Divide 14x3 − 21x2 − 7x by −7x. −2x2 + 3x + 1 −2x2 + 3x − 1 −2x3 − 3x2 − x −2x2 + 3x

The height of cliff is 62.50 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, the angle of elevation from point A to the top of a cliff is 38°, the point A is 80 feet from the base of the cliff,

Refer to figure attached,

The scene is making a right triangle, with an acute angle 38°, and base (distance from point to base of the cliff) 80 ft, we need to find the length of perpendicular line which is the height of the cliff,

Therefore,

We know that,

tan β = ratio of the perpendicular side to base of a triangle,

Therefore,

tan 38° = AB / 80

AB = 62.50

Hence, the height of cliff is 62.50 ft

Learn more about height and distance, click;

https://brainly.com/question/9965435

#SPJ1

99% confidence interval for the number of chocolate chips per cookie is

15.4 ± 1.1115

The mean of sample plus and minus the range of that sample constitutes a confidence interval.

Within a specific level of confidence, this is the range of values anticipated to fall within, if the test is repeated.

Number of cookies in the sample n = 55

Mean μ = 15.4

Standard deviation s = 3.2

Confidence = 99%

For 99% confidence interval Z-value = 2.576

Confidence interval

= μ ± Zs/√n

= 15.4 ± 2.576×3.2/√55

= 15.4 ± (8.2432/7.4162)

= 15.4 ± 1.1115

Hence, 15.4 ± 1.1115 is the 99% confidence interval for the number of chocolate chips per cookie.

Learn more about confidence interval here:

https://brainly.com/question/24131141

#SPJ1

Answer:

Step-by-step explanation:

5 seconds later acceleration of the car is 6m/h^2

We know that the initial velocity of a car is 50 mph.

In the end, the final velocity of a car is 80 mph.

The time difference is 5 seconds.

For the calculation of the acceleration, we have this formula,

α = δv/t

so here, according to our data, velocity and time are,

u = 50 mph

v = 80 mph

t = 5 s

Finally, the acceleration of the car can be calculated by,

α = (80 - 50) / 5

α = 30 / 5

α = 6 m/h^2

From the above calculations, the car's acceleration is 6 m/h^2.

Learn more on acceleration here;

https://brainly.com/question/605631

https://brainly.com/question/16946886

The equation that could be solved to get the same answer is B 5(x+23)=44.5

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

WE are given that Julia correctly solved a math problem by first dividing 44.5 by 5, then subtracting 23 from the answer.

First;

44.5 /5 = 8.9

Then subtracting 23 from it

8.9 - 23

= 14.1

Therefore, we can write as 5(x+23)=44.5

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

Based on the information provided, the greatest weight of a baby walrus in ounces is 2560 ounces.

According to the information provided, the weight of a baby walrus is between 100 and 160 pounds, which means 160 is the maximum weight for these animals.

Now, let's convert the pounds to ounces to know the maximum weight in ounces. For this, let´s consider that 1 pound = 16 ounces.

160 x 16 = 2560 ounces

Based on this, it can be concluded that the maximum weight is 2560 ounces.

Learn more about weight in https://brainly.com/question/10069252

#SPJ1

Commutative property of addition is the property that we used to get the answer for 27+29+31 = 87.

The commutative property of addition says that changing the order of addends does not change the sum. As the first civilization to study fractions, the Egyptians used fractions to address a variety of mathematical problems, including the division of food and supplies and the absence of a bullion currency.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

In the properties used for this question use the properties of the Commutative property of addition

If counted then the final result

31 + 27 + 29

= (30 +1) + (30 - 3) + (30 - 1)

= 3(30) + 1 - 3 - 1

= 90 - 3

= 87

Hence, 27+29+31 = 87

To learn more about fraction, Visit

https://brainly.com/question/78672

#SPJ1

Answer:

3906250

Step-by-step explanation:

They are multiplying each one by 5 to get the next number in the sequence so we just have to do it for each one until we get to the 10th sequence

1) 10 =

10

2) 10 x 5 =

50

3) 50 x 5=

250

4) 250 x 5=

1250

5) 1250 x 5=

6250

6) 6250 x 5=

31250

7) 31250 x 5=

156250

8) 156250 x 5=

781250

9) 781250 x 5=

3906250

10) 3906250

1/4 of all the students in the orchestra are girls who play string instruments.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's assume there are a total of 100 students in the school orchestra. Then, according to the problem, 2/5 of them are string players.

The number of string players is:

2/5 x 100 = 40

Out of these 40 string players, 5/8 are girls.

The number of girls who play string instruments is:

5/8 x 40 = 25

Therefore, the fraction of all the students in the orchestra who are girls who play string instruments is:

25/100 = 1/4

Therefore, 1/4 of all the students in the orchestra are girls who play string instruments.

To learn more about Algebraic expression from given link.

https://brainly.com/question/28884894

#SPJ1

If the cross-price elasticity of demand for two goods is 1.25, then the two goods are substitutes.

Cross Price Elasticity of Demand:

The cross elasticity of demand is an economic concept that measures the response of the quantity demanded of one good to changes in the price of another good. Also known as the cross-price elasticity of demand, this measure is calculated by dividing the percentage change in quantity demanded for one good by the percentage change in price of another commodity.

[tex]E_X_Y[/tex] = [tex]\frac{Percentage change in Quantity of X }{Percentage Change in Quantity of Y}[/tex]

[tex]E_X_Y[/tex] = ΔQ/Q ÷ ΔP/P

       = ΔQ/Q × P/ΔP

       = ΔQ/ΔP × P/Q

where:

Q = Quantity of good X

P = Price of good Y

Δ = Change

​The cross elasticity of demand for a substitute is always positive because an increase in the price of a substitute increases the demand for one good. For example, when the price of coffee rises, the demand for tea (alternative beverage) increases as consumers switch to cheaper but alternative beverages. This is reflected in the formula for the cross-elasticity of demand, as the numerator (the percentage change in demand for tea) and the denominator (the price of coffee) represent positive increases.

Items with a coefficient of 0 are unrelated and independent products. Commodities can be weak substitutes for which both products are positive but have a low cross-elasticity of demand. This is often the case with various alternative products such as tea or coffee. Commodities that are strong substitutes have a higher cross-elasticity of demand. Consider a different brand of tea. An increase in the price of green tea from one company has a greater impact on the demand for green tea from the other company.

The cross elasticity of demand is 1.25. Positive cross elasticity means that when the price of one good changes, the quantity demanded of another good changes in the same direction. For example, when the price of one good increases, the demand for another good increases.

This indicates that the two products are fungible. When the price of a product rises, consumers will prefer the cheaper product. As a result, the demand for alternatives will increase.

Learn more about Substitute:

https://brainly.com/question/13058734

#SPJ4

Answer:

120-90

=30

the change in stock price is $30 per share

Answer:

1 pin = 473.17 ml

Step-by-step explanation:

1 pin = 473.17 ml

To convert pin to ml, you need to take the number of pin times 473.17.

This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.

Here's an example Python function called count_characters that counts the number of times each character appears in a user-supplied string s:

def count_characters(s):

Given a string s, returns a dictionary containing the count of each character in the string.

char_count = {}

for char in s:

if char in char_count:

char_count[char] += 1

else

char_count[char] = 1

return char_count

This function creates an empty dictionary called char_count to store the counts of each character. It then loops through each character in the string s and checks if it's already in the char_count dictionary. If it is, it increments the count for that character. If it's not, it adds the character to the dictionary with a count of 1. Finally, the function returns the char_count dictionary.

You can call this function like this:

string = "hello world"

char_count = count_characters(string)

print(char_count)

Output:

python

{'h': 1, 'e': 1, 'l': 3, 'o': 2, ' ': 1, 'w': 1, 'r': 1, 'd': 1}

This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.

for such more question on count characters

https://brainly.com/question/21891513

#SPJ4

To convert 8 cups to quarts, you can divide the number of cups by 4 to get 2 quarts.

To convert cups to quarts, you can use the following conversion factor:

1 quart = 4 cups

Therefore, to convert 8 cups to quarts, you can divide the number of cups by 4:

8 cups ÷ 4 = 2 quarts

So, 8 cups is equal to 2 quarts.

It's important to keep in mind that cups and quarts are units of volume measurement commonly used in cooking and baking. Cups are often used to measure smaller amounts of liquid or dry ingredients, while quarts are used for larger amounts.

In many recipes, the measurements are given in cups, but in some cases, you may need to convert from cups to quarts or other units.

To learn more about measurement click on,

https://brainly.com/question/29133911

#SPJ4

Diane's monthly payment for borrowing $3,000 at 13.5% APR over 36 months is $101.81.

We can use an online finance calculator to compute the monthly payment, setting the following parameters.

The monthly payment shows the periodic payment that must be made to settle the loan with the finance charges.

N (# of periods) = 36 months

I/Y (Interest per year) = 13.5%

PV (Present Value) = $3,000

FV (Future Value) = $0

Results:

Monthly payments (PMT) = $-101.81

Sum of all periodic payments = $-3,665.01

Total Interest = $665.01

Thus, Diane will pay $101.81 monthly for 36 months.

Learn more about the monthly payment at https://brainly.com/question/28106777.

#SPJ1

90, They are measuring the same, therefore m4 = 90. Four right angles are produced when two lines overlap to form single right position.

Two full lines or rays intersect at a same terminus to make an angle. The centroid of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner."

Right angles are created when two straight lines cross at a 90° angle or are identical to one another at the intersection. The sign stands for a right angle.

To know more about intersection visits:

https://brainly.com/question/14217061

#SPJ1

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept of the line.

It allows for the easy representation of a linear equation in two variables, with the slope indicating how steep the line is and the y-intercept indicating where the line intersects the y-axis.

By rearranging an equation in standard form

or point-slope form

we can solve for y in terms of x to convert it to slope-intercept form. This form is commonly used in applications such as graphing and predicting values on a line.

Learn more about Slope Intercept Form:

https://brainly.com/question/1884491

#SPJ4

The equivalent of 1/4 acre in square feet according to the relation between the two is 10,890.

Square feet and acre are the units which are representative of area covered by a land. The conversion of square feet and acre is simple and can be performed through simple formula -

1 acre is equal to 43, 560 square foot

So, using this relationship to find the square feet equivalent of 1/4 acre.

Area covered by 1/4 acre = amount of area covered in acre × equivalent of one acre in square foot

Area covered by 1/4 acre = 1/4 × 43, 560

Performing multiplication on Right Hand Side of the equation

Area covered by 1/4 acre = 10, 890 square feet

Hence, 10, 890 square feet is occupied by 1/4 acre.

Learn more about unit conversion -

https://brainly.com/question/13016491

#SPJ4

On converting the weight of 166 lbs to Kg , we get that 166 lbs is equivalent to 75.29  Kg .

One Kilogram (Kg) is defined as the base unit of mass in the International System of Units (SI). and

One Pound (lb) is defined as a unit of mass which is commonly used in the United States to measure the weight .

We know that ; 1 pound is approximately equal to 0.4535 Kilograms ;

To convert 166 lbs to Kg ; we multiply the given weight with 0.4535 ;

We get ;

⇒ 166 lbs = 166 × 0.4535 Kg ;

⇒ 166 lbs = 75.281 Kg ≈ 75.29 Kg .

Therefore , 166 pounds is approximately equal to 75.29 Kilograms .

Learn more about Pounds here

https://brainly.com/question/30401000

#SPJ4

Answer:

Step-by-step explanation:

The meaning of the y-intercept of the given graph is the starting battery percentage of the tablet. In this case, the y-intercept is 30, which means that the tablet starts with 30 percent of battery remaining. As the x-axis represents time in hours, at the beginning, the tablet has not been in use yet, and it has a full charge of 30 percent. From the given graph, we can see that after 3 hours, the tablet's battery percentage drops to 0. Therefore, it can be concluded that the battery of the tablet does not last for more than 3 hours, and it has to be recharged after this time period.

So, the correct option that describes the meaning of the y-intercept in the context of the problem is "The tablet starts with 30 percent of battery remaining."

The critical value, zα/2, that corresponds to a 87% confidence level is approximately 1.514.

The critical value, zα/2, is the z-score that cuts off an area of α/2 in the tails of the standard normal distribution. In other words, it represents the number of standard deviations away from the mean that corresponds to a particular level of confidence.

To find the critical value for a 87% confidence level, we first need to determine the area that is left in the tails of the distribution. Since the confidence level is 87%, the area in the middle of the distribution is (1 - 0.87) = 0.13. We then divide this area in half to get the area in each tail, which is 0.065.

Using a standard normal distribution table or a calculator, we can find that the z-score that cuts off an area of 0.065 in one tail is approximately 1.514. Therefore, the critical value, zα/2, is:

zα/2 = ±1.514

However, since we want to find the z-score that corresponds to the middle 87% of the distribution, we need to add the absolute value of this number to the mean of the distribution, which is 0. This gives us:

zα/2 = |1.514| = 1.514

Therefore, the critical value, zα/2, that corresponds to a 87% confidence level is approximately 1.514

To know more on critical value

https://brainly.com/question/30168469

#SPJ4

--The question is incomplete, answering to the question below--

"Find the critical value, zα/2 that corresponds to the given confidence level 87​%"

230 lbs is approximately equal to 104.3260 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

230 lbs =  0.453592 × 230

Multiply the numbers

= 104.3260 kg ( rounded to four decimal places )

Therefore, 230 lbs is 104.3260 kg

Learn more about conversion factor here

brainly.com/question/23718955

#SPJ4

The value of the exponential equation is A = ( 8/7 ) x ^ -15/2

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = 8 / ( 7√x¹⁵ )   be equation (1)

On simplifying the equation , we get

The value of √x¹⁵ = x ^ 15/2

Now , the equation will be

A = ( 8/7 ) x ^ -15/2

Hence , the exponential equation is A = ( 8/7 ) x ^ -15/2

To learn more about exponents click :

https://brainly.com/question/28966438

#SPJ1

The statements and reasons to complete the two column proof are given in the explanation.

Two triangles will only be similar if on comparing the corresponding length of their sides, there exist some common properties or relations. Though the triangles are similar, but not congruent.

The expected statements and reasons to complete the two column proof are:

      STATEMENT                      REASON

1. LQ II NP                               Given

2. <Q ≅ <N                             Alternate interior Angles

3. <L ≅ <P                              Alternate Interior Angles

4. ΔLMQ ~ ΔPMN                  Two pairs of corresponding angles are equal

Learn more about similar triangles at https://brainly.com/question/8691470

#SPJ1

Yes we can say that 10 mm is a conversion factor because it is equals to 1 cm and that is what conversion factor is.

A millimetre is a unit of measurement smaller than a metre. Because of something called conversion factors, I know that a mm is smaller than a m.

Simply said, a conversion factor is a number that may be multiplied or divided to convert one set of units to another. Hence, when we need to translate 10 millimetres to centimetres, we utilise a conversion factor.

The mm to m conversion factor is:

10 mm = 1 cm

We can simply compute the conversion of 10 mm to m now that we know the conversion factor by multiplying 0.001 by the amount of millimetres we have, which is 10.

10 x 0.1 = 1 cm

Learn more about Conversion factor;

https://brainly.com/question/12103054

#SPJ4

(a) 27 outcomes in the sample space are : (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3), (2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3), (3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) All outcomes in the event that all three members go to the same station are : (1,1,1), (2,2,2), (3,3,3)

(a) The 27 outcomes in the sample space can be represented as ordered triples, where each element corresponds to the station that each family member is assigned to. The possible values for each element are 1, 2, and 3. Therefore, the sample space consists of the following 27 outcomes:

(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3),

(2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3),

(3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) The outcomes in the event that all three members go to the same station can be found by examining the 27 outcomes in the sample space and selecting those outcomes where all three elements are the same. Therefore, the outcomes in the event that all three members go to the same station are:

(1,1,1), (2,2,2), (3,3,3)

In these outcomes, all three family members are assigned to the same station. There are three such outcomes, since each family member can be assigned to any one of the three stations.

To know more on sample space

https://brainly.com/question/30206035

#SPJ4

The given statement about two variables is false. This is because to determine whether the respective two variables are related, we cannot compare two marginal distributions.

A correlation coefficient is used to assess the relationship between the two variables. The letter r is used to represent this coefficient. The r values range from -1 to  +1.

Based on this value, the correlation is classified into two types negative correlation and positive correlation. When the r value is -1, it is referred to as a perfect negative correlation. When the r value is +1, it is referred to as a perfect positive correlation. So to compare the relation of two variables, we require a correlation coefficient, not marginal distribution. Therefore, the given statement is false.

To know more about correlation coefficient:

https://brainly.com/question/29208602

#SPJ4

If the tens digit of a two-digit number is one more than the units digit and the number itself is 6 times the sum of the digits, then the solution is a two-digit number 54.

Let's assume that the units digit of the two-digit number is x. According to the problem statement, the tens digit is one more than the units digit, which means that the tens digit is x + 1. Therefore, the two-digit number can be expressed as 10(x+1) + x, which simplifies to 11x + 10.

The problem also states that the number is 6 times the sum of its digits. The sum of the digits is x + (x + 1) = 2x + 1. Therefore, we can set up an equation:

11x + 10 = 6(2x + 1)

Simplifying the equation, we get:

11x + 10 = 12x + 6

Subtracting 11x from both sides, we get:

10 = x + 6

Subtracting 6 from both sides, we get:

x = 4

Therefore, the units digit is 4, and the tens digit is one more than that, which is 5. The two-digit number is 54. We can check that this is indeed 6 times the sum of its digits:

54 = 6(4 + 5)

54 = 6(9)

54 = 54

To learn more about numbers click on,

https://brainly.com/question/17608141

#SPJ4