Start by finding the slope of the line.
m = y2 - y1 / x2 - x1
m = 5 - 2/1 - 0 ⇒ 3/1 ⇒ 3.
So the slope of the line is 3.
This can be used with either one of our two points
to write the equation of the line in point-slope form.
So let's go with the point (0, 2).
Point-slope form is written y - y1 = m(x - x1).
Since we are using the point (0, 2), y - y1 would be y - 2.
"m" would be 3 and x1 would be 0.
So we have y - 2 = 3(x - 0).
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.
PLEASE HELP (0.1)^5 simplified
Answer:
0.1^5=0.00001
Step-by-step explanation:
[tex]0.1^5\\0.1^5=0.00001[/tex]
Ana is purchasing new furniture and must pay a 10% sales tax. She can have the furniture delivered for an additional $25 fee that is not taxed. Which function represents the amount Ana will pay for furniture with a pretax price of x dollars?
Answer:
C) P(x)=1.10x+25
Step-by-step explanation:
The algebraic expression for the amount Ana will pay for furniture with a pretax price of x dollars = 1.1x + 25
What is algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.
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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
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.
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 + 2.5You are given f(x)=x/1+x. Evaluate f(2)+f(1/2).
Step-by-step explanation:
5/2f or 2.5f I think
..................
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.
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
Tickets to a play are $12.00 for adults. Children receive a discount and only have to pay $8.00. If 40 people attend the play and the play brought in $440, then __?__children attended the play.
The total number of children who attended play is 10 and this can be determined by forming the linear equation in two variables.
Given :
Tickets to a play are $12.00 for adults. Children receive a discount and only have to pay $8.00. 40 people attend the play and the play brought in $440.The following steps can be used in order to determine the total number of children attending play:
Step 1 - Let the total number of adults attending play be 'x' and the total number of children attending play be 'y'.
Step 2 - The linear equation that represents the total number of people attending the play is:
x + y = 40
x = 40 - y --- (1)
Step 3 - The linear equation that represents the price of all the tickets is:
12x + 8y = 440 --- (2)
Step 4 - Now, substitute the value of 'x' in the above expression.
12(40 - y) + 8y = 440
Step 5 - Simplify the above expression.
480 - 12y + 8y = 440
40 = 4y
y = 10
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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
Two ships a and b are firing cannons at each other. Ship A reaches its target 30% of the time, Ship B 60% of the time. The ships take turns firing at one another. When a ship is hit it sinks. Ship A fires first. What is Ship A's survival probability, rounded to the nearest 0.01?
a. 33%.
b. 38%.
c. 42%.
d. 50%.
Answer: c. 42%.
Step-by-step explanation:
P(ship A reaches target) : P(A) = 0.30
P(ship B reaches target) : P(B) = 0.60
P( Ship B not reaching target ) : P(B^c) = 1 - p(B) = 1 - 0.60 = 0.40
P( Ship A not reaching target ) : P(A^c) = 1 - p(B) = 1 - 0.30 = 0.70
NOW
define A for A wins
define A^c for A loss
define B for B wins
define B^c for B loss
A ⇒ P(A) = 0.30
A^c B^c A ⇒P(A^c B^c A) = 0.70 × 0.40 × 0.30
A^c B^c A^c B^c A ⇒ P(A^c B^c A^c B^c A) = ( 0.70 × 0.40)² × 0.30
↓↓↓
∴P(A survives) = sum of all probabilities
⇒ 0.30 + ( 0.70 × 0.40 × 0.30 ) + ( 0.70 ×0.40 )² × 0.30 +...........................
⇒ 0.30 [ 1 + ( 0.28) + (0.28)² +..........................]
Now sum of geometric series S∞ = a / 1-β = 1 / 1 - 0.28
∴ 0.30 × 1/1-0.28 = 0.42
now converting to percentage
0.42 × 100 = 42%
Ship A's survival probability is 42%
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
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
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
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.
Does anyone know the answer to number 1?
Answer:
Rectangles
Step-by-step explanation:
Answer:
[tex]\Large \boxed{\mathrm{Rectangles}}[/tex]
Step-by-step explanation:
Figure A and figure B are rectangles.
Rectangles have opposite sides equal and parallel.
Rectangles have 4 right angles and 4 pairs of perpendicular sides.
i need help asap !!!!!
Answer:
D.) MC≅MC
Step-by-step explanation:
We already know that the hypotenuses are the same (because of that tiny line), so we need the legs (HL: hypotenuse-leg). As we can see in the picture, MC is a shared side of both triangles, and this is also the leg. Option D is correct.
:Done
There are two different maps of California. The scale on the first map is 1 cm to 20 km. The distance from Fresno to SanFrancisco is 15 cm.The scale on the second map is 1 cm to 100 km.What is the distance from Fresno to San Francisco on the second map? Explain your reasoning.
Answer:
the distance from Fresno to San Francisco on the second map is 75cm
Step-by-step explanation:
The scale on the first map is 1 cm to 20 km
The distance from Fresno to SanFrancisco is 15 cm
1cm/20km = 15cm
The scale on the second map is 1 cm to 100 km.
1cm/100km = x
X= 15cm*100km/20km *1cm/1cm
X=15cm *5
X= 75 cm
the distance from Fresno to San Francisco on the second map is 75cm
Find the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject H0 for the given level of significance.
Two-tailed test with test statistic z= -1.94 and = 0.07.
P-value = ?
Answer:
Reject H0 as the critical region for alpha = 0.07 is z ≤ -1.82 and z≥ 1.82
Step-by-step explanation:
For the significance level ∝ = 0.07
For a two tailed test we divide it with 2 and get 0.035
When we subtract 0.035 from 1 we get 0.965
And when we look at the z- table and corresponding to 0.965 we find the value of z to be 1.82
Now the calculated value of z= -1.94 which is less than ±1.82.
Hence reject H0 if z ≤ -1.82 and z≥ 1.82
Therefore reject H0.
While ∝ =0.07
p- value = 0.06 should be examined
the p- value is the smallest value of ∝ where we reject H0.
Hence at ∝= 0.06 critical region is z ≤ -1.88 and z≥ 1.88
At ∝= 0.05 critical region is z ≤ -1.96 and z≥ 1.96
So p- value is near 0.06
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!
"Bob is dealing with discrete data and the samples are without replacement. Based on this information, what is the likely probability distribution"
Answer:
discrete probability distribution
Step-by-step explanation:
A discrete probability distribution is a term that describes a form of a probability distribution that is used in a situation where the set of possible outcomes is discrete.
While it also has a tendency to take on a countable number of values, it is a probability distribution where a sample is drawn from a larger population, this sample points possess an empirical distribution that is considered to be discrete, which resulted in information about the population distribution.
Hence, given that Bob is dealing with discrete data and the samples are drawn without replacement, the likely probability distribution is DISCRETE PROBABILITY DISTRIBUTION
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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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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the square of a number, x, is 16 less than 8 times the number. what is the number
Answer:
x=4
Step-by-step explanation:
Building an equation and solving it, it is found that the number is 4.
------------------------------
The number is unknown, so it is called x.The square of 1 is [tex]1^2 = 1[/tex], the square of 2 is [tex]2^2 = 4[/tex], thus the square of the number x is [tex]x^2[/tex].8 times the number is 8x.16 less than 8 times the number is 8x - 16.------------------------------
The equality is:
[tex]x^2 = 8x - 16[/tex]
[tex]x^2 - 8x + 16 = 0[/tex]
Applying the perfect square binomial:
[tex](x - 4)^2 = 0[/tex]
[tex]\sqrt{(x - 4)^2} = \sqrt{0}[/tex]
[tex]x - 4 = 0[/tex]
[tex]x = 4[/tex]
The number is 4.
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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
What is the equation of a vertical line passing through (−5, −2)? a: x = −5 b: x = −7 c: y = −3 d: y = −2
The answer is
A : x=-5
which expression is equivalent to 4^6 x 4^-8
Answer:
4^-2=1/16
Step-by-step explanation:
When we are multiplying exponents and the bases are the same, we add the exponents
4^6 * 4^-8
4^(6+-8)
4^-2
1/16
!!!!!!! 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
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 :)