Using linear functions, we have that:
a. Sara will have driven 2.25 hours when Pedro catches up with her.
b. They are 146.25 miles from home when Pedro catches up with Sara.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.We have to consider the starting time as when Pedro leaves, when Sara will be at position 45 miles. Considering the velocities as the slope, the functions are:
S(t) = 45 + 45t. P(t) = 65t.Pedro will catch up with Sara when:
P(t) = S(t)
Hence:
65t = 45t + 45
20t = 45
t = 45/20
t = 2.25 hours.
Sara will have driven 2.25 hours when Pedro catches up with her.
The distance from home will be given by:
P(2.25) = S(2.25) = 65(2.25) = 45(2.25) + 45 = 146.25.
They are 146.25 miles from home when Pedro catches up with Sara.
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As the degrees of freedom increase, the t distribution approaches the _____ distribution. a. exponential b. p c. normal d. uniform
As the degrees of freedom (DF) increase, the t distribution approaches the normal distribution. Therefore, the correct answer option is: C. normal distribution.
What is the degrees of freedom (DF)?The degrees of freedom (DF) in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses because they are the maximum number of logically independent numerical values (data points) in the final calculation of a statistical problem.
What is a normal distribution?A normal distribution is sometimes referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data that are far from the mean.
In this context, we can reasonably infer and logically deduce that the t-distribution generally approaches the normal distribution as the degrees of freedom (DF) increase.
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Salome's house went from a valuation of 4.5 million ZAR (South African Rand) on 1st January
2011, to 6 million ZAR on 1st January 2020.
If the value of the house compounded monthly, what was the annual rate of increase?
Give your answer as a percentage, correct to 1 decimal place.
Using compound interest, it is found that the annual rate of increase was of 3.10%.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For this problem, the parameters are given as follows:
t = 9, A(t) = 6, A(0) = 4.5, n = 12.
Hence we solve for r to find the interest rate as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]6 = 4.5\left(1 + \frac{r}{12}\right)^{12 \times 9}[/tex]
[tex]1 + \frac{r}{12}\right)^{108} = 1.33[/tex]
[tex]\sqrt[108]{1 + \frac{r}{12}\right)^{108}} = \sqrt[108]{1.33}[/tex]
[tex]1 + \frac{r}{12} = (1.33)^{\frac{1}{108}}[/tex]
1 + r/12 = 1.0026.
r/12 = 0.0026
r = 12 x 0.0026
r = 0.031.
The annual rate of increase was of 3.10%.
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A sample of n=225 scores has =103 and s2 =16. what is the sample standard deviation?
Based on the calculations, the sample standard deviation is equal to 4.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
[tex]Z=\frac{\bar x\;-\;u}{\delta}[/tex]
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:
Note: Variance, δ² = 16
Taking the square root of the variance, we have:
Standard deviation, δ = √16
Standard deviation, δ = 4.
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Complete Question:
A sample of n=225 scores has [tex]\bar x[/tex] = 103 and δ² = 16. What is the sample standard deviation?
W X Y Z is a square. If W T=3 , find each measure. m∠WTZ
Step-by-step explanation:
In this exercise we have to use the knowledge of quadrilaterals to calculate the measures of each side of the square, in this way we can say that it will be valid:
Given in the exercise that each the value of:
WT=3
The diagonals of a square are congruent, and bisect each other, that will help to find:
if <1 and <2 form a linear pair and m<1 is 18 degrees less than five times the measure of <2 find m<1
∠1 and ∠2 will have the values 33° and 147° respectively when they form a Linear Pair.
In the question, It is given that ∠1 and ∠2 form a Linear Pair.
So, ∠1 and ∠2 = 180°, Also it is stated that ∠1 is 18° lesser than 5 times ∠2.
Taking ∠2 = x we get ∠1 = 5x-18
Now for Linear Pair, we have ∠1 + ∠2 = 180°
putting values of ∠1 and ∠2 we get : (5x-18) + x = 180
Solving the equation => (5x-18) + x = 180 => 6x = 198
=> x = 33
Putting the value of x in both ∠1 and ∠2 we get :
∠2 = 33° and ∠1 = 5(33) - 18 => ∠1 = 147°
Hence, we get ∠1 and ∠2 measures 147° and 33° respectively.
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I need help asap!!!!
Answer: The first one is correct.
Step-by-step explanation:
x = 3
y = -2
So: 2 x 3 + 2 x (-2) = 6 + (-12) = -6
PLEASE HELP WILL MARK BRAINLIEST
Answer:y=-3, x=6
Step-by-step explanation:
Answer:
x=6 y=-3
Step-by-step explanation:
Determine the total number of roots f(x) = (3x^4 + 1)^2
[tex]f(x) = (3 {x}^{4} + 1) {}^{2} \\ f(x) = 0 \\ (3 {x}^{4} + 1) {}^{2} = 0 \\ 3x {}^{4} + 1 = 0 \\ 3x {}^{4} = -1 \\ x {}^{4} = \frac{ - 1}{3} [/tex]
[tex]f(x) \: admits \: no \: real \: roots[/tex]
Number 13 and 9 please
Answer:
9.5>6 41.8>0
Step-by-step explanation:
what three numbers come next in the sequence 1458,486,162,54? and how do you get these numbers?
Answer:
18,6,2
Step-by-step explanation:
To get from the first term to the second term we divide by 3 .
To get from the second term to the third term we divide by 3 .
So we continue this pattern to find the next 3 terms :
So 54 ÷ 3 = 18
18 ÷ 3 = 6
6 ÷ 3 = 2
Hope this helped and have a good day
Help with problem 20 please
The rate of change will be 0.074 grams per year.
How to calculate the rate?The change in hydrocarbon will be:
= 3.4 - 0.8
= 2.6
The number of years will be:
= 2007 - 1972
= 35
Therefore, the rate will be:
= Change in hydrocarbon / Years
= 2.6 / 35
= 0.074 grams per year.
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If two pounds of meat will serve 5 people, how many pounds will be needed to serve 13
people?
Answer:
Step-by-step explanation:
2 pounds / 5 people
x pounds / 13 people
2/5 pounds per person so 2/5 * 13 = 26/5
5 1/5 i think
sorry if its wrong
Answer: The answer of the question is 2 and 3/5.
Step-by-step explanation: Every pound of meat serves one person, because 10 divided by 2 people is 5. Then, there are 3 pieces of meat left over, and since every person eats 5/5, or 1 whole, then there are 3/5 pieces left over. You then add 2 and 3/5 together, getting your answer 2 3/5.
richard cuts a $ 4\frac{1}{2} ~\text{ft} \times 7\frac{1}{2} ~\text{ft} \times 11\frac{1}{4}~ \text{ft}$ rectangular prism into congruent cubes without any part of the prism leftover. if he makes the cubes as large as possible, how many will he produce?
If he makes the cubes as large as possible, the maximum number of cubes is equal to 900 cubes.
How to determine the number of cubes?In order to determine the number of cubes that would be produced by Richard when the rectangular prism is cut into congruent cubes without any part of the rectangular prism leftover, we would make the edges of the cube 100 times larger and then evaluate:
Length of cube = 4 1/2 ft × 100 = 450 feet.Breadth of cube = 7 1/2 ft × 100 = 750 feet.Height of cube = 11 1/4 ft × 100 = 1125 feet.Note: The greatest common factor (GCF) of the dimensions above is 75.
Next, we would divide each of the dimension by 75:
Length of cube = = 450/75 = 6 feet.
Breadth of cube = 750/75 = 10 feet.
Height of cube = 1125/75 = 15 feet.
Therefore, the maximum number of cubes is given by:
Maximum number of cubes = 6 × 10 × 15
Maximum number of cubes = 900 cubes.
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Complete Question:
Richard cuts a 4 1/2 ft × 7 1/2 ft × 11 1/4 ft rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?
9. The table shows the relationship between the number of targets a person
hits in a game of laser tag and that person's score.
Targets hit
3
4 5 6
Score
8 16 24 32 40 48
0 1 2
0
The table shows relationship between the number of targets a person
hits in a game of laser tag and that score of that person. The table shows is a continuous graph.
What is a continuous function in a graph?As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil. In calculus, learning about a function's continuity is crucial since without it, a function cannot be differentiated.
If a function's graph is a continuous curve without any holes, gaps, or breaks, it is said to be continuous.
Now,
x-axis on the graph show "Target hit" and y-axis shows "Score"
Graph the points using a graphing calculator.
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The complete question is:
"The table shows the relationship between the number of targets a person
hits in a game of laser tag and that person's score.
Target hit 0 1 2 3 4 5 6
Score 0 8 16 24 32 40 48"
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
+
A.
B.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
N N
C.
D.
finance
SURPRISE!
Here's a $10
financet
Instant Cred
Answer:
b , d
Step-by-step explanation:
Solve system of equations.
1/2x-y=-1
x-2 y=5
Answer:
No solution the lines are parallel
Step-by-step explanation:
see picture for reference.
consider a little league team that has 13 players on its roster. a. how many ways are there to select 9 players for the starting lineup? b. how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters? c. suppose 6 of the 13 players are left-handed. how many ways are there to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players?
There are 715 ways to select 9 players for the starting lineup.
Permutation is used whenever there is arrangement or where order is important . denoted by [tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]
n= no of item , r = no of items to be arranged.
Combination is used when there is selection . denoted by[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
n=no of item , r= no of item to be selected.
Part (a)
In the given question
we have to select 9 players out of 13 player , combination will be used
[tex]C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}[/tex]=715 ways.
Part(b)
In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.
Since the batting order is important , permutation will be used.
[tex]P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5[/tex]
=259459200 ways.
Part(c)
In this part we have to do selection of 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
Since order is not important Combination will be used.
To select 3 left handers from total 6 left handers = C(6,3)
& to select 6 positions of left handers from remaining 7 right handers=C(7,6)
No of ways of selection = C(6,3)*C(7,6)
[tex]=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\[/tex]
On solving further we get
[tex]= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways[/tex]
Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.
(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .
(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
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Write the equation of the line that is perpendicular to y = 2x+4 and passes through the
point (-4,-1).
y =____________ X+
Answer: (Likely) y = -2x
Step-by-step explanation:
1. We know the line y = 2x + 4, it intersects 4 and it's rate of change is 2. We also know the point it is passing, (-4,-1).
2. With this info, It is best to confirm the slope is likely -2, since it is likely that lines when perpendicular are likely to be congruent.
3. So, how about the y intercept? Well, it's simple as well, we will substitute x for 0, and 2 times 0 equals 0, and y = 0, so the perpendicular line is y = -2x
The diagram shows three lines with some marked angle measures.
?
?
70°
?
?
53°
?
Find the missing angle
measures marked with
question marks.
The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.
How to determine the measures of the missing angles of a geometric system
In this question we have a geometric system generated by three lines, where two lines pass through the first lines and four angles are generated on each intersection. The measures of the missing angles can be found by the following concepts:
Vertical angles - Two angles opposite to each other have the same measure.Supplementary angles - Two angles adjacent to each other that a total measure of 180°.The first intersection of the geometric system generates two vertical angles of 70° and two vertical angles of 110° and the second intersection of the geometric system generates two vertical angles of 53° and two vertical angles of 127°.
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Find each quotient a7/12÷1/7b -0.05÷(5/8÷1/2) c6 1/4÷(-5/16) d-1÷-(10/13)
The quotient of the problem given are 49/12, -1/25, -20 and 13/10 respectively
These are the simple problems of fractions
A) 7/12 ÷ 1/7
7/12×7/1
49/12
B) -0.05 ÷(5/8 ÷ 1/2)
- 5/100 ÷ ( 5/8 ×2/1)
-5/100÷ (5/4)
-5/100 ×4/5
-1/25
C) 6 1/4 ÷(-5/16)
25/4 × (-16/5)
-20
D) -1 ÷(-10/13)
-1 ×(-13/10)
13/10
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A triangle has an area of 15 square inches.
If the base is 5 inches, what is the height?
Draw the triangle and label its base and height with units
Answer:
The height is 5.
Step-by-step explanation:
Find this answer here in this link!
This is the correct answer
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On a road map, the distance from City A to City B is 4 inches. The map scale is 1 inch = 20 miles. What is the actual distance, in miles, between City A and City B?
(1 + 2 × 3)² + 7
please helppppooppppppppp
Answer:
56
Step-by-step explanation:
(1+2*3)^2+7
(1+6)^2+7
7^2+7
49+7
56
Answer:
Step-by-step explanation:
Using PEMDAS, first find the product of the parentheses. 2*3=6. 1+6=7. 7² is 49. 49+7=56.
The probability that Bob will make a free throw is 3/4 . What is the probability that Bob will make his next 2 free throws.
Answer:
9/16
Step-by-step explanation:
NEED HELP ASAP!!!!!!
Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?
A.
[tex]x > - 4[/tex]
B.
[tex]x \leqslant - 4[/tex]
C.
[tex]x \geqslant 8[/tex]
D.
[tex]x \leqslant 8[/tex]
THE ANSWER IS B.
Answer: Hope it helps!!
I believe it is B. as well
Desmos Graphing calculator is great for problems as well!
Solve system of equations.
x+y=-6
2 x-y=3
The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + y = -6 (equation 1)
2x - y = 3 (equation 2)
Express y in terms of x in one of the equations,
x + y = -6 (equation 1)
y = -x - 6
and then substitute it in the 2nd equation.
2x - y = 3 (equation 2)
2x - (-x - 6) = 3
2x + x + 6 = 3
3x = 3 - 6
3x = -3
x = -1
Substituting the value of x in the equation of y,
y = -x - 6
y = -(-1) - 6
y = 1 - 6
y = -5
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Find the midpoint of the segment with the given endpoints.
(-2,2) and (10,0)
Answer:
I think it’s (4,1)
this is a super difficult math worksheet for me so please help ASAP
Answer:
Step-by-step explanation:
function notation
1) -13
2) -4
3) 7
4) 23
5) 13
6) -4
7) 14
8) -1
9) 15
10) 0
function operations
1) -3x^2 + 11x -4
2) 6x - 12
3) 3x^2 - 2x + 5
4) x^2 - 4x + 5
5) 27x^2 - 32x
6) 2x^5 + 4x^4 - 5x^3 - 10x^2
7) -6x^4 + 8x^3 + 15x^2 - 20x
8) 3x^4 - 2x^3 - 16x^2
One of two supplementary angles measures 6 degrees less than twice
the other. How large are the angles?
Answer:
adding them together, x+2x−6=180 . this can be solved algebraically. the smaller angle is 62∘ . the supplement to that, 2x−6 , is (124−6)∘ , which is 118∘ .
16. SHORT RESPONSE The first story of a building is 24 feet high, and each
additional story is 18 feet high. Write an expression for the height to the top
of the nth story. Explain the meaning of each term in the expression
The height to the top of the nth story of the building is ( 24 + 18(n-1) ).
Height of first story of a building = 24 feet
Height of each additional story = 18 feet
Total number of stories in a building = n
The Height of first story of a building is fixed to be 24 feet and Height of each additional story is 18 feet. We first need to calculate total number of additional stories to write an equation.
The total number of additional stories = ( total number of stories in a building - 1) = (n-1)
The height of total additional stories = 18 (n-1)
Total height of the building = (Height of first story of a building + height of total additional stories) = ( 24 + 18(n-1) ).
The height to the top of the nth story of the building is ( 24 + 18(n-1) ).
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