by-step explanation:

To add in scientific notation, the exponents need to be the same for the bases of 10.  You can either make them both to the exponent of 6 or 5.  It does not matter.  I made them both to the power of 5

(8.6 x10^6 ) + (3.7 x10^5 )

(86 x 10^5) + (3.7x10^5)  

(86 x 3.7) x 10^5

89.7 x 10^5 Rewrite in scientific notation

8.97 x 10^6

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer: 48 more monthly payments

Step-by-step explanation:

Answer:

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

Answer:

\(\boxed{y=500-60x}\)

where:

Step-by-step explanation:

Define the variables:

Given:

Find the rate of change:

\(\implies \textsf{Rate of change}=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{500-200}{0-5}=-60\)

Therefore, for every hour that passes, the car is 60 miles closer to Austin.

Therefore, the function that describes the car's distance from Austin is:

\(\boxed{y=500-60x}\)

where:

Step-by-step explanation:

since the whole biggest triangle is a right triangle so ,

\( {x}^{2} = {20}^{2} + {18}^{2} \\ {x}^{2} = 400 + 324 \\ {x}^{2} = 724 \\ x = \sqrt{724} = 26.907 = 26.91\)

Take into account that the area of a circle is given by:

where,

r: radius = 7.8cm

π = 3.14

Replace the previous values of the parameters and simplify:

Hence, the area of the circle is approximately 191.13cm^2

Answer:

43.6 has 3 significant figures.