A car is parked at the to p o f a 50-m-high hill. It slips ou t o f II gear and rolls down the hill. How fast will it be going at the bottom

Answer:

To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 ​ miles. We are told that the car used \frac{2}{5} 5 2 ​ of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 ​ to get the total number of gallons used:

\frac{2}{5} \cdot 15\tfrac{1}{2} = 9

Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 ​ miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:

15\tfrac{1}{2} \div 9 = \frac{31}{18}

This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:

\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}

Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:

\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}

Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.

Answer:

\(y= \frac12 x^2 -2x +\frac32\)

Step-by-step explanation:

From the two zeroes, you can tell that the polynomial factors as \(y= A(x-1)(x-3)\). You have still one degree of freedom (determining how wide the parabola is. You can determine it with the other condition:

\(4 = A(5-1)(5-3) \rightarrow 4= A(4)(2) \rightarrow A= \frac12\)

Your function is \(y= \frac12 (x-1)(x-3) = \frac12 x^2 -2x +\frac32\)

The sampling technique best described here is systematic sampling. Systematic sampling is a type of probability sampling in which the elements in the population are selected in a systematic way

This sampling technique is used when the population size is too large to survey the entire population. In this example, the population size is 300 passengers and the sampling interval is determined by dividing the population size by the sample size. For example, if the sample size is 30, the sampling interval is\(10 (300/30=10).\) This means that every 10th passenger is randomly selected for the survey. The selection starts with a randomly chosen passenger and then the ninth passenger after that is selected and so on. The formula for Systematic sampling is n = N/n, where N is the population size and n is the sample size.

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Hey

here's ur answer ⤵️

Answer= 105

Step-by-step explanation:

The minimum value in a class is it's lower limit and the maximum value in a class is the upper limit. The given class is 90-120. So, the lower limit of this class is 90 and the upper limit is 120

Hence, the class mark of this class is 90-120= 105.

Hope it helps ✌

7) The minimum temperature is 31⁰F. So, the answer is option B.

The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.

Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.

7) The minimum value in the stem is 3

And the minimum value in the leaf is 1

So, according to the given key 4|3=43°F

Here | denotes the key symbol.

So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1

Therefore, it must be 3|1

Hence, from the given key

This can be written as 31⁰F

Therefore, the answer is option B.

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Answer:

8, 15, 17  and \(\sqrt{2} , \sqrt{2}, 2\)

Step-by-step explanation:

\(c=\sqrt{a^2+b^2}\)

\(33=/=\sqrt{5^2+\sqrt{8}^2 }\)

\(17=\sqrt{8^2+15^2}\)

\(2=\sqrt{\sqrt{2}^2+\sqrt{2}^2 }\)

The critical points for the function is (1, 1) which is also the a saddle point.

To find the critical points of the function, we need to find where its partial derivatives are equal to zero:

∂f/∂x = 2x - 2y = 0

∂f/∂y = -2x + 4y - 2 = 0

From the first equation, we get x = y. Substituting this into the second equation, we get -2x + 4x - 2 = 0, which simplifies to 2x = 2 and thus x = 1. Since x = y, we have y = 1 as well. Therefore, the only critical point of the function is (1, 1).

To classify this critical point, we need to examine the second partial derivatives of the function:

∂2f/∂x2 = 2

∂2f/∂y2 = 4

∂2f/∂x∂y = -2

At the critical point (1, 1), we have:

∂2f/∂x2 = 2 > 0

∂2f/∂y2 = 4 > 0

∂2f/∂x∂y = -2 < 0

Since the second partial derivative test tells us that ∂2f/∂x2 > 0 and (∂2f/∂x2)(∂2f/∂y2) - (∂2f/∂x∂y)2 > 0, we can conclude that the critical point (1, 1) is a saddle point.

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Answer:

Step-by-step explanation:

To compute the magnitude of the cross product |u x v|, we need to know the values of u and v. However, you mentioned that u and v are unit vectors, which means their magnitudes are both equal to 1.

The magnitude of the cross product between two vectors u and v is given by |u x v| = |u| * |v| * sin(theta), where theta is the angle between the two vectors.

In this case, since u and v are unit vectors, their magnitudes are both equal to 1. Additionally, you mentioned that the angle between u and v is π/4.

Therefore, |u x v| = 1 * 1 * sin(π/4) = 1 * 1 * (√2/2) = √2/2.

Hence, the magnitude of the cross product |u x v| is equal to √2/2.

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Answer:

first step

convert 180m and 1 cm in mm that is 180000mm and 10mm

then

ples mark me brainlist

The value of x is 3/2 or 1.5.

To find the value of x, we need to equate the means of the two expressions and solve for x.

Mean of x + (x + 2) + (x + 4) = Mean of x + (x + 3x) + 3

First, let's simplify both sides of the equation:

Mean of x + (x + 2) + (x + 4) can be simplified as (3x + 6)/3, since there are three terms with equal intervals of x.

Mean of x + (x + 3x) + 3 can be simplified as (5x + 3)/3, as there are three terms with equal intervals of x.

Now, we can set up the equation:

(3x + 6)/3 = (5x + 3)/3

To remove the denominators, we can multiply both sides of the equation by 3:

3(3x + 6) = 3(5x + 3)

Expanding the brackets:

9x + 18 = 15x + 9

Next, let's isolate the x term by moving the constants to the other side:

9x - 15x = 9 - 18

Simplifying:

-6x = -9

Dividing both sides of the equation by -6:

x = -9 / -6

Simplifying further:

x = 3/2.

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Answer:

Ok I got it it’s 50

Step-by-step explanation:

because To divide by

1

5

, multiply by its reciprocal, 5.

10÷

1

5

= 105

= 50

Answer:

Step-by-step explanation:

1. 7x+7

2. 2y+5

Not sure about 3 or 4

5. 11x

6.5x+7

7.10x-9y

8. 5x+5y

Not sure about 9

10. 4x+4

Answer:

7x+7

2y+5

6x^2+3y

5a^3+4a^2+3a (This one is the same because none of the terms are alike)

11x

5x+7

10x-9y

5x+5y

x^2+6x

4x+4

Step-by-step explanation:

Combine like terms for all of these, meaning adding or subtracting anything that has the same variable or power of a variable attached to it.

Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

Let's calculate the z-score:

Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.

Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).

Therefore, approximately 87.1% of people have an IQ score less than 117.

Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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Answer:

8.325 pounds

Step-by-step explanation:

Step 1: Multiply 90 by 0.0925.

Therefore, 8.325 pounds of silver are in the statue.

The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is \(\frac{N!}{n!(N-n)!}\)

=\(\frac{10!}{2!(8)!}\)

=\(\frac{10 \times 9 \times \times 8!}{8! \times 2 !}\)

=45

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Answer:

r=1.37

Step-by-step explanation:

so first we have to change 32/2 to a decimal

to do that you have to divide 32÷3=10.66...7

the formula to find the radius when given the volume is r=(\(\frac {v}{4*pi}\))^1/3

r=(\(\frac {10.6666666667}{4*pi}\))^1/3

r= 1.37

then to check your work-

v=4/3π1.37^3

v=10.77

technically 10.77 and 10.6666666667 aren't equal but that's as close as it'll get

good luck :)

i hope this helps

have a nice day !!

Step-by-step explanation:

To find the smallest number by which 9408 must be divided so that the quotient is a perfect square, we have to find the prime factors of 9408.

9408 = 2*2*2*2*2*2*3*7*7

Prime factors of 9408 are 2, 2, 2, 2, 2, 2. 3, 7, 7

Out of the prime factors of 9408, only 3 is without pair.

So, 3 is the number by which 9408 must be divided to make the quotient a perfect square.

9408/3 = 3136

Square root of 3136

             56

       _____________

  5   |    3136

  5   |    25

___  |______

106  |      636

  6   |      636

       |_______

       |      000

So, √3136 = 56

Answer.              

Let's assume the number of cars that require 5 quarts of oil is represented by x, and the number of cars that require 6 quarts of oil is represented by y. We know that 75% of the cars require 5 quarts and 25% require 6 quarts. The calculations show that x = 600 and y = 540.  Since x represents the number of cars that require 5 quarts of oil and y represents the number of cars that require 6 quarts of oil,

From this information, we can set up the following equations:

0.75x + 0.25y = total number of cars

5x + 6y = 2520 (the total amount of oil used, given in quarts)To solve these equations, we can multiply the first equation by 5 to eliminate the decimals: 3.75x + 1.25y = total number of cars Now we have a system of two equations: 3.75x + 1.25y = total number of cars 5x + 6y = 2520 By solving this system of equations, we can find the values of x and y. the total number of cars that got an oil change at Ami's shop last month is x + y = 600 + 540 = 1140. Therefore, 1140 cars received an oil change at Ami's shop last month.

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Answer:

I believe they are equal but I'm not for sure

Answer:it’s b

Step-by-step explanation:

Answer:

The value of x = 110°

Step-by-step explanation:

=> x° + 90° + 90° + 70° = 360 ° { sum of angles of a quadrilateral is 360 }

=> x + 250° = 360°

=> x = 360 - 250

=> x = 110°

a) \(6x^2−x^3=12+5x;x=4\) For verifying that the given values of x solve the corresponding polynomial equations, we have to substitute the given values of x in the equation. x = 3 does not solve the equation.Hence, both the given values of x do not solve the corresponding polynomial equations.

If we get true equations, it means the given values of x solve the corresponding polynomial equations. Now, we will put the value of x in the equationa)\(6x^2−x^3=12+5xPut x = 46(4)^2 - (4)^3 = 12 + 5(4)64 - 64 ≠ 32\)

Thus, x = 4 does not solve the equationb)

\(9x^2 − 4x = 2x^3 + 15; x = 3Put x = 39(3)^2 - 4(3) = 2(3)^3 + 153(27) - 12 ≠ 45\)

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Answer:

7.50$

Step-by-step explanation:

3+3+1.5=7.50$.

Answer:

Length = 9 cm

Weight = 6 cm

Height = 3 cm

Step-by-step explanation:

Given the height of rectangular piece = \(x\) cm

Length = 3 times the height = \(3x\)

Width = 2 times the height = \(2x\)

Volume of rectangular piece = 162 cubic cm

Let us have a look at the formula for volume of a rectangular shape 3D sculpture i.e. a Cuboid.

Volume = Length \(\times\) Width \(\times\) Height

Putting all the given values:

\(162=3x\times 2x\times x\\\Rightarrow 6x^3=162\\\Rightarrow x^3=\dfrac{162}{6}\\\Rightarrow x^3 =27\\\Rightarrow \bold{x =3 \ cm}\)

Therefore, the answer is:

Length = 3 \(\times\) 3 = 9 cm

Width = 3 \(\times\) 2 = 6 cm

Height = 3 cm

You can infer causality from a correlational result, but only when the r value is greater than:

C. 1

Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.

However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.

In addition, there are other factors that need to be considered when assessing causality from a correlational result.

For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.

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Current trends in math instruction are likely to lead to graduates who are able to "find precise answers quickly by consulting texts and tables."

A analysis of studies on mathematics instruction encompassing students with educational disabilities discovered a variety of behavioral, cognitive, & metacognitive approaches that have been shown to improve both mathematical computation & mathematical solving problems in students with LD.

Some key features regarding the math instruction are-

Some points regarding the importance of the math instruction are-

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Answer:

5 weeks

Step-by-step explanation:

She would need to work at least 8 weeks because the bicycle is $80 and she has $35.

Answer:

5 weeks

Step-by-step explanation:

i took 80 - 35 to get 45 (money she still needs)

then took 45 divided by 10 to get 4.5 ( how many weeks till she has the money)

and if you get 10 dollars per week and its asking how many weeks

you have to up the 4 by one because it has a .5

so it would be 5 weeks

The total cashback you will get back is\($ 49.75}\)

The Given, original price \($=\$ 50$\) Sales fax\($=9.5 \%$\\\)

For first sale

                 \(\begin{aligned}\text { Price of item } & =\$ 50 \\\text { sales tax } & =+\$ 4.75 \\10 \% \text { discount } & =\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

A sale is a transaction between two or more parties that involves the exchange of tangible or intangible goods, services, or assets for money. In some cases, assets other than cash are paid to a seller.

In the financial markets, a sale can also refer to an agreement that a buyer and seller make regarding a financial security, its price, and specific arrangements for its delivery.

Regardless of the context, a sale is essentially a contract between a seller of a particular good or service and a buyer who is willing to pay for that good or service.

for second Sale:-

There is no tax

So price\($=\$ 50$\)

For third sale: - Buy 3 and get 1 half of

\(\begin{aligned}\text { Price }=50 \times 3 & =\$ 150 \\\text { Sales tax }= & +\$ 14.25 \\\text { Discount } & =\frac{-\$ 25}{\$ 139.25}\end{aligned}\)

So, price of 1 piece \($=\$ 46.42$\)

for fourth Sale; - Buy anything over \(\$40\) and get \($\$ 5$\) gift card.

\(& \text { Price }=\$ 50 \\& \text { sales tax }=+\$ 4.75 \\& \text { Gift card }=\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

Therefore, the cashback you will get back is \($ 49.75}\)

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