Answer:
[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]
Step-by-step explanation:
a basketball court is a rectangle, therefore its area is length x width.
the length given is (x+16)
the width given is (x-2)
substitute into the rectangular area equation:
length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32
specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].
therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].
i hope that helps :)
Answer:
therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].
Step-by-step explanation:
Write the name of each of these polygons
Answer:
In geometry, a polygon can be defined as a flat or
plane, two-dimensional closed shape bounded with
straight sides. It does not have curved sides. The
sides of a polygon are also called its edges. The
points where two sides meet are the vertices (or
corners) of a polygon
1. polygon with four sides is called a Quadrilateral
2. polygon with six sides is called hexagon
3. polygon with five sides is called pentagon
Hope this helps?
What is the ratio of 4 red pens to 7 black pens
Answer:
There could be 12 red pens and 21 black pens
Step-by-step explanation:
7 time a number , increased by 4
Answer:
7 times a number increased by 4 times the number
Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
7 times a number: 7x
4 times the number: 4x
The phrase increased by means we add 4x to 7x:
7x + 4x
Simplifying, we get: (7 + 4)x
11x
Step-by-step explanation:
ccording to the Australian Bureau of Agricultural and Resource Economics, Queensland egg farmers produce millions of eggs every year. Suppose egg production per year in Queensland is normally distributed, with a standard deviation of 83 million eggs. If during only 3% of the years Queensland egg farmers produce more than 2,655 million eggs, what is the mean egg production by Queensland farmers (in million)?
Round your answer to 1 decimal place.
The standard deviation of 83 million eggs and 2,655 millions eggs represent that of 3% of the farmers, of the production that is normally distributed, indicates that the mean egg production by Queensland farmers is about 2498.1 million eggs.
What is a normal distribution?A normal distribution is a probability distribution such that the values of the distribution are symmetrical around the mean value of the distribution.
The standard deviation, σ = 83 million eggs
The percentage of farmers that produce more than 2,655 million eggs, x = 3%
The formula for the z-score is; [tex]Z = \dfrac{x - \mu}{\sigma}[/tex]
Therefore, we get;
[tex]Z = \dfrac{2655 - \mu}{83}[/tex]
From the z-score table for P(Z > Z₁), where Z₁ is the z-score corresponding to Φ(1 - 0.03) = Φ(0.97)
The z-value corresponding to Φ(0.97) is about 1.89
Therefore;
[tex]Z = \dfrac{2655 - \mu}{83} \approx 1.89[/tex]
83 × 1.89 ≈ 2655 - μ
μ ≈ 2655 - 83 × 1.89 = 2498.1
The mean egg production by Queensland farmers is about 2498.1 million eggs per year
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Please help me please
Two triangles are shown.
Complete the statement to prove that triangle
ABD is similar to triangle ECD. Fill in the blank
to complete the statement.
∠ ABD and ∠ ECD are _____
and angle ___________ is shared by both triangles,
therefore the figures are __________
by ________ __________ __________
On solving the provided question, we can say that - the given triangles ECD and triangle PQR
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
here,
EC = PQ
CD = PR
ED = QR
therefore both triangles are similar by SSS property
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Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest, compounded annually. What is the balance after 8 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Balance after 8 years is $2,306.86 at an interest rate of 15 % compounded yearly.
What is compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.
given, Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest
from the general formula of compound interest
A = [tex]P(1 + r/n)^{nt}[/tex]
where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Given, P = 700$
r = 15%
t = 8 years
A = 700(1 + 15/100)⁸
A = 2306.86$
Therefore, At a 15% annual compounded interest rate, the remaining balance after 8 years is $2,306.86.
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Peter is building a ramp at his home. He wants to build it 11 inches high with aa 60 inch base. How long will the ramp be that Peter is building? Round to the 10ths if needed.
Explanation:
You have a right triangle with legs of 11 and 60. The hypotenuse is unknown.
Use the pythagorean theorem to find the hypotenuse.
[tex]a^2 + b^2 = c^2\\\\11^2 + 60^2 = c^2\\\\121 + 3600 = c^2\\\\3721 = c^2\\\\c^2 = 3721\\\\c = \sqrt{3721}\\\\c = 61\\\\[/tex]
The ramp is exactly 61 inches long.
The volume of
a refrigerator, in cubic centimeters, is given
by the function V(x) = (x)(x + 1)(x – 2). Write a
new function for the volume of the refrigerator
in cubic millimeters if x is in centimeters.
The newly rewritten function expression of V(x) is V(x) = (x)(x + 1)(x – 2)/1000
How to rewrite the function expression?From the question, we have the following parameters that can be used in our computation:
A function expression
The function expression is given as
V(x) = (x)(x + 1)(x – 2)
Where if x is in centimeters and V(x) is in cubic centimeters
The new function for the volume of the refrigerator is stated to be in cubic millimeters
Using the above as a guide, we have the following:
1 cubic centimeters = 1000 cubic millimeters
So, we have
V(x) = (x)(x + 1)(x – 2)
1 cubic centimeters = 1000 cubic millimeters
Cross multiply
V(x) * 1000 = 1* (x)(x + 1)(x – 2)
Divide both sides by 1000
V(x) = (x)(x + 1)(x – 2)/1000
Hence, the function is V(x) = (x)(x + 1)(x – 2)/1000
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Help me I do t know how to do this
Show that 100 divided by 20 is 5, using at least five daily life examples.
Answer:
true
Explanation
1. if a man has a hundred apples and like to share between 20 men. this has to be equal.
5 to 1man.
my mom will kill me please help
If the perimeter of the triangle is 64 units, then the length of the side PR is 24 units.
What is a Triangle?This is referred to as a three-sided polygon that consists of three edges and three vertices and the longest side is referred to as the hypotenuse.
The perimeter of a triangle is the sum of all the sides which is:
P = a + b + c
64 = 3x +4x - 1 + x + 1
64 = 8x
x = 64/8 = 8 units
Therefore the length of side PR is :
3x = 3 (8) = 24 units.
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If f(x) = 2x4 - 3x + 3, then what is the remainder when f(x) is divided by x - 1?
The remainder on dividing 2x⁴-3x+3 by x-1 is 2
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: 2x⁴-3x+3 by x-1
The remainder theorem states that when a polynomial p(x) is divided by (x - a), then the remainder = f(a)
∴ The remainder would is f(1) = 2×1-3+3
=2
Hence, The remainder on dividing 2x⁴-3x+3 by x-1 is 2
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Which integer in the set has the greatest value (4, -4, -3, 3)?
A. 4
B. 3
C. -3
D. -4
Answer:
A. 4
Step-by-step explanation:
4 is a positive number which is larger to 3 and bigger than negative numbers.
Answer:
Step-by-step explanation:
i\
i \
i \
i /
i /
In a certain chemical, the ratio of zinc to copper is 3 to 14. A jar of the chemical contains 686 grams of copper. How many grams of zinc does it contain?
Answer:
Ratios and fractions are connected. A ratio of 3 to 14 is the same thing as 3/14. Multiply 686 by 3/14. You will get 147. That is your amount of zinc. If we simplify 147/686, or 147:686, we get 3:14 confirming our answer.
Answer:
147 grams of zinc-----------------------------------
Let the amount of zinc be x. Then we have equal ratios:
3/14 = x/686Solve it for x:
x = 686*3/14x = 147You want to buy a $135,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at
6.1% interest for the rest.
How much is the loan amount going to be?
What will your monthly payments be?
How much total interest do you pay?
Suppose you want to pay off the loan in 15 years rather than 30. What will your monthly payment be?
On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is 500
obtained is 400
so, percentage - 400/500 X 100 = 80%
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Explain what an exponential form is but leveled down for high schoolers
The required exponential function is given as y = aˣ where the value of a should be positive always.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
Since from the above definition exponential function is given as y = aˣ,
This shows the exponential increase and decrease, by means of exponential increase and decrease, a sudden in increase and sudden decrease of function as the value of a varies, see in the graph after the answer. And the value of an always remains positive.
Thus, the required exponential function is given as y = aˣ where the value of a should be positive always.
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Xavier buys 4 snacks and 2 cans of
soda. Each snack costs $1.25, and each
can of soda costs S dollars. Xavier's
total for the snacks and soda was $8.
How much did each can of soda cost
Total cost is the sum of all expenses incurred to produce a particular type of product. The answer is $1.50.
What is the definition of total cost?Total cost is the sum of all expenses incurred to produce a specific kind of output. Financial reporting, when overhead costs must be allocated to specific assets, is where the total cost approach is more useful from an accounting standpoint.
$8 was spent in total.
Xavier bought four $1.25 snacks.
4 x 1.25 = $5
The 2 cans cost $3 because 5 + 3 = 8, and we know how much the snacks cost ($5), making the total cost ($8).
Each can cost $1.50 because, if the price of the two cans was $3, we would have to divide it by two to get the price of the second can, which comes out to be $1.50. As a result, each can was $1.50.
Therefore, the answer is $1.50.
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A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?
tysm ;-;
The kind of sequence that you will obtain when you list the number of tickets sold over time is given as follows:
A geometric sequence.
How to classify the sequence?A sequence can be classified as either arithmetic or geometric, as follows:
Arithmetic sequence: the difference between consecutive terms is constant.Geometric sequence: the ratio between consecutive terms is constant.If none of these statements is true, then the function is neither arithmetic or geometric.
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before, which means that there is a constant ratio of 7 between the amounts of tickets sold each year, and thus this sequence is a geometric sequence.
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Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and 51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
If we compare the given values then we can find that database B is more likely to have a smaller standard deviation.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given that the values in database A are 0 from 100 and have a mean of 50 and Database B has entries from 49 to 51 and also has a mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding the mean. The square of a standard deviation is known as a variance.
Database A has values from 0 to 100 and has a mean of 50. Because the values are somewhat very larger than 50 and database B has values from 49 to 51, there are more chances that the standard deviation of database B will have a smaller value than the standard deviation of database A.
Hence if we compare the given values then we can find that database B is more likely to have a smaller standard deviation.
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Read the situations in the table below. Then drag a graph and equation to represent each situation. Indicate whether each of the relationships is proportional or non-proportional.
The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
What are linear equations?
Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, graph 1 varies 4 times the x value every time there is an increase of 1 in the x-axis and in graph 2 it is a linear equation with intercept at 4 and thus the graph increases with +4 and A proportional relationship exists between two values x and y when they can be expressed in the general form y = kx,
Hence, The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
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what is reference angle for 7pi/4
The reference angle of 7pi/4 is pi/4
What is reference angle?The acute angle formed by the terminal arm or side and the x-axis is known as the reference angle.
There is always a positive reference angle. The reference angle is, in other words, the angle formed by the terminal side and the x-axis. It must always be positive and less than 90 degrees.
considering angle 7 pi/4, the angle is pi/4 away from 2 pi.
7 pi/4 + pi/4 = 8 pi/4 = 2 pi
We can therefore conclude that 7 pi/4 is an angle on the third quadrant and the reference angle is pi/4.
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1 Chinese yuan= $0.14567. How many Chinese yuan can u buy for a dollar
The Chinese yuan you can buy for a dollar is 6.86483 Chinese yuan
How to determine how many Chinese yuan you can buy for a dollarFrom the question, we have the following parameters that can be used in our computation:
1 Chinese yuan= $0.14567
Divide both sides of the equation by 0.14567
So, we have the following representation
1/0.14567 Chinese yuan= $0.14567/0.14567
Evaluate the quotient
1/0.14567 Chinese yuan= $1
Evaluate the other quotient
6.86483 Chinese yuan= $1
This means that
$1 = 6.86483 Chinese yuan
Hence, you can buy 6.86483 Chinese yuan for $1
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A linear relationship is given in the table.
X-2
y-12-7-238
What is the slope of the relationship?
05
0-5
O
-10 12
01/130
5
0_1
5
The slope of the relation is 1/4
What is the slope of the table?You should know that slope is the rate of change of y with respect to x. slope is denoted by change in y over change in x
The table of values is given as:
x −2 −1 0 1 2
y −13 −9 −5 −1 3
The slope is calculated as:
Slope = y₂ - y₁/x₂ - x₁
So, we have
Slope = 2 - 1/3 + 1
Evaluate the like terms
Slope = 1/4
In conclusion, the slope of the relation is 1/4
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FIND C.
Give your answer in the simplest form
Answer:
3
Step-by-step explanation:
[tex] \sin(45) = \frac{a}{7 \sqrt{2} } [/tex]
[tex]a = 7[/tex]
[tex] \tan(30) = \frac{7}{c} [/tex]
[tex]c = 7 \sqrt{ 3} [/tex]
therefore 3 is required in the green box
each minute your heart pumps 1.5 gallons of blood around your body. How many pints of blood will your heart pump in a day? PLEASE HELP ME
Answer:
So there are 60 minutes in an hour, and since there are 24 hours in a day you will multiply 60 by 24:
60 * 24 = 1440.
That multiplied by 1.5 is 2160, so that would be your answer.
Step-by-step explanation:
Hope it helps! =D
Rami's glass is 1/2 full. Will's glass is 3/8 full. Whose glass is fuller? How much fuller is it?
Rami's glass is fuller than Will's glass by 1/8
How to determine whose glass is fuller?From the question, we have the following parameters that can be used in our computation:
Rami's glass is 1/2 full. Will's glass is 3/8 full.
Convert the fractions to decimal
This gives
Rami's glass is 0.5 full. Will's glass is 0.375 full.
0.5 is greater than 0.375
So, Rami's glass is fuller
How much fuller is it?To do this, we calculate the difference
So, we have
Difference = 0.5 - 0.375
Evaluate
Difference = 0.125
Rewrite as
Difference = 1/8
Hence, it is 1/8 fuller
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Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed
1 meter = 3.28 feet
1 Liter = 0.26 gallons
1 kilogram = 2.20 pounds
0.828 oz=________cg
Using the conversion between metric and U.S systems the value of 0.828oz is 2347.34 cg.
What is metric conversion?A system of measurements is called the metric system. It is employed in calculations and research across the globe. Some examples of metric system are distance in lengths, weights in grams, volume in milliliters and much more.
The conversion between ounces (oz) into centigram (cg) is given as follows:
1 oz = 2834.95
To convert 0.828 oz into centigram we need to multiply the value 0.828 oz with 2834.95 as follows:
(0.828) (2834.95)
2347.35
Hence the value of 0.828 oz is 2347.34 cg according to the conversion from metric to US system.
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What is the greatest common factor of 20 and 65
Answer:
5
Step-by-step explanation:
Answer:I believe it would be 5
Step-by-step explanation:
because if you do it on a table chart you reach five first as the same number
gretchen buys a sweater at a clearance sale for $35.74. The original price of the sweater was $59.99. Find the percent discount.
Answer:
59.5765%
Step-by-step explanation:
$35.74/$59.99