The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The standard equation of a circle is:
[tex]x^{2} +y^{2} +2gx+2fy+c=0[/tex]
Given circle equation:
[tex]x^{2} +y^{2} -2x-8=0[/tex]
on comparing
2gx = -2x
g = -2
2fy = 0
f = 0
Center = (2,0)
radius r = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]
= [tex]\sqrt{9}[/tex]
r = 3 units.
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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7 times some number is 28. What is the number?
Equation:
Solution:
Answer:
4
Step-by-step explanation:
aint no way...this is literally 1st grade math...anyways
7(x)=28
divide both sides by 7
x=4
Danielle cecils driver rating factor is 1.60 and her car is in age group d and insurance rating group d. She wants 100/300 bodily injury and $50000 property damage coverage a)anual base premium B) anual premmium
a. The annual base premium when Danielle cecils driver rating factor is 1.60 and her car is in age group is $709.
b. The annual premium is $1134.40
What is a premium?It should be noted that the annual premium simply refers to the amount of premium that's paid yearly by the entity. The insurance company has premium payment options for the clients.
The annual base premium will be:
= Liability premium + Collision premium + Comprehensive premium
= $383 + $240 + $86
= $709
The annual premium will be:
= Annual base premium × Driver rating factor
= $709 × 1.60
= $1134.40
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Given that f(x) = x² 13x + 30 and
g(x)= x-3, find f(x) · g(x) and
express the result as a polynomial in simplest form.
The simplest polynomial form of f(x)×g(x) is x³ - 16x² + 69x - 90.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, makeup polynomials. For instance, the polynomial 3x+2x-5: A description of polynomials.So, f(x) × g(x):
Calculate as follows:
Therefore, the simplest polynomial form of f(x)×g(x) is x³ - 16x² + 69x - 90.
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accounts recivable of 88000 and accounts payable of 39000 and has revenues of 121000 and expenses of 83000 what is the companies net income
The required net income of the companies is given as 49,000.
Given that,
Accounts receivable of 88000 and accounts payable of 39000 and have revenues of 121000 and expenses of 83000 what is the company's net income is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Total income = 88000 + 121000 = 209000
Total outflow = 39000 + 83000 = 122000
Net income = 209000 - 122000 = 49000
Thus, the required net income of the companies is given as 49,000.
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What is your country name?
Select all true statements (pick 3)
A. ∠3 ≅ ∠2 because they are alternate interior angles.
B. m∠1 + m∠3 = 180 because they form a straight angle.
C. ∠3 ≅ ∠6 because they are alternate interior angles.
D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.
E. ∠1 ≅ ∠3 because they are vertical angles.
Examining the figure, the correct options are
B. m∠1 + m∠3 = 180 because they form a straight angle.C. ∠3 ≅ ∠6 because they are alternate interior angles.D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.What are congruent angles?Two angles are said to be congruent when they are equal to each. The symbol to represent congruency is ≅
The following angles are congruent in the figure
∠3 ≅ ∠6 alternate interior angles.∠2 ≅ ∠6 corresponding anglesWhen are corresponding angles said to be equal ?Corresponding angles refers to angles that are in a position that are in matching position to another angle.
Corresponding angles are said to be equal when there are parallel lines intersected across by a line called transversal line.
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3/5 - 1/3 simplified
Answer:
4/15
Step-by-step explanation:
[tex]\frac{3}{5}=\frac{9}{15} \\ \\ \frac{1}{3}=\frac{5}{15} \\ \\ \frac{3}{5}-\frac{1}{3}=\frac{9}{15}-\frac{5}{15}=\frac{4}{15}[/tex]
|y + 4| < 1
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.
What is an inequality?An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Less than or equal to (≤).Greater than (>).Less than (<).Adding -1 to both sides of the inequality, we have:
|y + 4| + (-1) < 1 + (-1)
|y + 4| - 1 < 0
Evaluating the absolute value function, we have the following:
y + 4 < ±1
For the positive interval, we have:
y < -4 + 1
y < -3
For the negative interval, we have:
y < -4 - 1
y < -5
Finally, we would express the solution to this inequality as an interval as follows:
-5 < y < -3.
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Complete Question:
What is a solution to this inequality |y + 4| < 1?
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
In which of these cases should the mean be used
write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation (0,0) y=-3x+2
Please solve I do not understand it
The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.
The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as
[tex](\frac{1}{4^{-3 } } )^{2}[/tex]
What is expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)
Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.
[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]
using law of indices,
[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]
4⁻⁶ = 1 / 4⁶ = 1 / 4096
Hence,
1 / 4096 = 0.00024414062
Therefore, the value is less than 1.
Let's change one sign to make the expression greater than 1.
Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]
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Which answer choice represents the difference of 20 and 3 times a number?
The difference of 20 and 3 times a number x is represented by 20 - 3x , the correct option is (c) .
In the question ,
it is given that
the number is x ,
we have to find the expression , that represents the difference of 20 and 3 times a number .
three times the number x is denoted by 3x .
and the difference of 20 and three times the number x is 20 - 3x .
the expression is (20 - 3x).
Therefore , The difference of 20 and 3 times a number x is represented by 20 - 3x , the correct option is (c) 20 - 3x .
The given question is incomplete , the complete question is
Which answer choice represents the difference of 20 and 3 times a number x ?
(a) 3x + 20
(b) 20(3x)
(c) 20 – 3x
(d) (20 · 3)x
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If 5/11 of the class are girls, what is the ratio of girls to boys?
Answer:
5:6
Step-by-step explanation:
The entire class is 11/11.
Girls: 5/11 of the class.
Boys: 11/11 - 5/11 = 6/11
Ratio of girls to boys:
5/11 / 6/11 = 5/11 × 11/6 = 5/6
Answer: 5:6
step by step explanation to-4x = -x + 3
The value of x is -1 for equation -4x = -x + 3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -4x = -x + 3
In the given equation minus four times of x equal to minus x plus three
x is the variable
Plus and minus are operators
-4x = -x + 3
Take the variables to one sides
Add +x on both sides
-4x+x=-x+x+3
-3x=3
Divide both sides by -3
x=-1
Hence, the value of x is -1 for equation -4x = -x + 3
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Evaluate (6x+3y)-z^(2)÷(2x) when x=-3,y=4,z=-6
24.
Step-by-step explanation:1. Write the expression.[tex](6x+3y)-\frac{z^{2}}{(2x)}[/tex]
2. Substitute the variables by the respective given value using parenthesis.[tex](6(3)+3(4))-\frac{(6)^{2}}{(2(3))}[/tex]
3. Simplify the expression by applying the hierarchy or mathematical operations.a) Solve parenthesis.
[tex](18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}[/tex]
b) Solve the exponent.
[tex]30-\frac{36}{6}[/tex]
c) Divide.
[tex]30-6[/tex]
d) Subtract.
[tex]24.[/tex]
Glass cases how many gumballs are in the gumball machine one student guesses 456 counting it was determined that they were actually 408 gumballs in the machine what is the percent error of the guess
According to the solving the percent error = 11.764%
What does "percent mistake" mean?The percent error is the distinction between the estimated value and the real value in relation to the actual value. In those other words, the relative error is multiplied by 100 to calculate the percent error.
What does a high percent error rate mean?The difference between an approximate number and an exact value is measured in percent error. The bigger the percentage error, the further your estimated value deviates from the known value; conversely, the smaller the percentage error, more closer your approximation to the true value.
According to the given data:Actual value = 408
Expected value = 456
We know that the percent error :
= (expected value - actual value)/actual value.
= (456 - 408)/ 408
= 48/408
= 11.764
= 11.764%
According to the solving the percent error = 11.764%
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i need the answers to these
Required values are to be put in blank space,
a. 99
b. 10
c. 5
after using logarithmic properties.
What is logarithm?The other technique to write exponents in mathematics is using logarithms. A numbers base based logarithms is equal to other number. A logarithm performs exponentiation's exact opposite function
For example:
If 10² = 100 then log₁₀¹⁰⁰ = 2.
Some logarithmic properties used are:
logₐˣ + logₐⁿ = logₐˣⁿ logₐˣ - logₐⁿ = logₐ[tex]^{x/n}[/tex] logₐ⁽ˣ⁾ⁿ = n logₐˣAll of the questions are based on simple logarithmic properties:
a. In this properties used are,
logₐˣ + logₐⁿ = logₐˣⁿ
log₅⁹ + log₅¹¹ = ?
comparing with general form, we get
log₅⁹ + log₅¹¹ = log₅⁹⁹
b. In this properties used are,
logₐˣ - logₐⁿ = logₐ[tex]^{x/n}[/tex]
? - log₉⁷ = log₉[tex]^{10/7}[/tex]
comparing with general form, we get
log₉¹⁰ - log₉⁷ = log₉[tex]^{10/7}[/tex]
c. In this properties used are,
logₐ⁽ˣ⁾ⁿ = n logₐˣ
log₂[tex]^{1/25}[/tex] = log₂⁽[tex]^{1/5}[/tex]⁾² = -2 log₂⁽⁵⁾
Comparing with general form, we get
log₂[tex]^{1/25}[/tex] = -2log₂⁵
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3/5 of a fruit punch is orange juice.
What percentage of the fruit punch is orange juice?
60% of the fruit punch is orange juice.
In this question, we have been given 3/5 of a fruit punch is orange juice.
We need to find the percentage of the fruit punch is orange juice.
3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.
Using the percentage formula,
3/5 * 100
= 0.6 * 100
= 60%
Therefore, 60% of the fruit punch is orange juice.
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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.
As given in the question,
Ratio of orange juice in the given fruit juice = 3/5
From the given ratio it indicates out of 5 fruits 3 are orange
Percentage of fruit punch is orange juice in the given juice is equal to
= ( 3 / 5 ) × 100
= ( 3 × 100 ) / 5
= 300 / 5
= 60%
60% of the fruit punch is orange juice.
Therefore, for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.
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Find the rectangular coordinates of the point with the polar coordinates (-7,5 π/3)
Rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2 by using the relation between rectangular and polar coordinates
What do you mean by rectangular coordinates?
Rectangular coordinates, commonly known as cartesian coordinates, are a way to represent graphs and show where points are located on a two-dimensional surface or in three-dimensional space.
The origin is the intersection of the two perpendicular axes that make up the Cartesian plane.
The xy plane is another name for the Cartesian plane.
Given polar coordinates are (-7,5π/3)
To change polar coordinates to recatngular coordinate use
x = rcosθ , y = rsinθ
here r = -7 and θ = 5π/3
x = -7cos5π/3 = -7 × 1/2 = -7/2 = -3.5
y = -7sin5π/3 = -7 × -[tex]\sqrt{3}[/tex]/2 = 7[tex]\sqrt{3}[/tex]/2
Therefore, rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2
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A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size required?
The way the decrease in confidence affect the sample size required is: A. Decreasing the confidence level decreases the sample size needed.
How to find the sample size ?Using this formula to find the decrease in sample size
n = [zs/E]^2
Where:
n = Sample size
zs = z-score
E= margin of error
Confidence coefficient for 99% = 2.58
Hence,
2.58 × 13.8/sqrt(n) = 0.04
2.598 × 13.4 /0.04 = sqrt(n)
( 2.598× 13.8 /0.04)^2 = n
n=803,371.6
So,
Confidence coefficient for 90% = 1.64
n= (1.64× 13.8/0.04)^2
n =320,129.64
Therefore the correct option is A.
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The complete question is:
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size required?
How does the decrease in confidence affect the sample size required
A. Decreasing the confidence level decreases the sample size needed.
B. The sample size is the same for all levels of confidence.
C. Decreasing the confidence level increases the sample size needed.
Given f(x) = −2x^2 + 5, evaluate f(4)
Responses
The composition f(4) has a value of -27
How to evaluate the function composition?The definition of the functions is given as
f(x) = -2x^2 + 5
Rewrite the above function properly
So, we have the following representation
f(x) = -2x² + 5
To find the function f(4), we set the value of x in the equation f(x) = -2x² + 5
This is represented by
Calculate f(x), when x = 4
Substitute 4 for x in the equation f(x) = -2x² + 5
So, we have the following equation
f(4) = -2(4)² + 5
Evaluate the exponents
This gives
f(4) = -2 * 16 + 5
Evaluate the products
This gives
f(4) = -32 + 5
Evaluate the sum
f(4) = -27
Hence, the value of the function is -27
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The price of a toy usually costing £50 is increased to £65
Work out the percentage increase.
Answer:
[tex]\frac{50}{50\\}[/tex] [tex]= \frac{65}{50}[/tex]
Now cross-multiply
Let p represent the percentage
50(50) = 50(65) ; 2500p = 3250
now divide 2500 on both sides to find p
2500p/2500 and 3250/2500
p = 1.3 ; percentage change is equal to %1.3 increase
A client is to receive 1,800 mL of fluid during a 24-hour period. The client is to receive 3/4 of the fluid between 7 AM and 10 PM. Calculate how many mL the client will drink during that time
Answer:
1350 ml
Step-by-step explanation:
(1800 : 4) * 3
450 * 3
1350 ml
A computer routine selects one of the integers 1, 2, 3, 4, 5 at random and replicates the process a total of 100 times. Let S denote the sum of the 100 numbers selected. Calculate the approximate probability that S assumes a value between 280 and 320 inclusive.
Probability that S assumes a value between 280 and 320 inclusive is 0.853.
S = Σ[tex]X_{i}[/tex] where [tex]X_{i}[/tex] has a uniform distribution on 1, 2, 3, 4, 5, with mean 3 and variance (25 – 1)/12 = 2 (result known, or calculated via E[[tex]X^{2}[/tex]] = 11, or from book of formulae, p10, with a = 1, b = 5, h = 1).
So S ~ N(300, 200) approximately.
P(280 ≤ S ≤ 320) = [tex]P(\frac{279.5-300}{\sqrt{200} } < Z < \frac{320.5-300}{\sqrt{200} })[/tex]
= [tex]P(-1.450 < Z < 1.450)[/tex]
= 0.853.
Hence, probability is 0.853.
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Calculate total of (A) current assets, (B) plant assets, and (C) stockholders' equity from these selected titles: Cash $7,500, Common Stock $30,000, Retained Earnings $51,000, Prepaid Rent $12,000, Accounts Payable $1,900, Accounts Receivable $6,000, Merchandise Inventory $19,000, Land $16,000, Building $11,000. (Enter your answers as a whole dollar amount.)
The value of the current assets is $44500.
Plants asset = $27000
Equity = $81000
How to calculate the current assets?The value of the current asset will be:
Cash $7,500
Prepaid Rent $12,000
Accounts Receivable $6,000
Merchandise Inventory $19,000,
Current asset = $44500
Plant assets will be:
Land $16,000
Building $11,000.
Plant asset = $16000 + $11000 = $27000
Stockholders equity will be:
Common stock = $30000
Retained earnings = $51000
Equity = $81000
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Which letter(s) on the diagram below represents a radius of the circle?
Answer: AB
Step-by-step explanation:
Radius of a circle is defined as the distance from the center of a circle to its perimeter (the edge). Line AB is the only choice that meets this definition. CE is the diameter of the circle.
Answer:
AB
Step-by-step explanation:
radius goes in half the circle
1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
The equation of the relationship is 2x + 4y = 45 and the graph is attached
How to sketch the graph?From the question, we have the following parameters:
Amount = $45Price of each bucket of popcorn = $4Price of each drink = Half the price of each bucket of popcornThis means that
Price of each drink = Half $4
Evaluate
Price of each drink = $2
Represent the number of drinks with x and the number of bucket of popcorn with y
So, we have the following representation
Total amount of popcorn + Total amount of drinks = Total amount
This gives
2x + 4y = 45
Next, we sketch the graph
See attachment for the graph of the equation
The explanation of the graphThe graph is represented by a straight line
This means that it is a linear equation
Also, the graph touches the axes at (0, 11.25) and (22.5, 0)
This means that the highest number of drinks and buckets are 11.25 and 22.5 respectively
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Marissa has a savings account with $48 in it that earns 2% simple
interest per year.
How much money, to the nearest penny, will Marissa have in 7 years?
Give your answer in dollars.
Marissa will have $720 in 7 years when she has $48 in her saving account that earns 2% simple interest per year.
What is simple interest?Simple interest is a quick and simple approach to figuring out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.S.I. = P R T,where
P = Principal, R = Rate of Interest in% per annum, and T = Time periodThe interest rate is expressed as r/100 and is expressed as a percentage or r%.Principal: The principal is the sum that was first invested or borrowed from the bank. P stands for the principal.Rate: Rate is the interest rate at which the principal sum is granted to someone for a specific period of time; examples of rate interest are 5%, 10%, and 13%. R stands for the interest rate.Time: The amount of time that the principal is given to someone. T represents time.Amount: When a borrower repays a bank loan, the term "Amount" refers to the sum of the principal borrowed plus the interest paid.Amount = Principal + Simple Interest or A = P(1 + RT)Calculation
From, A = P(1 + RT)
where, p = $48
R = 2%
T= 7 years
A = 48(1 + 2*7)
A = $720
Hence, Marissa will have $720 in her bank account after 7 years.
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6x-5=6x+5 pls help me fast
Answer:
No solution
Step-by-step explanation:
6x - 5 = 6x + 5
6x = 6x + 10
0 = 10
0 cannot be equal to 10 at anytime, so this equation has no solution
Answer: No solution.
Step-by-step explanation:
Given:
6x - 5 = 6x + 5
Add 5 to both sides of the equation:
6x = 6x + 10
Subtract 6x from both sides of the equation
0 ≠ 10
Since 0 does not equal 10, there is no solution to this equation.
Which graph could be used to find the distance between the points (-3,-13) and (11, 9)?
The distance between the two point of the line segment is 26.07
Distance Between Two PointsDistance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates
d = √((x₂ – x₁)² + (y₂ – y₁)²
Substituting the values into the equation;
d = 2√170 = 26.07.
Kindly find the attached graph of the two points.
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