so, we know his average speed is 1¾ of a mile in 1 hour, so how long is it to cover 9⅝ miles then?
[tex]\bf \begin{array}{ccll} miles&hour\\ \cline{1-2} 1\frac{3}{4}&1\\\\ 9\frac{5}{8}&x \end{array}\implies \cfrac{~~1\frac{3}{4}~~}{9\frac{5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{1\cdot 4+3}{4}~~}{\frac{9\cdot 8+5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{7}{4}~~}{\frac{77}{8}}=\cfrac{1}{x}[/tex]
[tex]\bf \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{11}{~~\begin{matrix} 77 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} =\cfrac{1}{x}\implies \cfrac{2}{11}=\cfrac{1}{x}\implies 2x=11\implies x=\cfrac{11}{2}\implies x=5\frac{1}{2}[/tex]
The required time is 5.5 hours.
Simple linear equation:Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.
It is given that,
Speed=[tex]1\frac{3}{4}[/tex] mile per hour.
Distane:=[tex]9\frac{5}{8}[/tex] mile
[tex]Time=\frac{Distance}{Speed}[/tex]
Now, substituting the given values into the above formula we get,
[tex]T=\frac{\frac{77}{8} }{\frac{7}{4} }\\ =\frac{77\times4}{8\times 7} \\=\frac{11}{2}\\ T=5.5 hour[/tex]
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multiply (2x^2 + 3x - 6)(x - 1)
Answer:
2x^3 + x^2 - 9x + 6
Step-by-step explanation:
(2x^2 + 3x - 6)(x - 1)
2x^3 + 3x^2 - 6x - 2x^2 - 3x + 6
2x^3 + x^2 - 9x + 6
Please help me with this question
Answer:
I
Step-by-step explanation:
At least means greater than or equal to
a ≥ 10
That is a closed circle
We have a closed circle at 10
We have to be at least 10 years old
Closed circle at 10, line going to the right
What is the vertex of the graph of the function below?
y= x^2 - 8x+ 12
O A. (2,0)
O B. (4,0)
O C. (2,-4)
O D. (4,-4)
Answer:
D. (4, -4)
Step-by-step explanation:
Convert to vertex form by completing the square.
For a polynomial y = x² + bx + c, first add and subtract (b/2)² to the polynomial. Then factor.
Here, b = -8. So (b/2)² = (-8/2)² = 16.
y = x² − 8x + 12
y = x²− 8x + 16 − 16 + 12
y = (x − 4)² − 16 + 12
y = (x − 4)² − 4
The vertex is (4, -4).
The vertex of the function y = x2 - 8x + 12 is found by first using the formula -b/2a to find the x-coordinate of the vertex, and then substituting that value into the equation to find the y-coordinate. This results in the vertex being at the point (4,-4).
Explanation:The vertex of a quadratic function given in the form y = ax2 + bx + c is found using the formula -b/(2a) for the x-coordinate, and substituting that value into the equation to find the y-coordinate. In the given function y = x2 - 8x + 12, a is equal to 1, and b is equal to -8.
Using the vertex form, the x-coordinate of the vertex can be found by using -b/2a, or --8/(2*1), which equals 4. This becomes the x-coordinate of our vertex. Substituting x = 4 into our equation, we find y = (4)2 - 8*4 + 12 = -4. Therefore, the vertex of the given graph is at the point (4,-4), which corresponds to option D.
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(4x-4) (3x+17)
The lines. intersect at point C. What is the value of X?
Answer:
(21, 80)
Step-by-step explanation:
We have the two lines y = 4x -4 and y = 3x + 17. The point 'C' will be given by the interception of them, as follows:
4x -4 = 3x + 17
Solving for 'x':
x = 21
Now, to find 'y' we have:
y = 4(21) -4 = 80
Therefore, they intercept at: (21, 80)
For this case we must find the value of "x":
We have that, by definition:
[tex]4x-4 = 3x + 17[/tex]
Because they are opposite the vertex.
Then, subtracting[tex]3x[/tex] on both sides we have:
[tex]4x-3x-4 = 3x-3x + 17\\x-4 = 17[/tex]
Adding 4 to both sides:
[tex]x = 17 + 4\\x = 21[/tex]
So, the value of x is 21
Answer:
[tex]x = 21[/tex]
The diagram shows a scale drawing of a rectangular banner with a scale of 1:30. Calculate
itu,
the actual length, in m, of the banner.
the area, in m', of the banner.
The diagram showed a banner with the length of 4cm and width of 9cm.
Thank you
Answer:
Part 1) The actual length of the banner is [tex]1.2\ m[/tex]
Part 2) The area of the banner is [tex]3.24\ m^{2}[/tex]
Step-by-step explanation:
we know that
The scale of the drawing is [tex]\frac{1}{30}[/tex]
That means ----> 1 cm on the drawing represent 30 cm in the actual
Using proportion
Find out the actual dimensions of the banner
Let
L the actual length of the banner
W the actual width of the banner
For a length of 4 cm in the drawing
[tex]\frac{1}{30}=\frac{4}{L}\\ \\ L=30*4\\ \\L=120\ cm[/tex]
Convert the actual length to meters
[tex]L=120/100=1.2\ m[/tex]
For a width of 9 cm in the drawing
[tex]\frac{1}{30}=\frac{9}{W}\\ \\ W=30*9\\ \\W=270\ cm[/tex]
Convert the actual width to meters
[tex]W=270/100=2.7\ m[/tex]
Find the area of the banner
[tex]A=1.2*2.7=3.24\ m^{2}[/tex]
SOS I need help with this question
Equation: 2x^2 + 10x - 3x - 15
Step1: Factor completely (10 points)
step2: after the polynomial is factored, solve the zeroes of the function
step3: describe the end behavior of the graph
step4: will the vertex of the function be minimum or maximum function?
Answer:
1) (2x - 3)(x + 5)
2) 1.5, -5
3) Open upwards from both ends
4) Minimum
Step-by-step explanation:
Step 1:
The given polynomial is:
[tex]2x^{2}+10x-3x-15[/tex]
Taking out commons, we get:
[tex]2x(x+5)-3(x+5)\\\\ =(2x-3)(x+5)[/tex]
This is the factorized form of the polynomial.
Step 2:
The zeros of the functions occur when the function is equal to zero.
i.e.
[tex](2x-3)(x+5)=0\\\\ \text{According to the zero product property}\\\\ 2x-3=0, x+5=0\\\\ x =\frac{3}{2}=1.5, x = -5[/tex]
This means, the zeros of the polynomial are 1.5 and -5
Step 3:
The end behavior of a graph depends on its degree and the sign of leading coefficient. Since the degree is even and the coefficient is positive the graph of the polynomial will opens upwards from left and right side.
Step 4:
The given polynomial is a quadratic function with positive leading coefficient. Since it open vertically upwards, its vertex will be the lowest most point. So, the vertex will be the minimum of the function.
work out the area of a circle when the radius is 7cm given your answer in terms of pie
Answer:
49π cm²
Step-by-step explanation:
area = πr²
fill in r=7cm
What is the x intercept of
f(x)=(x-7)^2
Answer:
The x-intercept is (7,0).
Step-by-step explanation:
See the graph below for explanation
What is the factored form of 3x+24y?
Both 3 and 24 have 3 in common. This means that you can factor a three out of this equation like so:
3(x + 8y)
If you distribute the three back into the equation then you would then get 3x + 24y (the equation before factoring)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
3 ( x + 8 y )
Step-by-step explanation:
Since 3 is the LCM ( lowest common multiple ) which goes into both numbers, it will go on the outside of the brackets. To get the insides of the brackets you have to divide the original expression by 3
3 ÷ 3 x = x
24 y ÷ 3 = 8 y
And our final factored form is 3 ( x + 8 y )
Determine the general form of the equation for the circle (x – 1)2 + (y + 2)2 = 3.
x2 + y2 – 2x + 4y + 2 = 0
x2 + y2 – x + y + 3 = 0
x2 + y2 – 2x + 4y – 4 = 0
x2 + y2 – x + y + 2 = 0
(x-1)(x-1) + (y+2)(y+2) = 3
x2 -1x -1x + 1 + y2 +2y +2y +4=3
x2 +y2 -2x +4y + 2=0
A is the answer
-42.8451
Round the result to the nearest tenth and then to the nearest hundredth
Answer:
Tenth:-42.8
Hundredth: -42.85
To explain:
To the right of the decimal point every name of the place ends with -th.
If a number is bigger than 5 you round the number left to it by 1
If it's 4 or smaller you don't do anything.
Sidney has 46,880 marbles to put into giant jars. She wants to put the same number of marbles in each jar with no extra marbles. How many jars could Sidney use?
Select all possible numbers:
4 , 2 , 10 , 5
Answer:
4 , 2 , 10 , 5
Step-by-step explanation:
46,880
Since this is an even number, we can divide by 2
46,880/2 =23440
Since this number ends in either a 0 or a 5 we can divide by 5
46880/5 =9376
Since the number is divisible by 2 and 5, we know it is divisible by 10
46880/10 =4688
The only number we need to check is 4
If the last 2 numbers are divisible by 4 then the number is divisible by 4
80/4 = 20 so the number is divisible by 4
46880/4 =11720
46880 is divisible by 4,2,10,5
Answer:
all of the are correct
. Pots
What is the solution to this equation?
x – 9 = 17
ОА. x= 28
Ов. х = 8
Ос. х = 26
OD. х = 12
Answer:
с. х = 26
Step-by-step explanation:
x – 9 = 17
Add 9 to each side
x – 9+9 = 17+9
x = 26
If you buy a car for 15500 an average on an average a new car loses 11% of its value the moment that is driven off the lot once you driving the car back to your new car off the lot what is the value be
Answer:
$13,795
Step-by-step explanation:
15500/x=100/11
(15500/x)*x=(100/11)*x - we multiply both sides of the equation by x
15500=9.0909090909091*x - we divide both sides of the equation by (9.0909090909091) to get x
15500/9.0909090909091=x
1705=x
x=1705
now we have:
11% of 15500=1705
For the following geometric sequence find the recursive formula: {-1, 3, -9, ...}.
Based on these first few terms, we can deduce that the next term is computed by switching the sign of the previous one, and multiplying it by 3: we start with -1, we switch the sign (1) and multiply by 3 (3); then again we switch the sign (-3) and multiply by 3 (-9), and so on.
Since switching sign is the same as multiplying by -1, we can compute every next term by multiplying the previous one by -3:
[tex]a_1 = -1\\a_2 = a_1\cdot(-3) = (-1)\cdot(-3)=3\\a_3 =a_2\cdot(-3)=3\cdot(-3)=-9[/tex]
So, the recursive formula is
[tex]a_n = -3a_{n-1}[/tex]
because it states precisely that the next term is -3 times the previous one.
In a population of 1000 individuals, 100 new individuals were born and 200
individuals died over the course of 1 year. Which equation shows how to
calculate the population growth rate of this population?
O
A. 0.10 0.20 = 0.02
O
B. 0.10 - 0.20 = -0.10
O
C. 0.20 +0.10 = 0.30
O
D. 0.20 - 0.10 = 0.10
Answer:
the answer to this question is b.
Answer:
The correct option is B.
Step-by-step explanation:
It is given that In a population of 1000 individuals, 100 new individuals were born and 200 individuals died over the course of 1 year.
We need to find the population growth rate of this population.
Rate of birth = [tex]\frac{100}{1000}=0.10[/tex]
Rate of death = [tex]\frac{200}{1000}=0.20[/tex]
The formula for rate of change is
Rate of change = Rate of birth - Rate of death
Rate of change = 0.10 - 0.20
Rate of change = -0.10
The required equation is 0.10 - 0.20 = -0.10.
Therefore, the correct option is B.
Find the perimeter of the triangle
Answer:
=136
Step-by-step explanation:
Lets solve the triangle using the sine formula.
c/sine C=a/sine A
C= 180-(72+16)
=92°
61/Sin 92=a/sin 72
a=(61 sin 72)/sin 92
=58.0
Solving for b:
c/sin C= b/Sin B
61/sin 92= b/Sin 16
b=(61 Sin 16)/Sin 92
=16.82
Perimeter = 61 +58+ 16.82 = 135.82
Answer =136 to the nearest whole number.
factor the GCF: 12a^3b + 8a^2b^2 — 20ab^3
Answer:
GCF = 4ab
Step-by-step explanation:
We need to factor the GCF of
12a^3b+8a^2b^2-20ab^3
Finding the common term: 4ab
So, GCF = 4ab
Factoring the common term
12a^3b+8a^2b^2-20ab^3= 4ab(3a^2+2ab-5b^2)
Factor completely. X^3+6x+x^2+6
Answer:
(x+1) (x^2+6)
Step-by-step explanation:
x^3+6x+x^2+6
Rearranging the order
x^3+x^2 + 6x+6
We can factor by grouping
Taking an x^2 from the first two terms and a 6 from the last two terms
x^2(x+1) +6(x+1)
Now we can factor out an (x+1)
(x+1) (x^2+6)
Two events are disjointed. Find P(A or B), if P(A) = 1/7
and P(B) = 3/7.
1/7
3/7
4/7
2/7
Answer:
4/7
Step-by-step explanation:
P(A or B) when A and B are disjointed is P(A)+P(B)
P(A or B)=P(A)+P(B)
P(A or B)=1/7 +3/7
P(A or B)=4/7
The value of P(A or B) is 4/7 (3rd option)
What is the formula of P(A or B) of disjoint events ?Let A and B be two disjoint events.
Then, probability of A is P(A) & probability of B is P(B).
In this case, the probability of A or B is the sum of P(A) & P(B)
∴ P(A or B) = P(A) + P(B)
What is the required probability ?Given, P(A) = 1/7 & P(B) = 3/7
So, P(A or B) = P(A) + P(B)
= 1/7 + 3/7
= (1+3)/7
= 4/7
Required value of P(A or B) is 4/7
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What’s x-2 = 3x-84
I just need this answered to be able to answer another equation.
30 points
Answer: x = 41
Step-by-step explanation: You need to isolate x. First, subtract x from each side. You will get:
-2 = 2x - 84
Next, add 84 to each side.
82 = 2x
Divide by 2 on each side.
X = 41
Answer:41
Step-by-step explanation:x-3x=-84+2
-2x=-82
X=-82/-2
X=41
what is 10.15384615 as a fraction?
Answer:
The answer is an attachment I hope it helps!!!
The solutions to the inequality y> -3x + 2 are shaded on
the graph. Which point is a solution?
0 (0,2)
O (2,0)
0 (1,-2)
O (-2,1)
Answer:
(2,0)
Step-by-step explanation:
y> -3x + 2
Substitute the points into the inequality to see if they are a solution
(0,2)
2 > -3(0)+2
2 > 2 False
(2,0)
0> -3(2) + 2
0>-6+2
0> -4 True
(1,-2)
-2> -3(1) + 2
-2 > -3+2
-2 >-1 False
(-2,1)
1> -3(-2) + 2
1 >6+2
1>8 False
find the quotient of 226.84 round your answer to the nearest tenth
Answer: 226.8
Step-by-step explanation: Find the number in the tenth place 8 and look one place to the right for the rounding digit 4 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
The weights of steers in a herd are distributed normally. The standard deviation is
100lbs
100lbs
and the mean steer weight is
1200lbs
1200lbs
. Find the probability that the weight of a randomly selected steer is between
1000
1000
and
1369lbs
1369lbs
. Round your answer to four decimal places.
Answer:
0.9317
Step-by-step explanation:
Standard deviation of the weights = [tex]\sigma[/tex]=100 lbs
Mean weight = u = 1200 lbs
We need to find the probability that the weight(x) of a randomly selected steer is between 1000 lbs and 1369 lbs i.e. P(1000 < x < 1369)
Since, weights follow the normal distribution we can use the z values to find the required weight. For this we have to convert both the values to z score. The formula for z scores is:
[tex]z=\frac{x-u}{\sigma}[/tex]
1000 converted to z scores is:
[tex]z=\frac{1000-1200}{100}=-2[/tex]
1369 converted to z scores is:
[tex]z=\frac{1369-1200}{100}=1.69[/tex]
So, we have to find the values from z table that lie between -2 to 1.69
P( 1000 < x < 1369 ) = P(-2 < z < 1.69)
P(-2 < z < 1.69) = P(z < 1.69) - P(z < -2)
From the z table:
P(z < 1.69) = 0.9545
P(z < -2) = 0.0228
So,
P(-2 < z < 1.69) = 0.9545 - 0.0228 = 0.9317
Thus,
P( 1000 < x < 1369 ) = 0.9317
From this we can conclude that:
The probability that the weight of a randomly selected steer is between 1000 lbs and 1369 lbs is 0.9317
Final answer:
The probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean of 1200lbs and standard deviation of 100lbs, is approximately 0.9326 or 93.26%.
Explanation:
To find the probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean (μ) of 1200lbs and a standard deviation (σ) of 100lbs, we first convert the weights into z-scores.
The z-score for a value x is given by the formula:
z = (x - μ) / σ
Calculating the z-scores for both weights:
For 1000lbs: z = (1000 - 1200) / 100 = -2
For 1369lbs: z = (1369 - 1200) / 100 = 1.69
We then look up these z-scores in a standard normal distribution table or use a calculator with statistical functions to find the probabilities for each. The probability for a z-score less than -2 is approximately 0.0228, and for a z-score less than 1.69 is approximately 0.9554.
To find the probability that a steer's weight falls between 1000lbs and 1369lbs, we subtract the smaller probability from the larger probability:
Probability = P(z < 1.69) - P(z < -2) = 0.9554 - 0.0228 = 0.9326
Therefore, the probability that a steer weighs between 1000 and 1369lbs is 0.9326, or 93.26% when rounded to four decimal places.
find the slope and the y-intercept of the line 7x-2y=-8
Answer:
slope = 7/2
y-int = 4
Step-by-step explanation:
parent formula is y=mx+b ; where m is slope and b is y-int.
begin by rewriting formula to isolate y ; 7x+8=2y ; divide bothe sides by 2 ; so
7/2 x+4=y. slope/m=7/2 and y-int/b=4
What is the value of y?
Answer:
y=3
Step-by-step explanation:
The vertical sides of the rectangle must be equal
10 =2y+4
Subtract 4 from each side
10-4 =2y+4-4
6 = 2y
Divide each side by 2
6/2 =2y/2
3=y
find the permutation of these letters (a,b,c) taking a letter at a time
Answer:
List the letters in alphabetical order
Step-by-step explanation:
ABC,ACB
BAC,BCA
CAB,CBA
Answer: 6 permutations
Step-by-step explanation: A permutation is an arrangement of objects in which order is important. In this problem, to find the number of permutations of the letters A, B, and C, we find the number of ways we can arrange the order of the letters A, B, and C.
Image provided.
Therefore, there are 6 permutations of the letters A, B, and C.
use the formula to find the value of $400 invested in 4%
Answer:
Some part of the question is missing , you are requested to kindly recheck it once. There must be some time provided in the problem
Step-by-step explanation:
What is the circumference of the circle shown below, given that the length of
AB (the minor arc) is 4?
Answer:
A
Step-by-step explanation:
The following ratio is true for any circle
[tex]\frac{arc}{C}[/tex] = [tex]\frac{centralangle}{360}[/tex] ← C is circumference
[tex]\frac{4}{C}[/tex] = [tex]\frac{30}{360}[/tex] ( cross- multiply )
30C = 1440 ( divide both sides by 30 )
C = 48 → A
Answer:48
Step-by-step explanation:i got it right