Answer:
50
Step-by-step explanation:
a = # of apples
b = # of bananas
5a + 3b = 570
3a + 5b = 470
Solve with substitution or elimination. To solve by elimination, multiply the first equation by 5 and the second equation by 3.
25a + 15b = 2850
9a + 15b = 1410
Subtract:
16a = 1440
a = 90
Plug into either equation to find b.
5(90) + 3b = 570
450 + 3b = 570
3b = 120
b = 40
So apples are 90 cents, and bananas are 40 cents. Therefore, apples are 50 cents more than bananas.
Use inductive reasoning to determine the next two terms in each sequence: a) 1, 3, 7, 15, 31 ....
Answer:
63,127
Step-by-step explanation:
the interval between each number is multiplied by 2
such as between 1 and 3 we have 2 so 2×2=4
the 4+3=7 and so on
Answer: 63, 127
Step-by-step explanation: 1+2=3; 3+4=7; 7+8=15; 15+16=31; 31+32=63; 63+64=127
Or, if we call the first value a1 , the sequence is given by an=2n−1
The first approach to analyzing almost any sequence is to look at the differences of successive elements. In this sequence, that’s 2, 4, 8, 16, 32. That makes the answers above pretty easy.
what is f(3) for f(x) = 3x + 2
Answer:
11
Step-by-step explanation:
f(x) = 3x + 2
Let x = 3
f(3) = 3*3 +2
f(3) = 9+2
= 11
Answer:
f(3) = 11Step-by-step explanation:
f(x) = 3x + 2
In order to find f(3) substitute the value of x that's 3 into f (x) that's replace every x in f (x) by 3
That's
f(3) = 3(3) + 2
= 9 + 2
We have the final answer as
f(3) = 11Hope this helps you
A person filing his federal income tax return with the Single filing status had a
taxable income of $31,850. According to the table below, how much of that
income will he have left over after paying his federal income tax?
A) 27,490.00
B) 28,325.00
C) 3525.00
D) 4360.00
The solution is Option A.
The amount of income left over after paying the federal income tax is given by the equation A = $ 24,490.00
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of income left over be represented as A
Now , the equation will be
The amount of taxable income is $31,850.00
And , the taxable income is in the range $ 8,350 - $ 33,950
So , the fixed tax for the amount is $ 835.00
The percentage of tax is 15 % of the amount over
So , the amount over = $ 8,350
Substituting the values in the equation , we get
The amount over = $31,850.00 - $ 8,350.00
The amount over = $ 23,500.00
Now , 15 % of amount over = 23,500 x ( 15/100 )
15 % of amount over = $ 3,525.00
And , Total tax = 15 % of amount over + fixed tax for the amount
Total tax = $ 3,525.00 + $ 835.00
Total tax = $ 4,360.00
Now , the amount of income left over A = amount of taxable income - Total tax
Amount of income left over A = $31,850.00 - $ 4,360.00
Amount of income left over A = $ 27,490.00
Therefore , the value of A is $ 27,490.00
Hence , the amount left over is $ 27,490.00
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Identify the y intercept of the following equation
y=-3x + 5
Answer:
5
Step-by-step explanation:
y=mx+b
B is always the y intercept.
find the value of
(-3)^5/(-3)^6
Answer:
[tex] \boxed{ \bold{ \frac{1}{3} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ \frac{ { - 3}^{5} }{ { - 3}^{6} } }[/tex]
To divide two terms with the same base , the power of divisor is subtracted from the power of the dividend and the same base is taken
⇒[tex] \mathsf{ { - 3}^{5 - 6} }[/tex]
⇒[tex] \mathsf{ { - 3}^{ - 1} }[/tex]
Applying law of negative index
⇒[tex] \frac{1}{3} [/tex]
Hope I helped!
Best regards!!
Application of Linear Function
Problem: Dunkin Donuts
found that the cost to produce 100 cups of coffee is
$11.02, while the cost to produce 400 cups is $40.12.
Assume the cost C(x) is a linear function of x, the number
of cups produced
(a) Find a formula for C(x).
(b) What is the fixed cost?
(c) Find the total cost of producing 1001 cups.
(d) Find the marginal cost of any cup and what does this
mean to the manager?
Answer:
see below
Step-by-step explanation:
Find the slope
m= ( 40.12 - 11.02)/ (400-100)
= 29.1 / 300
=.097
We can use the linear form y = mx+b
y =.097x +b
40.12 = .097 ( 400) +b
40.12 = 38.80 +b
1.32 = b
y = 0.097x + b
C(x) = .097x + 1.32
The fixed cost is b = 1.32
C(1001) = .097(1001) + 1.32
=98.417
The marginal cost is the cost of adding one more item, which is the slope
.097 is the marginal cost
It means to make one more cup of coffee will cost $.097
Apolitical researcher believes that the fraction p1 of Republicans strongly in favor of the death penalty is greater than the fraction p2 of Democrats strongly in favor of the death penalty. He acquired independent random samples of 200 Republicans and 200 Democrats and found 46 Republicans and 34 Democrats strongly favoring the death penalty. Does this evidence provide statistical support for the researcher’s belief? Use α = .05.
Answer:
The evidence provided does not statistically support the researcher’s belief
Step-by-step explanation:
From the question we are told that
The sample size of each political party is [tex]n = 200[/tex]
The number of democrats that favor death penalty is [tex]k = 34[/tex]
The number of republicans that favor death penalty is [tex]u = 46[/tex]
Generally the sample proportion for Republicans is
[tex]\r p_1 = \frac{ 46}{200}[/tex]
[tex]\r p_1 = 0.23[/tex]
Generally the sample proportion for Democrats is
[tex]\r p_2 = \frac{ 34}{200}[/tex]
[tex]\r p_1 = 0.17[/tex]
The null hypothesis is [tex]H_o : \r p _1 = \r p_2[/tex]
The alternative hypothesis is [tex]H-_1 : \r p_1 > \r p_2[/tex]
Generally the pooled population proportion is evaluated as
[tex]\r p = \frac{ k + u }{n + n }[/tex]
[tex]\r p = \frac{ 34 + 46 }{200 + 200 }[/tex]
[tex]\r p = 0.2[/tex]
The test statistics is evaluated as
[tex]t = \frac{ \r p _1 - \r p_2 }{\sqrt{ \r p (1 - \r p ) [\frac{1}{n} +\frac{1}{n} ]} }[/tex]
[tex]t = 1.5[/tex]
The p-value is obtained from the z-table the value is
[tex]p-value = P(Z> 1.50 ) = 0.066807[/tex]
=> [tex]p-value = 0.066807[/tex]
Given that [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis this mean that there is no sufficient evidence to support the researcher’s belief
Glenn bought 3 pounds of tomatoes. He used 5/8 of them to make sauce.
The quantity of tomatoes that are left is equal to 1.875 pounds.
Given the following data:
Quantity of tomatoes = 3 pounds.Fraction used = [tex]\frac{5}{8}[/tex]To determine the quantity of tomatoes that are left:
In order to determine the quantity left from the tomatoes Glenn bought, we would use the following mathematical expression:
[tex]Quantity\;left = Fraction\; used \times Total\;quantity[/tex]
Substituting the given parameters into the formula, we have;
[tex]Quantity\;left = \frac{5}{8} \times 3\\\\Quantity\;left = \frac{15}{8}[/tex]
Quantity left = 1.875 pounds
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find compound amount annually of p= RS.4800 ,time= 3/2 and rate =10%
Answer:
Step-by-step explanation:
[tex]Amount=P(1+r)^t\\=4800(1+0.1)^{\frac{3}{2}}\\=4800(1.1)^{\frac{3}{2}}\\\approx 5537.72 ~Rs[/tex]
The letter b represents a nonzero constant. Solve 2bx-bx= -8 for x?
Answer:
x = -8/b
Step-by-step explanation:
2bx-bx= -8
bx = -8
Divide by b since b is nonzero
x = -8/b
The graph of f(x) = x2 is shifted 3 units to the right to obtain the graph of g(x). Which of the following equations best describes g(x)?
Answer:
Hey there!
The correct answer would be f(x)=(x-3)^2
Let me know if this helps :)
Find two whole numbers that the 407 falls in between. Justify your answer.
Answer:
407 falls between whole numbers 406 and 408.
Step-by-step explanation:
whole numbers set of numbers which begins with 0 add has sequence of number differing by one unit.
set of whole numbers will be 0,1,2,3,4,5...........................till infinity.
Given whole number = 407
No. before 407 will be one less than 407 i.e 407 -1 = 406
No. after 407 will be one more than 407 i.e 407 + 1 = 408
Thus, 407 falls between 406 and 408 which are part of whole numbers.
You choose to tip a taxi driver 20%. If the tip is $2.00, how much was the original cost of the ride?
Answer:
10.00
Step-by-step explanation:
because 2.00 x 5 is 10 which is a hundred percent hope this helps!
In 1961, it was discovered that the drug thalidomide, given to pregnant mothers for morning sickness, caused birth defects. Fifty years later, the manufacturer of the drug issued a but those affected by the drug felt that the company's statement wasn't enough.
A. Mea Culpa
B. Non Sequitur
C. Tabula Rasa
D. Mano a Mano
Answer:
A) mea culpa
Step-by-step explanation:
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answer:
1/4Step-by-step explanation:
Probability is the likelihood or chance that an event will occur. Mathematically,
Probability = Expected outcome/Total outcome
If the spinner has 10 equally sized sections 5 of which are gray and 5 of which are blue, the total outcome will be equal to 10.
The probability that spinning lands on blue = 5/10
The probability that spinning lands on gray = 5/10
The probability that the first spin lands on gray and the second spin lands on blue is 5/10*5/10 = 25/100
25/100 = 1*25/(4*25) = 1/4
Hence, the probability that the first spin lands on gray and the second spin lands on blue in its simplest form is 1/4
A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the amount of DDT toxin present. Ideally he will be able to rank the species based on the mean level of toxin found in each of the three species.
How many factors are present in this study? Choose which one
a. 50
b. 3
c. 1
d. 6
Answer:
1.
Step-by-step explanation:
We are being told that:
A scientist is hoping to compare the mean levels of DDT toxin found in three species of fish in a local river.
He randomly samples 50 of each species to use in the analysis.
i.e sample size n = 50
For each fish, he measures the amount of DDT toxin present. The amount of DDT toxin present will be use to rank the species based on the mean level of toxin.
From the information above, we will realize that the factors that are present in this study is just only one and which is the amount of DDT in a Fish because, it is the major focus in this question.
The point C (4, 4) has been rotated by 180⁰ counter clock wise about the point (1, 3). Determine the coordinates for the point C’.
Answer:
C'(-3, -1)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a new position. Types of transformation are reflection, rotation, dilation and translation.
If a point A(x, y) is rotated 180 degrees counterclockwise about the origin the new coordinates is A'(-x, -y)
Since C(4, 4) is rotated about point (1, 3), we have to make point (1, 3) the origin. This means the new origin O' is at (1, 3). The horizontal and vertical distance between the new origin and point C gives the new coordinate of point C. Point C x coordinate is 3 units from the new origin and y coordinate is 1 unit from the new origin, hence the new coordinate of point C is (3, 1).
A 180⁰ counter clock wise rotation of point C would give a new point at C'(-3, -1)
If a rectangle has a perimeter of 56 inches and a width of 8 inches,what is the perimeter
Answer:
192 inches ²Step-by-step explanation:
P= (l+w)
56 = 2(l+8)
56=2l+8
56-8= 2l
48=2l
Length=24
Area = ?
A = l×w
A=24×8
Area= 192inches²
Write the point slope of the equation of the line described show work.
through: (3,-2), parallel to y= -3/2x - 1
Answer:
y= -3/2x + 5/2
Step-by-step explanation:
Given:
Line y= -3/2x - 1 and point (3, -2)To find:
Equation for the line parallel to the given that passes through the given point.SolutionThe given line has a slope of -3/2
The parallel line will have the same slope
The point-slope form:
y - y1 = m(x -x1)We have m = -3/2, y1= -2, x1 = 3, plug in:
y - (-2) = -3/2(x - 3)y + 2 = -3/2(x - 3)y = -3/2x + 9/2 - 2y = -3/2x + 5/2or
y = -1.5x + 2.5consider the statement p:x+9=10.which of the following is a equivalent statement
Answer:
The equivalent expression for x+9=10 is x=1.
Step-by-step explanation:
We have a statement i.e. x+9=10
We need to find an equivalent statement for the above statement.
If we subtract 9 on both sides of the above statement,
x+9-9=10-9
We know that, 9-9=0 and 10-9 =1
x+0=1
x=1
So, the equivalent expression for x+9=10 is x=1.
On a distant planet, a ball is thrown upwards from ground level , reaching a maximum height of 12m and hitting the ground again in eight seconds. Determine a quadratic equation in the form a * x ^ 2 + bx + c =0 that could be used to calculate when the ball is a height of 3m. Do not solve the equation
Answer:
(-3/4)x^2 + 6x = 3
Step-by-step explanation:
It takes 8 seconds for the ball to reach its maximum height and then return to ground level; thus, the highest point (vertex) the ball will reach is reached after 4 seconds. The graph showing this motion is a parabola that opens down. Thus, the coefficient 'a' must be negative.
Returning to a * x ^ 2 + bx + c, we write out two instances of this formula, one for x = 0 and the other for x = 8. This is because {0, 8} are the x-intercepts.
Then, for x = 0, a * x ^ 2 + bx + c becomes a * 0 ^ 2 + b*0 = 0,
and for x = 8, a * x ^ 2 + bx + c becomes a(8)^2 + b(8) + c = 0
The first equation tells us that 'c' must be 0. The second equation tells us that 64a + 8b = 0, which is equivalent to 8a = -b, or a = -b/8.
We then have the quadratic function (-b/8)x^2 + bx + 0. All we have to do now is to find the value of b. The vertex of this parabola is (4, 12), and so the quadratic becomes
(-b/8)(4)^2 + b(4) = 12. To solve this for b, multiply all terms by 8:
-b(16) + 32b = 96, or
16b = 96, or b = 6. Since a = -b/8 (see above), a = -6/8 or a = -3/4.
Then the equation of motion is
height of ball = (-3/4)x^2 + 6x
We want to know when the ball is at a height of 3 m. Thus, set this equation of motion = to 3 and solve for x (the times at which height = 3 m):
(-3/4)x^2 + 6x = 3 This is the desired quadratic equation.
7.142857143
How is this rounded to two decimal places?
Answer:
you look at the third decimal place which will affect the second decimal place.
in this case: 2 affects 4 -- leaves it as 4
so the number rounded to two decimal places is 7.14
Identify the type of study used. A town obtains current employment data by polling 10,000 of its cit izens this month.
A) Cross-sectional
B) Prospective
C) Retrospective
D) None of these
Answer:
A) Cross-sectional
Step-by-step explanation:
A cross-sectional study is a type of study that involves the data i.e. taken from a population for a specific time period.
Here study shows the peoples interest in variables that are be chosen
In the given situation, since a town obtains a data of the current employment for 10,000 of its total citizens
So this represents the cross-sectional
hence, the correct option is A. Cross-sectional
Which ideas about functions do you think might be the most helpful to you in your day-to-day planning?
Answer:
It helps in calculating the price of groceries such as fruits.
Step-by-step explanation:
Remember, functions are mathematical expressions that represent or shows the relationship between one or more variables.
For example, let's say a young girl wants to shop for 20 oranges in a mall. If we express the price using the function [tex]y = 20x[/tex] where;
y represents the total cost of the oranges,
20 represents the number of oranges,
x represents the cost per orange (assumed to $0.99)
Then, by means of the knowledge of function, the girl determines the total cost she to be $19.8 (20*0.99).
Functions are mathematical representation of the relationship which exists between input and output variables. Hence, an helpful day-to-day usage of function could be in calculating daily spending on food items.
One could stipulate the daily amount spent on food based on the number of meals consumed per day. For instance, if a meal cost $5.60, then the total amount spent on food can be represented thus ;F(x) = total cost ; x = number of meals consumedF(x) = 5.60x
Hence, if 3 meals is consumed in a day, the total amount spent would be ;
F(3) = 5.60(3)
F(3) = $16.80
Hence, functions could be helpful in calculating the daily amount expended on food.
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Blake randomly chose a letter from alphabet.
What is the probability that this letter has at
least one line of symmetry, given that it is a
consonant?
Answer:
Hey there!
The letters B, C, D, H, K, M, T, V, W, and X have at least one line of symmetry.
A, E, I, O, U and Y are the vowels.
So we have a total of 21 consonants, and 10 are symmetrical.
Thus, the probability is 10/21.
Let me know if this helps :)
!!!!!!! Why isn't A the correct answer? I am having trouble to reason why A is wrong so please help if can!
Answer:
d. x = -3
Step-by-step explanation:
[tex]\sqrt{(x + 3)}[/tex]÷ (x+8)(x-2) = 0
f(x) / g(x) = 0
Variable x cannot be equal to any of the values −8,2 since division by zero is not defined. Multiply both sides of the equation by (x−2)(x+8).
[tex]\sqrt{(x + 3)}[/tex] = 0 ------ square both sides
x + 3 = 0
solve for x:
x = -3
Add. (7s+5)+(2s+9) help please
Answer:
9s+ 14
Step-by-step explanation:
(7s+5)+(5+9)
(7s+2s) +(5+9)
(9s)+(14)
Start by moving your numbers around so your like terms are by each other.
Then combine you like term so numbers with letters with numbers and letters the plain numbers and plain numbers.
once you do that your equation is simplify as far as possible
You are given f(x)=x/1+x. Evaluate f(2)+f(1/2).
Step-by-step explanation:
5/2f or 2.5f I think
..................
snailpace coach company is running a trip to "the anoraks" concert. they have seven 52-seater coaches and eight 12-seater minibuses. the coach company forks out £23 for each ticket. it also costs them £150 to run each coach and £80 per minibus. how much will the company have to pay in total to run the trip
Total seats: 52 x 7 + 8 x 12 = 364 + 96 = 460
Total cost for total seats = 460 x 23 = 10,580
Cost for buses: 150 x 7 + 80 x 8 = 1050 + 640 = 1690
Total cost = 10,580 + 1,690 = $12,270
The functions f(x) and g(x) are graphed. Which represents where f(x) = g(x)? f(2) = g(2) and f(0) = g(0) f(2) = g(0) and f(0) = g(4) f(2) = g(0) and f(4) = g(2) f(2) = g(4) and f(1) = g(1)
Answer:
The given graph shows the relationship between the f(x) and g(x).
Since the problem is to find the points where f(x) becomes equal to g(x) then we will be focusing only to the x-axis and ignore the points of y-axis.
Out of the four choices, the correct answer for the given functions of x will be f(2) = g(2) and f(0) = g(0), f(0) and g(0) is located at the origin. So the points where the curve and line are intersecting is at f(2) and g(2) and the other point is at f(0) and g(0), neglecting the y-axis.
Step-by-step explanation: