Answer:
x = 160 ft
Step-by-step explanation:
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is given by:
[tex] v_{f}^{2} = v_{0}^{2} + 2ax [/tex]
Where:
[tex]v_{f}[/tex]: is the final speed of the car = 0 (since it stops)
[tex]v_{0}[/tex]: is the initial speed of the car = 80 ft/s
a: is the acceleration of the car = -20 ft/s²
x: is the distance recorred by the car
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is:
[tex] x = \frac{v_{f}^{2} - v_{0}^{2}}{2a} = \frac{0 - (80 ft/s)^{2}}{2*(-20 ft/s^{2})} = 160 ft [/tex]
Therefore, the car travels 160 ft between the time the brakes are applied and the time the car comes to a stop.
I hope it helps you!
A recursion formula and the initial term of a sequence are given. Write out the first five terms of the sequence. a Subscript font size decreased by 1 1equals6, a Subscript n plus font size decreased by 1 1equalsminusa Subscript n
Answer:
6, -6, 6, -6 and 6.
Step-by-step explanation:
Given the recursion formula for a sequence
[tex]a_{n+1}=-a_n\\$where a_1=6\\[/tex]
The first five terms of the sequence are:
[tex]\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6[/tex]
Therefore, the first five terms of the sequence:
[tex]a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.[/tex]
A certain bridge arch is in the shape of half an ellipse 106 feet wide and 33.9 feet high. At what horizontal distance from the center of the arch is the height equal to 12.3 feet
Answer:
The horizontal distance from the center is 49.3883 feet
Step-by-step explanation:
The equation of an ellipse is equal to:
[tex]\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1[/tex]
Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.
Then, replacing a by 106/2 and b by 33.9, we get:
[tex]\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1[/tex]
Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:
[tex]\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883[/tex]
So, the horizontal distance from the center is 49.3883 feet
Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.9 and 1.5 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.2 pH units to all of the values and then multiply the result by 1.3. Find the mean and standard deviation of the corrected pH measurements.
Answer:
The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.
Step-by-step explanation:
We can correct the values of the mean and standard deviation using the properties of the mean and the variance.
To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:
[tex]Y=1.3(X+0.2)[/tex]
The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.
Then, we can apply the properties of the mean as:
[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]
For the standard deviation, we apply the properties of variance:
[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]
The properties that have been applied are:
[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]
A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
Answer:
D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3)
Step-by-step explanation:
Adding (-1, 2) to each of the coordinates gives ...
D +(-1, 2) = (-1-1, 3+2) = D'(-2, 5)
E +(-1, 2) = (4-1, 3+2) = E'(3, 5)
F +(-1, 2) = (4-1, 1+2) = F'(3, 3)
G +(-1, 2) = (-1-1, 1+2) = G'(-2, 3)
Answer:
The answer is B.
Step-by-step explanation:
I got it correct on Edge 2020
Please help i do not understand this one!
Answer:
B. [[0,4]
[-6,1]
[3,-4]]
Step-by-step explanation:
If you multiply the matrices, you get the answer.
What value of x is in the solution set of 3(x – 4) ≥ 5x + 2? –10 –5 5 10
Answer:I think it -5 wait lemme check answer again
The solution to the inequality will be greater than or equal to –5. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
3(x – 4) ≥ 5x – 2
Simplify the equation, then the solution to inequality will be
3(x – 4) ≥ 5x –2
3x – 12 ≥ 5x –2
5x – 3x ≤ – 12 + 2
2x ≤ – 10
x ≤ –5
The solution to the inequality will be greater than or equal to –5.
Then the correct option is B.
The correct equation is 3(x – 4) ≥ 5x – 2.
More about the inequality link is given below.
https://brainly.com/question/19491153
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How many 1/2 are there in 6/4
Answer:
3
Step-by-step explanation:
6/4 (divide numerator and denominator each by 2)
= 3/2
= 3 x (1/2)
hence there are 3 halves in 6/4
Answer:
3
Step-by-step explanation:
To find out, we need to divide.
[tex]\frac{6}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex]
When dividing fractions, you multiply the 1st term by the second term's reciprocal.
so
[tex]\frac{6}{4}[/tex] x 2
If you simplify you get [tex]\frac{6}{2}[/tex] or 3.
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.7 degrees. Low Temperature (circleF) 40 minus 44 45minus49 50 minus 54 55 minus 59 60 minus 64 Frequency 2 7 9 5 1 The mean of the frequency distribution is nothing degrees. (Round to the nearest tenth as needed.)
Answer:
51.2°FStep-by-step explanation:
Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;
[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]
[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]
The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)
One number is 1/2 another number. The sum of the two numbers is 33. Find the two numbers.
Answer:
11
Step-by-step explanation:
I looked it up for you so no problem
Answer: 11 and 22
Step-by-step explanation:
We can start by making an equation. Since we know we have two numbers added to make 33. One number can be represented by x and the other is half of this x number so we can write this equation.
33 = 1/2x + x
Now we can combine like terms.
33 = 3/2x
Then either multiply by the reciprocal or divide by 1.5 on both sides.
x = 22
And the other number is half this number so divide by 2.
y = 11
On a game show, 14 contestants qualified for the bonus round and 6 contestants did not.
What is the experimental probability that the next contestant will qualify for the bonus round?
Write your answer as a fraction or whole number.
Answer:
The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
The experimental probability of an outcome is the number of trials in which the desired outcome happened divided by the total number of trials.
What is the experimental probability that the next contestant will qualify for the bonus round?
14 contestants qualified out of 14+6 = 20 contestants. So
[tex]p = \frac{14}{20} = \frac{7}{10}[/tex]
The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]
The ratio of boys to girls in a club is 4:3. If there are 48 boys, how many members of the club are there?
Answer:
84
Step-by-step explanation:
Basically the ratio was multiplied by 12 to get the number of boys so you do the same to the other one.
Answer:
number of boys+number of girls=48boys+36girls=84members
Step-by-step explanation:
FIRST WE FIND THE NUMBER OF GIRLS BY STATISTICAL METHOD
4:3=48:x
4/3=48/x
By cross multiplication
4×x=48×3
4x=144
Dividing 4 on both sides
4x/4=144/4
x=36=number of girls
The arithmetic sequence a1 is defined by the formula:
a1 = 4
a1=ai-1 +11
Find the sum of the first 650 terms in the sequence.
Answer:
2,322,775
Step-by-step explanation:
Given a1 = 4 and ai =ai-1 +11
when i = 2
a2 = a2-1+11
a2 = a1+11
a2 = 4+11
a2 = 15
when i = 3
a3 = a2+11
a3 = 15+11
a3 = 26
The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;
4, 15, 26...
Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}
a is the first term = 4
d is the common difference = 15-4 = 26-15 = 11
n is the number of terms.
Since we are to find the sum of the first 650 terms in the sequence, n = 650
S650 = 650/2{2(4)+(650-1)11}
S650 = 325{8+(649)11}
S650 = 325(8+7,139)
S650 = 325×7147
S650 = 2,322,775
15 divided by 6 2/3=
Answer:
The answer is D.
Step-by-step explanation:
First, you have to convert the mixed number into improper fraction :
[tex]6 \frac{2}{3} [/tex]
[tex] = \frac{3 \times 6 + 2}{3} [/tex]
[tex] = \frac{20}{3} [/tex]
Next, you can divide it by cutting out the common factor :
[tex]15 \div \frac{20}{3} [/tex]
[tex] = 15 \times \frac{3}{20} [/tex]
[tex] = 3 \times \frac{3}{4} [/tex]
[tex] = \frac{9}{4} [/tex]
[tex] = 2 \frac{1}{4} [/tex]
The value of the expression after divide is,
⇒ 2 1/4
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ 15 divided by 6 2/3
Now,
We can divide as;
⇒ 15 divided by 6 2/3
⇒ 15 ÷ 6 2/3
⇒ 15 ÷ 20/3
⇒ 15 × 3/20
⇒ 45/20
⇒ 9/4
⇒ 2 1/4
Learn more about the divide visit:
https://brainly.com/question/28119824
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What is the decimal equivalent of 23/9
Answer:
2.555555
Step-by-step explanation: Nine times 2 is 18. When we subtract 18 from 23 we get 5. In the quotient we add a decimal point and add a zero to 5 which is 50. Nine times 5 is 45. When we subtract 45 from 50 we get 5 again and again and again . In decimal form it is 2.5555555.
Answer:
2.55 Hope this helps!
10,25,35,45... What's the pattern?
Answer:
15
Step-by-step explanation:
The pattern is going by 15 because 10+15=25 and then continue going.
Answer:
15 is the answer
Step-by-step explanation:
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Tangents that meet at a point are equal in length so DB = CB
Let's form an equation:
10x + 16 = 5x + 20
- 16 from both sides
10x = 5x + 4
- 5x from both sides
5x = 4
/5 on both sides
x = 4/5
Sub this value into the expression for CB
5(4/5) + 20 = 24
Thus, the answer is option D. 24
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
4TH OPTION
Step-by-step explanation:
IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.
ie BD = BC
ie 10x +16 = 5x+20
10x - 5x = 20 -16
5x = 4
x = 4/5
therfore BC = 5x+20 = 5*4/5 +20
BC= 4+20
BC = 24
HOPE IT HELPS...
You look at a caterpillar under a magnifying glass. The image of the caterpillar is three times the caterpillar's actual size and has a width of 4 in. Find the actual dimension of the caterpillar. Select one: a. 12 in. b. 3 in. c. 4/3 in. d. 3/4 in.
Answer: c
Step-by-step explanation: 4/1 x 1/3 = 4/3
An attendant at a car wash is paid according to the number of cars that pass through. Suppose that following payments are made with the following probabilities: Payment Probability $7 0.18 $9 0.08 $11 0.09 $13 0.16 $15 0.08 $17 0.41 Find the standard deviation of the attendant's earnings.
Answer:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
Payment $7 $9 $11 $13 $15 $17
Probability 0.18 0.08 0.09 0.16 0.08 0.41
For this case we can calculate the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
Find the point estimate for the true difference between the given population means.
Weights (in Grams) of Soap Bar A: 121, 122, 124, 123, 120, 124, 121, 121, 121, 123, 120
Weights (in Grams) of Soap Bar B: 121, 120, 122, 119, 121, 122, 122, 120, 120, 121, 122, 123, 119
Answer:
0.9 grams
Step-by-step explanation:
The point estimate for the average weight of Soap Bar A is:
[tex]A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams[/tex]
The point estimate for the average weight of Soap Bar B is:
[tex]B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams[/tex]
Therefore, the point estimate for the true difference between the given population means is:
[tex]Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams[/tex]
The point estimate for the difference is 0.9 grams.
Answer the question above?
Answer:
m>n
Step-by-step explanation:
The value of m
The sum of the angles of a triangle are 180
50+30 + m = 180
m = 180-50-30
m = 100
The value of n
The sum of the angles of a triangle are 180
28 + 58+n = 180
n = 180-58-28
n=94
m>n
The area of the trapezoid is 24 in.2.
True or false
Answer:
The answer is true
Step-by-step explanation:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2
Does anyone know this? I think its B? Am i correct?
Yes, B. Rising action is correct
100 points for brainiest
absurd answers WILL be recorded!
Please try!!!
Answer:
462cm^3
Step-by-step explanation:
Volume of a pyramid = 1/3 × base area × height
Now the base is a rectangle with sides 7cm and 18cm; area of base is;
7 × 18 = 126cm^2
Therefore volume =
1/3 × 126 × 11 = 42 × 11= 462cm^3
Add. Write your answer in simplest form. 7/10 + 1/4
Answer:
[tex] \frac{19}{20} [/tex]
Step-by-step explanation:
[tex] \frac{7}{10} + \frac{1}{4} \\ \frac{14 + 5}{20} \\ = \frac{19}{20} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Suppose the high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 10 feet above the height of the low tide. Low tides occur 6 hours after high tides. Suppose there are two high tides and two low tides every day and the height of the tide varies sinusoidally.
a) Find a formula for the function y = h(t) that computes the height of the tide above low tide at time t. (In other words, y = 0 corresponds to low tide)
b) What is the tide height at 11:00 am?
Answer:
The low tide, when it is 10 feet below the high tide would be at 7am and 7pm
Step-by-step explanation:
Write an equation that would represent the following word problem: Billy buys one candy bar for $2 and 3 lollipops. If he spends $3.98 in total, how much is each lollipop? [USE x AS YOUR VARIABLE - DO NOT USE SPACES IN YOUR ANSWER]
Leap years are years in which February has 29 days instead of 28. The device of leap year was invented to keep the calendar in sync with the "True time of year" because a year has approximately 3651/4 days, but actually slightly less, most, but not all, years divisible by 4 have been made leap years. The rule that is used to keep the calendar in sync is:
Answer:
As you know, a year has around 365 + 1/4 days.
This means that in two years, we have:
365 + 356 + 1/4 + 1/4 = 730 + 1/2
and so on.
adding this up, when we have 4 years we have a full day extra, this is:
1460 + 1
When we divide 1461 by 4, we have 365 with a surpass of 1.
The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.
So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.
The "math rule" used to know if a year is leap or not is:
if a year is not divisible by 4, then it is a common year
else if the year is not divisible by 100 then it is a leap year,
else if the year is not divisible by 400, then it is a common year
if not, the year is a leap year.
Where "year" represents the number of the year.
hiii guys i need help with my homewrok [tex]-9\leq 7-8x[/tex]
Answer:
The answer is x ≤ 2.
Step-by-step explanation:
Firstly, you have to move the unrelated term to the other side :
[tex] - 9 \leqslant 7 - 8x[/tex]
[tex] - 9 - 7 \leqslant - 8x[/tex]
[tex] - 16 \leqslant - 8x[/tex]
Next you can solve it :
[tex] - 8x \geqslant - 16[/tex]
[tex]x \leqslant - 16 \div - 8[/tex]
[tex]x \leqslant 2[/tex]
*Remember to change the symbol, when it is dividing by a negative value
value of 2 to the 3 power
Answer:
two to the thrid power is 8.
Step-by-step explanation:
2^3= 8
Answer:
I'm not sure what exactly the question is but it should be 8
Step-by-step explanation:
2^3
2×2×2=8
Which point satisfies both ƒ(x) = 2x and g(x) = 3x?
Answer:
(0,0)
Step-by-step explanation:
If a point satisfies both functions, they must be equal to each other. Thus, we have:
[tex]f(x)=g(x)[/tex]
[tex]2x=3x[/tex]
The only x that satisfies this is 0.
Therefore, the y is also zero.
The point is (0,0).
Alternatively, you can also visualize the graphs. The only point where the graphs will touch is the origin point or (0,0).