The 16 feet distance from Chase to his older brother and the 20 feet distance from his older brother to his younger sister, using Pythagorean, Theorem, indicates that the distance from Chase to his younger sister in the assembly is 12 feet
What is Pythagorean Theorem?Pythagorean Theorem states how the length of the sides of a right triangle are related, that is the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.
The location of Chase, his younger sister, and his older brother forms a right triangle.
The distance from Chase to his older brother = A leg of the right triangle
The distance from Chase to his sister = A second leg of the right triangle
The distance from his older brother to his sister = The hypotenuse side of a right triangle
From the question, we get;
Distance between Chase and his older brother = 16 feet
Distance between Chase's older brother and his sister = 20 feet
According to Pythagorean Theorem, we get;
Distance between Chase and his younger sister = √(20² - 16²) = 12
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Use algebra to show that the product of any two terms in the sequence is also a term in the
sequence.
I have already done A
(a) The first four terms of the geometric sequence are 3, 9, 27, 81.
(b) The product of any two terms of the sequence is present in the sequence.
What is geometric sequence?A geometric sequence is one where each phrase is obtained by multiplying the term before it by the same number.
Formula to find nth term of geometric sequence is aₙ = a₁ rⁿ⁻¹. The common ratio is expressed as the value r.
Given that,
The nth term of the geometric sequence uₙ = 3ⁿ.
(a)
The first term of the sequence u₁ = 3¹
Second term of the sequence u₂ = 3² = 9
Third term of the sequence u₃ = 3³ = 27
And the fourth term of the sequence u₄ = 3⁴ = 81
The four terms of the sequence are 3, 9, 27, 81.
(b)
To prove that product of two term is also present in the sequence.
Product of first two terms = 3 x 3² = 3 x 9 = 27
27 is present in the sequence.
Further, product of next two terms,
9 x 27 = 243 = 3⁵
3⁵ will also present in the sequence.
Therefore, product of any two terms is present in the sequence.
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A shoe store sells sneakers, loafers, and boots in narrow, medium, and wide widths. They are available in sides 6, 6.5 7, 7.5, 8, 8.5, 9, 9.5, 10, and 10.5. Find the number of pairs of shoes available. Then find the probability of selecting a size 8 in medium width sneakers. Is it likely or unlikely the the size would be chosen?
The answer to this Question based on probability is 0.1
What is Probability?
Probability is the measure of the likelihood of a certain event or outcome happening. It is expressed as a number between 0 and 1, where 0 means the outcome or event is impossible and 1 means the outcome or event is certain. Probability can be used to calculate the chances of certain outcomes occurring in a variety of situations. Probability can be used to determine the likelihood of events happening in games of chance, in business and finance decisions, in science and medicine, and in a variety of other contexts. Probability can also be used to help us make decisions and understand the relationships between different events.
to calculate the probability of getting show of size 8 we just need to calculate how many favourable cases are and here we can see it is 1 only
now we will calculate total cases that are 10 here
so we are ready with our answer that probability = 1/10 = 0.1
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Brian opens a new savings account, with an annual interest rate of 3. 5%. If his initial deposit is gbp 3000, write an expression for his savings, s, after t years.
The expression for savings after t years, based on the principle amount and annual interest rate is 3000 + 105t.
The formula to be used for computation of savings is -
Interest = (Principal × Rate of interest × Time)/100
Keep the values in formula -
Interest = (3000 × 3.5 × t)/100
Performing division and multiplication
Interest = 10,500t/100
Performing division on Right Hand Side of the equation to find the interest
Interest = 105t
Now, savings will be sum of amount and the interest earned
Savings = 3000 + 105t
Thus, the savings will be 3000 + 105t.
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1. Your company needs to lease office space in two buildings. The annual cost is $24.75 per square foot in the first building that is near downtown and $17 per square foot in the second building that is located just outside of town. The company has $95,000 budgeted for rent. Write an equation that models the possible amounts of space rented in the buildings.
a) Identify your variables
b) Write your equation in Standard form
c) Solve your equation
d) Write your answer in sentence form.
2. How many square feet of space can be rented in the first building if 2650 square feet are rented in the second?
x²+10x+x+10 what is the answer using grouping
Answer:
Step-by-step explanation:
?
Diagram shows two circles of the same size with centres A and C, touching each other at point B.
ACE is an equilateral triangle.
[Guna/Use =22/7
The circumference of each circle is 66cm and EB = 29.7cm. Find the area, in cm², of the shaded
region. Give the answer correct to three significant figures.
Answer:
Let us label the point where the two circles touch as point B. Since the two circles have the same size and are tangent to each other at point B, the radii of both circles must be equal. Let the radius of the circle be r.
Since triangle ACE is equilateral, all sides of the triangle must be equal in length. Since the circumference of each circle is 66 cm, the length of each side of triangle ACE must be 66/3 = 22 cm.
Since the radius of the circle is tangent to the side of the triangle at point B, the length of line segment EB must be equal to the radius of the circle. Since the length of line segment EB is 29.7 cm, the radius of the circle must be 29.7 cm.
The area of the shaded region can be found by subtracting the area of the smaller circle from the area of the larger circle. The area of a circle with radius r is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since the radius of the smaller circle is 29.7 cm, the area of the smaller circle is 29.7²π = 869.43π cm².
Since the radius of the larger circle is half the length of the side of the triangle, the radius of the larger circle must be 22/2 = 11 cm. The area of the larger circle is therefore 11²π = 121π cm².
The area of the shaded region is therefore 121π - 869.43π = -748.43π cm². Since the area of a region cannot be negative, the answer to the question must be 0 cm². The area of the shaded region is therefore 0 cm².
Find the solutions to x² = 28.
Answer:
[tex]2 \sqrt[]{7} , and -2\sqrt[]{7}[/tex]
Step-by-step explanation:
or:
x=5.29150262…,−5.29150262
a recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. a simulation was conducted that consisted of 50 trials with a population parameter of 0.9. each trial consisted of a sample size of 10. the number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. five possible simulation results are shown. which simulation is the best match to the one described?
In repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time.
By simulation, what do you mean?A simulation is a model that replicates how a current or proposed system functions, offering evidence for decision-making by allowing the testing of various scenarios or process improvements. A more immersive experience can be had by combining this with virtual reality technology.
What accomplishes the simulation?The fundamental goal of simulation is to illuminate the underlying processes that regulate a system's behavior. A system's future behavior can be predicted (forecasted) using simulation, and you can use it to figure out how to influence that behavior in the future.
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A bag contains the same number of each of four different colors of marbles.
A marble is drawn, its color is recorded, and then the marble is placed back
in the bag. This process is repeated until 40 marbles have been drawn. The
table shows the results. For which marble is the experimental probability of
drawing the marble the same as the theoretical probability?
Yellow=12
Red=10
Blue=7
Black=11
Answer: Red.
Step-by-step explanation:
There are 10 marbles of each colour as described here: 'A bag contains the same number of each of four different colors of marbles.' The theoretical probability of drawing any marble of a select colour is 1/4. The red marble was drawn 10 times, making it fit this 1/4 theoretical probability.
5000 people attended a football game. If 25% of the people who attended were teenagers, how many teenagers attended the game?.
The football game was attended by 1250 teenagers out of 5000 people who attended the game.
The number of teenagers who calculated the game can be calculated by finding the percentage of people who were teenagers. The word formula for the calculation will be -
Number of teenagers in the game = 5000 × 25%
Writing the percentage as fraction
Number of teenagers in the game = 5000 × 25/100
Cancelling zero as common in numerator and denominator
Number of teenagers in the game = 50 × 25
Performing multiplication on Right Hand Side of the equation
Number of teenagers in the game = 1250
Hence, there are 1250 teenagers.
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A horse galloped along seven and three sevenths miles of trail. There were hurdles spaced evenly throughout the trail every four sevenths of a mile. How many hurdles did the horse jump?
Answer:
13 Hurdles
Step-by-step explanation:
If a horse galloped along seven and three sevenths miles of trail and hurdles spaced evenly throughout the trail every four sevenths of a mile then there are 13 such hurdles after solving all the fractions.
Given that a horse galloped along seven and three sevenths miles of trail and hurdles spaced evenly throughout the trail every four sevenths of a mile.
We are required to find the number of hurdles. All the values are given in fractions.
Ability of horse to gallop=7+3/7
=(49+3)/7
=52/7
Distance between two hurdles=4/7
Number of hurdles=52/7/4/7
=52*7/4*7
=52/4
=13 hurdles
Hence if a horse galloped along seven and three sevenths miles of trail and hurdles spaced evenly throughout the trail every four sevenths of a mile then there are 13 such hurdles after solving all the fractions.
Is 1 the first square number?
Yes, 1 is the first square number.
What is a square number?
A square number, sometimes known as a perfect square, is an integer that is an integer squared; in other words, it is the result of multiplying an integer by itself. Because it equals 3² and can be represented as 3 *3, the number 9 is an example of a square number.
Given that 1 x 1 equals 1, the initial square number is 1.
Due to the fact that 3 x 3 = 9, the third square number is 9, and so forth. Following are the first fifteen square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, and 225.
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in a test of hypothesis the p-value was 0.24 . if the level of significance is 10 % . what is the potential type of statistical error ?
If the level of significance is 10 %, then the potential type of statistical error is type II error.
What is statical error?
The term "error" (also known as "statistical error") refers to the discrepancy between a value obtained through a data gathering procedure and the population's "actual" value. The data are less representative of the population the higher the inaccuracy.
In the given test,
The p-value = 0.24
Level of significance (a) = 0.10
Here,
0.24 > 0.10
P-value > level of significance
Therefore, We failed to reject the null hypothesis that is actually false
This is type II error,
The type II error occurs when one fails to reject a null hypothesis that is actually false itself.
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An airplane make a 10° angle of elevation from the runway when it take off. The airplane hown i 2,000 feet along the ground from it take-off point
Therefore, by using trigonometry and ratios of trigonometry the height of the airplane is 426 feet.
What is trigonometry?Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometric functions (also known as circular functions) include the cosecant, cosine, cotangent, secant, sine, and tangent.
With this drawing, we can see that this is a right triangle, which can be solved using some trigonometry. To solve the height, we must use the tangent:
for the diagram see the image.
[tex]tanA = \frac{opposite}{adjecent} \\tan (12) = \frac{opposite}{adjecent} \\\frac{0.213}{1} = \frac{height}{2000}\\height = 2000(0.213)\\\\[/tex]
height = 426 feet
Therefore, the height of the airplane is 426 feet.
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A study was conducted of 155 species of mammals worldwide. The
scientists conducting the study found that 28 species could be found
in Europe and 73 species could be found in North America; and of
those, 28 could be found in both continents.
What is the probability of randomly selecting a species of mammal
that is neither found in Europe nor North America? Write your answer
as a fraction.
51.6is the likelihood of the given sample.
The likelihood of choosing is what?A population unit's likelihood of being included in a sample obtained using probability sampling is known as probability of selection. Interpretation, each subgroup of a population is assigned a probability of being chosen in the sample according to the sampling design.P (X) is equal to n/N, where n is the number of favorable outcomes and n is the total number of outcomes that are feasible.(N-n/N-(n-1)). The probability P is given here, along with the sample size n and the population N. The result will be P = n/N if 1-(N-n/n) is now cancelled. Additionally, it is required that a sample have a possibility of being chosen more than once: P = 1-(1-(1/N)) n.Explanation:
P (X) is equal to n/N,
155/3 = 51.6.
The likelihood of choosing at random a mammal species that is not present in either North America or Europe is 51.6.
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51.6 is the likelihood of the given sample.
The likelihood of choosing is what?A population unit's likelihood of being included in a sample obtained using probability sampling is known as probability of selection.
Interpretation, each subgroup of a population is assigned a probability of being chosen in the sample according to the sampling design.
P (X) is equal to n/N, where n is the number of favorable outcomes and n is the total number of outcomes that are feasible.
(N-n/N-(n-1)). The probability P is given here, along with the sample size n and the population N. The result will be P = n/N if 1-(N-n/n) is now cancelled. Additionally, it is required that a sample have a possibility of being chosen more than once: P = 1-(1-(1/N)) n.
P (X) is equal to n/N,
155/3 = 51.6.
The likelihood of choosing at random a mammal species that is not present in either North America or Europe is 51.6.
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PLEASE HELP!! I don’t understand this
jan has four times as many songs on her computer as ian has on his computer. if jan has 516 songs, how many songs does ian have on his computer?
129 many music on his Computer if Jan has 516 when on Jan's computer, there are four times as many songs as there are on Ian's.
Given that,
On Jan's computer, there are four times as many songs as there are on Ian's.
We have to find Ian has how many music on his Computer if Jan has 516.
We know that,
Let x be the number of songs lan has.
Since Jan has 4 times as many songs than lan then multiply x by 4.
Then equate this expression to 516.
4x=516
Divide 4 on both sides
4x/4=516/4
x=129
Therefore, 129 many music on his Computer if Jan has 516 when on Jan's computer, there are four times as many songs as there are on Ian's.
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the number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked. find the constant of proportionality k to 2 decimal places if 675 workers work 3 hours and can produce 11198.25 widgets.
If 675 workers work for 3 hours and can produce 11198.25 widgets then the constant of proportionality is 5.53 .
In the question,
it is given that ,
the number of widgets production varies with the number of workers and the time that they have worked ,
let the number of workers be "w" and
let the number of time they worked be "t" ,
let the number of widgets produced be "n".
So , the equation becomes
n ∝ w × t
n = k × t × w
Substituting the values of w = 675 , t = 3 and n = 11198.25
we get ,
11198.25 = k × ×675 × 3
k = 11198.25/2025
k = 5.53
Therefore , the constant of proportionality is 5.53 .
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5. Two more than a certain number is 15 less than the product of
8
a. Equation:
and the number.
b. Solution:
help?? :,)
Answer:
x = -136
Step-by-step explanation:
x + 2 = 7/8 x -15 Multiply all the way through by 8
8x + 16 = 7x -120 Subtract 7x from both sides
x + 16 = -120 Subtract 16 from both sides
x = -136
factorise fully the following 3x^3 - 9x
The rectangle below has an area of x^2-7x+10x
2
−7x+10x, squared, minus, 7, x, plus, 10 square meters and a width of x-5x−5x, minus, 5 meters.
What expression represents the length of the rectangle?
By using the quadratic equation that can be written with the given information:
x² -7x + 10 = (x - 5)*(x - a)
We will see that the length is:
L = x - 2
How to get the length of the rectangle?Remember that for a rectangle of length L and width W, the area is given by the product:
A = L*W
Here we know that:
The area is: x² -7x + 10
The width is: x -5
The length will be another factor of the quadratic equation, and we know that it should be of the form:
(x - a)
Using the area formula, we will get:
x² -7x + 10 = (x - 5)*(x - a)
Expanding the right side we get:
x² -7x + 10 = x² -5x -ax + 5a
x² -7x + 10 = x² + (-5 - a)*x + 5a
Comparing like terms, we can see that:
-5 - a = -7
5a = 10
The solution of both of these is:
a = 7 - 5 = 2
a = 10/5 = 2
Then the length of the rectangle is:
L = (x - 2)
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call a 33-digit number geometric if it has 33 distinct digits which, when read from left to right, form a geometric sequence. find the difference between the largest and smallest geometric numbers.
The difference between the largest and smallest geometric numbers is 840.
Assume that the largest geometric number starts with a 9.
We know that the common ratio must be a rational of the form k/3 for some integer k, because a whole number should be attained for the 3rd term as well. When k = 1, the number is 931.
When k = 2, the number is 964. When k = 3, we get 999, but the integers must be distinct.
By the same logic, the smallest geometric number is 124.
The largest geometric number is 964 and the smallest is 124. Thus the difference is 964 - 124 = 840.
Hence, the difference between the largest and smallest geometric numbers is 840.
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the function y=2^x+4 is shifted left 10 units what is the new equation of the new function?
The new equation of the function y = 2^x + 4 shifted 10 units to the left is y = 2^(x-10) + 4
What is translation?translation moves a shape left, right, up, or down but does not turn. The translated shapes (or the image) appear to be the same size as the original shape, indicating that they are congruent.
Since the function is shifted 10 units to the left, it means the x coordinate of the function is reduced by 10. making the exponent (x) to become (x - 10)
So the function's new equation is y = 2^(x-10) + 4
In conclusion, the new equation is y = 2^(x-10) + 4
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Which pair of triangles can be proven congruent using the hypotenuse-leg theorem?.
Answer: hypotenuse and leg of one right triangle
Step-by-step explanation:
The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
find the slope:(-8,-3) and (-2,1)
Answer:
2/3
Step-by-step explanation:
To find slope, we have:
change in y /(over) change in x
1-(-3) = 4, and -2-(-8) = 6, so 4/6 = 2/3, which is our answer.
our data analytics team often surveys clients to get their feedback. if you were on the team, how would you ensure the sample is representative of the population as a whole?
To ensure the sample is representative of the population as a whole, try to use some random samples.
What do you mean by sample?A sample refers to a small quantity that is examined to get the knowledge of how the whole product/population will be.
Now, we need feedback from our clients. To ensure that our sample is representative of the population as a whole, we should include clients with different attributes.
Like, choosing 10 clients all living in the same place, same gender, and same age group will be the worse sample.
The best way to do this is to select samples randomly, ensuring that our sample includes people with different ages, gender, height, disabilities(if any) and statuses, etc.
So, A randomized sample is the best for ensuring that the sample is representative of the population as a whole.
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the buses at the zoo express bus company depart as scheduled 80% of the time. the buses depart and arrive as scheduled 68% of the time. what is the probability that a zoomy express bus arrives as scheduled if it departs as scheduled?
The probability that a zoomy express bus arrives as schedule if it departs as schedule is 0.85.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty. An event's likelihood of occurring increases with its probability.
now , let D = depart on time and A = arrives on time
given that ,
P(D) = 80% = 0.80
P(A∩D) = 68% = 0.68
P(A/D) = [tex]\frac{0.68}{0.80}[/tex]
= [tex]\frac{68}{80}[/tex]
= [tex]\frac{17}{20}[/tex]
= 0.85
Hence , the probability is 0.85.
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evaluate the expression for the given value of the variable. 56 + 1/6r r= 1/2
Answer:
337 = 3
Step-by-step explanation:
Multiply by LCM
337 = 3
and the sides are not equal so I guess there is no answer but
337 = 3
Solve.
(3√3)^−x+1 =1/3⋅27^x−5
The required simplified value of the given expression is x = 0.67.
Given that,
To determine the simplified solution of the expression, [tex]\left(3\sqrt{3}\right)^{-x}+1=\frac{1}{3}\left[27^x-5\right][/tex]
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
In order to simplify the given expression, we have to transpose the number across the equal sign as exponents numbers tobe either side and constant on the other side.
[tex]=\left(3\sqrt{3}\right)^{-x}+1=\frac{1}{3}\left[27^x-5\right]\\=\left(\left(3\sqrt{3}\right)^x\right)^{-1}+1=\frac{1}{3}\left[\left(\left(3\sqrt{3}\right)^x\right)^2-5\right]\\= 2 / 3\\= 0.67[/tex]
Thus, the required simplified value of the given expression is x = 0.67.
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if f(x) = 3x - 4 and g(x) = x^2, find the value of f(3) - g(2)
Answer:
[tex]\huge\boxed{\sf 1}[/tex]
Step-by-step explanation:
Given functions:f(x) = 3x - 4
Put x = 3
f(3) = 3(3) - 4
f(3) = 9 - 4
f(3) = 5 ------------------(1)Also,
g(x) = x²
Put x = 2
g(2) = (2)²
g(2) = 4 --------------(2)Subtract Eq. (2) from Eq. (1)
f(3) - g(2):= 5 - 4
= 1[tex]\rule[225]{225}{2}[/tex]
Answer:
F(3) -g(2) = 1
Step-by-step explanation:
F(3)= 3(3) -4= 5
g(2)= [tex]2^{2}[/tex] = 4
f(3) -g(2)= 5-4 =1