The cost of the present is $20.67
Given,
The cost of the present = x
Amount given by cousin = $13.78
Amount given by cousin is 2/3 of x.
That is,
13.78 = 2/3 of x
Lets find x
13.78 = 2/3 × x
13.28 = 2x/3
Multiply with 3 on both sides
13.78 × 3 = (2x/3) × 3
We get,
41.34 = 2x
Divide 2 on both sides
That is,
41.34/2 = 2x/2
We get,
x = 20.67
Here, x is the cost of the present
Therefore, the cost of the present is $20.67
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Fill in the table using this function rule.
y = 5x-4
3.A car starts from A and is driven 50km to B on a bearing of 072 0 . It is then driven 30km to C on a bearing of 326 0 .
Answer:
aaaaaaaaaa
Step-by-step explanation:
aaaaaaaa
Seema used compatible numbers to estimate the product of (–25.31)(9.61). What was her estimate?
If Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.
Total estimateGiven data or information :
Product = ( – 25. 31 ) (9. 61)
Now let estimate the product by first approximating the product to the nearest tenth.
Approximation :
So,
-25.31 = - 25 ( Approximately )
9.61 =10 ( Approximately )
Hence , her estimate can be calculated as :
Estimate :
Estimate = (-25) (10)
Estimate =-250
Therefore based on the information or data given if Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.
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The polynomial -17x^2 + 165x + 14,481 represents the electricity generated (in gigawatts) by geothermal sources during 2002-2007. The polynomial 879x^2 - 72x + 10,140 represents the electricity generated (in gigawatts) by wind power during 2002-2007. In both polynomials, x represents the number of years after 2002. Find a polynomial for the total electricity generated by both geothermal and wind power during 2002-2007.
The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is given by adding the two other ones, we will get:
862x^2 + 93x + 24,621
How to find the polynomial for the total electricity?Here we have two polynomials:
Polynomial -17x^2 + 165x + 14,481 represents the electricity generatedby geothermal sources during 2002-2007. Polynomial 879x^2 - 72x + 10,140 represents the electricity generated by wind power during 2002-2007Both of these are in gigawatts, so are in the same units, which means that we can directly add the two polynomials to get a polynomial for the total electricity.
-17x^2 + 165x + 14,481 + 879x^2 - 72x + 10,140
Now we group like terms:
(-17x^2 + 879x^2) + (165x - 72x) + (14,481 + 10,140)
862x^2 + 93x + 24,621
This polynomial represents the total electricity generated during 2002-2007
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If 4 bags of chips cost $3.00, how
much would 5 bags cost?
Answer: 6.67
Step-by-step explanation: first you divide 4 and 3 to then get 1.3 and times that by 5
1 If you are paid $232.95 for 22 hours of work, what amount should you be paid for 33 hours of work at this same rate of pay? 2 You should be paid $ (Round to the nearest cent as needed.) Question 3 of 12 for 33 hours of work.
Answer:
349.42499999998
Step-by-step explanation:
$232.95 divided by 22 hours of work = amount per hour = 10.588636363636
If you get paid 10.588636363636 per hour then multiply this by 33 hours to get the answer of : $349 and 42499999998 cents
Evaluate ∫(15x2+x2‾‾√34) dx. Here C is the constant of integration.
We use the following formula for integration:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex]We have the following integral:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx[/tex]Separate into two integrals:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=\int15x^2dx+\int\frac{\sqrt[3]{x^2}}{4}dx[/tex]Calculate the first integral. Take the coefficient out of the integral:
[tex]\int15x^2dx=15\int x^2dx[/tex]Apply the integration formula:
[tex]\int15x^2dx=15\frac{x^3}{3}+C=5x^3+C[/tex]Calculate the second integral. Take the coefficient out of the integral:
[tex]\int\frac{\sqrt[3]{x^2}}{4}dx=\frac{1}{4}\int\sqrt[3]{x^2}dx[/tex]Express the radical as a fractional exponent:
[tex]\frac{1}{4}\int\sqrt[3]{x^2}dx=\frac{1}{4}\int x^{2/3}dx[/tex]Apply the integration formula:
[tex]\frac{1}{4}\cdot\frac{x^{5/3}}{5/3}+C=\frac{3}{20}\sqrt[3]{x^5}+C[/tex]The total integral is:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=5x^3+\frac{3}{20}\sqrt[3]{x^5}+C[/tex]Your original grades on your exams were: 75, 85, 90, 90, 100, 75, 80, 100, 90. You retake the exams and now your scores are: 85, 85, 100, 90, 100, 85, 80, 100, 90. By how many percentage points did you improve your average score? Hint: Find the mean of both sets of data. Then find the difference between the two. Round to the nearest %.
Based on your original grades in your exams and the scores after you retake your exams, the percentage points you improved your average score by is 3.83%
How to find the percentage improvement?To find the percentage that you improved by, the first thing to do is to find your average score in the first exam:
= (75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90) / 9
= 785 / 9
= 87.22
The average score after the exam was retaken was:
= (85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90) / 9
= 815 / 9
= 90.56
The percentage increase is:
= (90.56 - 87.22) / 87.22 x 100%
= 0.0382939692731024994267369869296 x 100%
= 3.83%
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What are the minimum and maximum possible measures of 31 centimeters
The the minimum and maximum possible measures of 31 centimeters is {30.5. 31.5}
How do you find the minimum and maximum measurements?To find it, one need to add the biggest possible inaccuracy to each measurement, then multiply to get the biggest volume you can. Also Subtract the largest potential mistake from each measurement, then multiply, to to know the smallest volume that can be produced.
Note that the smallest value in the data set is the minimum. The highest value in the data collection is called the maximum.
Since only one data set is given, the possible measures can only be around it hence the largest and the smallest value close to it.
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Explain why when multiplying powers you add rather than multiply the exponents.
use real numbers for the proof
3^3 times 3^2 =
27 times 9 =
243 which is
3^5
Find the distance between the two points in simplest radical form (-6,8) and (-1,-4)
Answer:
13
Step-by-step explanation:
d) = √(-1 - -6)2 + (-4 - 8)2
= √(5)2 + (-12)2
= √169
= 13
Answer:
13
Step-by-step explanation:
We use the distance formula to find the distance between two points
d = sqrt ( (x2-x1)^2 + y2-y1) ^2)
Where ( x1,y1) and ( x2,y2) are the two points
d = sqrt( ( -1 - -6) ^2 + ( -4 - 8) ^2)
= sqrt ( ( -1+6) ^2 + ( -12) ^2)
= sqrt( 5^2 + 144)
= sqrt ( 25+ 144)
= sqrt ( 169)
= 13
$6500 earning 25% compounded
weekly for 1 year. What number goes in
the circle?
$8,125 is the compound interest.
What is compound interest?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year. Compound interest allowed you to earn 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.P = $6500
R = 25%
T = 1
compound Interest A = P( 1 + r/100)ⁿ
= 6500( 1 + 25/100)¹
= 6500( 5/4)
= 6500 * 5/4
= $8,125
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Solve the following linear equation using equivalent equations to isolate the variable. Express youranswer as an integer, as a simplified fraction, or as a decimal number rounded to two places.3y - y = -5AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutsy =
3y - y= -5
2y= -5
y= -5/2
y= -2.5
rounded of answer is 3
The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called _______.
The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called turning point.
What is a turning point?A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.
A turning point is a location on a graph where the trend shifts from rising to dropping or from decreasing to increasing (falling to rising). To determine the point, identify the leading term of the polynomial function if the function were enlarged. A polynomial of degree n will have at most n1 turning points. Next, determine the polynomial function's degree.
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If N = 15 and P = .50, what is the probability of getting exactly 12 P events? Please go to 4 decimal places.
The probability of getting 12 p events is 0.0139
The expected value, or mean, of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.
The binomial distribution formula is calculated as:
[tex]P(x:n,p) = ^nC_x * p^x*(1-p)^ {n-x}[/tex]
where:
n is the number of trials (occurrences)
X is the number of successful trials
p is probability of success in a single trial
is the combination of n and x. A combination is the number of ways to choose a sample of x elements from a set of n distinct objects where order does not matter and replacements are not allowed.
So, we have given that N = 15, P = 0.50 , and x = 12
So,
[tex]^{15}C_1_2 * (0.50)^{12}*(1-0.50)^ {15-12}\\^{15}C_1_2 * 0.50^{12}*(0.50)^ {3}\\[/tex]
=0.0139
Therefore, the probability of getting exactly 12 P events is 0.0139
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How can the rational zero theorem be used to find the zeros of polynomials
P is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P if P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P() = 0). (x).
The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.
What does the theorem of rational zeros state?According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(xconstant )'s term and q is a factor of P's leading coefficient (x).
What does rational number theorem determines?Finding the rational solutions to a polynomial equation is done using the rational root theorem, as its name suggests (or zeros or roots of a polynomial function). The answers obtained from any polynomial equation are referred to as the roots or zeros of polynomials. It's not necessary for a polynomial to have rational zeros.
So, to find rational zero theorem states:
If P(x) is a polynomial with integers coefficients and if is a zero of P(x)(P()=0), then
P is a factor of the constant term of P(x) and q is a factor of of the leading coefficient
Of P(x).
To find all the rational zero of a polynomial we can use the rational zeros theorem
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Q/ evaluate.
(27) 2 over 3
Plot the points (-8, 7) and (5, 7) on the coordinate plane below.
What is the distance between these two points?
The distance between two points is 15.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points. Counting each number in between them is a quick and easy approach to determine how far apart two numbers are on a number line. Finding the distance by taking the absolute value of the values' difference is a quicker method. For instance, |4| and |-4| have the same absolute value of 4, which is 4.
Given Data
Points (-8,7) and (5,7)
Formula of distance between two points
d = [tex]\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }[/tex]
x₂= 7 x₁= -8
y₂ = 7 y₁ = 7
d = [tex]\sqrt{(7-(-8))^{2}+(7-7)^{2} }[/tex]
d = [tex]\sqrt{(7+8)^{2}(0) }[/tex]
d = [tex]\sqrt{15^{2} }[/tex]
d = 15
The distance between two points is 15.
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Select the correct answer from each drop-down menu.
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
co N
The graph represents the system of inequalities
The test point
v satisfies both of the inequalities in the system represented by the graph.
Reset
Next
Only D satisfies both of the inequalities in the system represented by the graph. (Please check the graph attached)
What is inequalities ?Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.
To test point in that system satisfies both of the inequalities
The system of inequalities is shown by the graph.
While x + 2y is more than or equal to 3, 2x + 3y is less than or equal to 4.
Both of the system's inequalities represented by the graph are satisfied at the test point (4, -1).
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Send answers for the question please and thanks.
Answer:
7⁻²=[tex]\frac{1}{49}[/tex]
3⁻⁴ [tex]=\frac{1}{81}[/tex]
9⁰=1
11⁻¹=[tex]\frac{1}{11}[/tex]
8x^2+9=313 match to correct answer round to nearest 10th if Necessary
Based on the equation, the value of x in 8x^2 + 9 = 313 is 6.2
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to evaluate the quadratic equation?The quadratic equation is given as
8x^2 + 9 = 313
Subtract 9 from both sides of the quadratic equation
So, we have
8x^2 + 9 - 9 = 313 - 9
Evaluate the difference in the above equation
So, we have
8x^2 = 304
Divide both sides of the quadratic equation by 8
So, we have
8x^2/8 = 304/8
Evaluate the quotient in the above equation
So, we have
x^2 = 38
Take the square root of both sides
x = 6.2
Hence, the value of x in the quadratic equation given as 8x^2 + 9 = 313 is 6.2
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when x is decreasd by 2 and then that number is divided by 2, the result is 2. what is the number
Answer:
lets denote x as 6
so,
(x-2)÷2
(6-2)÷2
4÷2
2(proved)
An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 10 in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.
The length of each side of the octagon would be 8.23 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
We are aware that one side of the square is 20 inches long and that one side is made up of the length of the octagon added. We also know that two sides of a right triangle have smaller angles inside that are 45 degrees, making those two sides equal to one another. Therefore, we add the two sides of the right angle triangle to the side of the octagon, which equals 20 inches, to determine the value of x, which is designated as the side of the octagon.
Since a side of the square is 20 inches
Here, y is the two equal sides of the right-angle triangle
So y + x + y = 20
Using Pythagoras's theorem for the right angle triangle
y² + y² = x²
2y² = x²
y² = (x²)/2
y = x /√2
So substitute the value of y = x /√2 in the equation
x /√2 + x + x /√2 = 20
2x /√2 + x = 20
2x /√2 + x√2 /√2 = 20
x[2/√2 + √2 /√2] = 20
x[(2 + √2) /√2] = 20
x(2 + √2) = 20√2
x = 20√2/(2 + √2)
x = 28.2843/3.4142 = 8.2343
Round to the nearest hundredth of an inch
x = 8.23
Therefore, the length of each side of the octagon would be 8.23 inches.
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For
f(x) = (x − 1)3
and
g(x) = 1 − 6x,
find the following.
(a)
(f ∘ g)(x)
(b)
(g ∘ f)(x)
(c)
f(f(x))
(d)
f 2(x) = (f · f)(x)
For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
As given,
Given function :
f(x)=(x − 1)³
g(x)=1-6x
The value of following functions are:
a.(f ∘ g)(x)
=f(g(x))
=f(1-6x)
=(1-6x -1)³
=(-6x)³
=-216x³
b. (g ∘ f)(x)
= g(f(x))
=g(x − 1)³
=1 -6(x − 1)³
=1 -6(x³ -3x² +3x -1)
=-6x³+18x² -18x+7
c. f(f(x))
=f(x-1)³
=((x-1)³ -1)³
=(x³ -3x² +3x -1-1)³
=(x³ -3x² +3x -2)³
d. f²(x)= (f · f)(x)
=f(x) × f(x)
=(x-1)³ × (x -1)³
=(x -1)⁶
Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
The complete question is:
For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.
a. (f ∘ g)(x)
b. (g ∘ f)(x)
c. f(f(x))
d. f²(x)= (f · f)(x)
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a line intercepts the points (13,-4) and (1, 12) whats the slope
Answer:
m=-4/3
Explanation:
Given the points: (13,-4) and (1, 12)
To determine the slope of the line that joins the point, use the formula below;
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substitute the given points:
[tex]\begin{gathered} m=\frac{12-(-4)}{1-13} \\ =\frac{12+4}{-12} \\ =-\frac{16}{12} \\ =-\frac{4}{3} \end{gathered}[/tex]The slope is -4/3.
Some cars depreciate at rates as high as 75% per year for the first two years; this means that after one year the car is only worth 25% of the original cost. Suppose that you purchase a car for $16,500 that has a depreciation rate of 75%, then what will be the value of your car in 2 years? Hint: use f(x) = 16500(0.25)*, where x is the time in years. Round your answer to the nearest = dollar. $1.568 7765 then
Given:
Depreciation rate = 75% per year.
[tex]\begin{gathered} f(x)=a(1-0.75)^x \\ \\ f(x)=a(0.25)^x \end{gathered}[/tex]Let's find the value of the car in 2 years.
Given:
Cost = $16,500
Depreciation rate = 75%
From the equation we have:
Present value, a = 16500
x is the number of years = 2
Thus, we have:
[tex]\begin{gathered} f(2)=16500(0.25)^2 \\ \\ f(x)=16500(0.0625) \\ \\ f(x)=1031.25\approx1031 \end{gathered}[/tex]Therefore, the value of the car in 2 years is $1,031
ANSWER:
$1,031
In a jail cell, there are 5 Democrats and 6 Republicans. Four of these people will be randomly chosen for
early release. What is the probability that a group consisting of 2 Democrats and 2 Republicans will be chosen
for early release?
The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be 5/11.
What is probability?It should be noted that probability simply means the likelihood that a particular event will happen.
In this case, there are there are 5 Democrats and 6 Republicans and rour of these people will be randomly chosen for early release.
The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be:
Number of Democrats = 5
Number of Republicans = 6
Total number = 5 + 6 = 11
This will be illustrated through the combination formula:
= (5C2 × 6C2) / 11C4
= (10 × 15) / 330
= 150/330
= 5/11
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Mr. Vigrass was driving at a constant speed he drove 168 miles in 3 1/2 hours at that speed how many miles will he drive in one hour
Using speed, distance and time relation, Mr. Vigrass will travel 48 miles in an hours.
What is the relation between speed, distance and time?If we know how far something travels and how long it takes, we can determine how fast something is moving in a straight line. This equation illustrates the link between journey time, distance, and speed:
Distance divided by travel time equals speed.
Distance equals Time * Speed
Time = Speed / Distance
Distance x Time equals Speed
Given,
distance = 168 miles
time = 3 1/2 hours
speed = distance / time
speed = 168 × 2/7
speed = 48 miles/hour
At same speed,
distance travelled in 1 hour will be
distance = speed × time
distance = 48 × 1
distance = 48 miles.
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b. Evaluate 2w-60 when w=140.
Answer: 220
Step-by-step explanation: quick maths ;)
The graph of an absolute value function has a vertexat(-2.3) and passes through the point (-1,0).Using transformations of the parent function, has thegraph been dilated by a scale factor other than 1?Explain.
Step 1 of the solution:
Let the parent function of the absolute value function is f(x) = |x|
Step 2 of the solution:
This function passes through (0, 0) and slope = 1 or -1.
Step 3 of the solution:
After transformation vertex (0, 0) becomes (-2, 3) and a point through which this function passes through is (-1, 0)
Step 4, let's find the slope of the absolute value funtion, this way:
[tex]S\text{lope = (3 - 0)/(-2 + 1) = 3/}-1\text{ = -3}[/tex]Step 5: Interpretation
Since slope of the absolute value function is less than the parent function: -3 < -1
Therefore, the parent function will be dilated by a scale factor other than 1.