Answer:
6 miles
Step-by-step explanation:
The time Johnny rode was ...
1 h 11 min = (60 min) +(11 min) = 71 min = 71 × (60 sec) = 4260 sec
The distance of one revolution of the bike tire is ...
C = πd = 3.14(30 in) = 94.2 in
So, the total distance Johnny rode was ...
(4260 sec)×(94.2 in/sec) = 401,292 in
__
We know there are 5280 feet in a mile, and each of those is 12 inches. So, the number of inches in a mile is ...
5280 ft = 5280×(12 in) = 63,360 in
__
The number of miles Johnny rode can be found by dividing the total distance by the distance in 1 mile:
(401,292 in)/(63,360 in/mile) = 6.33 mile
Johnny rode about 6 miles in 1 hour 11 minutes.
PLEASE HELP FAST Convert the following equation to logarithmic or exponential form:
log subscript 49 left parenthesis 7 right parenthesis equals 1 half
Your answer:
49 to the power of 7 equals 1 half
7 to the power of 49 equals 1 half
open parentheses 1 half close parentheses to the power of 7 equals 49
49 to the power of 1 half end exponent equals 7
Answer:
D
Step-by-step explanation:
I interpret your problem as log49(7)=1/2
This would be the same as 49^1/2=7 because taking a number to the 1/2 power is the same as taking its square root [sqrt(49)=7].
Kenny wants to take his dog to an obedience school. At sit and stay school, 12 lessons cost $96. At canine community center,25 lessons cost $125. Which is the better deal? Find the unit rate for lessons at sit and stay school.Show your work
The cost of one lesson in obedience school is $8 and in community center is $5. Therefore, canine community center is better choice.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Cost of 12 lessons to obedience school = $96
Cost of 1 lesson to obedience school = 96/12 = $8
Also, cost of 25 lessons at canine community center = $125
Cost of 1 lesson at canine community center = 125 / 25 = $5
Since, the cost of one lesson in obedience school is $8 and in community center is $5.
So, the canine community center is better school.
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What is the solution to the proportion 6/11 = m/121
Answer:
m=66
Step-by-step explanation:
Answer:
m=66
Step-by-step explanation:
Solve the system of equations.
- 4x + 11y = 15
x = 2y
y =
x=
Convert the following to find the unknown measure.
1) 42 Km = ?
miles
2) 37 oz = ?
grams
3) 15.3 L = ?
Quarts
Answer:
1. 26.0976
2. 1048.93
3. 16.16733
2. You put $3,800 dollars in a savings account. The bank will provide 1.8% interest every year. Write and solve a model that describes how much money will be in the account in 15 years.
Answer:
The money that will be in her account in 15 years is $4965.84
Step-by-step explanation:
Given data
Principal p= $3800
rate r= 1.8% - - - - - - 1.8/100=0.018
Time t= 15 years
Final amount A=?
The model that describes the e amount in the account is the compound interest model
A = P(1 + r)^t
Substituting our given data into this model we have
A= 3800(1+0.018)^1 5
A=3800(1.018)^15
A=3800*1.3068
A= $4965.84
In a basketball tournament, Team A scored 5 less than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Let the variable b represent Team B's total points. The equation representing this scenario is (2b – 5) + b + (b + 80) = 983. Team B scored 227 total points.
Answer:
Team B scored 227 points.Step-by-step explanation:
The expression that models this problem is
[tex](2b-5)+b+(b+80)=983[/tex]
To know the total points Team B scored, we just need to solve the expression for [tex]b[/tex]
[tex]2b-5+b+b+80=983\\4b=983-80+5\\4b=908\\b=\frac{908}{4} \\b=227[/tex]
Therefore, Team B scored 227 points.
Notice that the problem specifies each term of the expression.
"Team A scored 5 less than twice as many points as Team B": [tex]2b-5[/tex]
"Team C scored 80 more points than Team B": [tex]b+80[/tex]
"They combined score was 983 points": = 983.
With all this information, we defined the expression to find [tex]b[/tex]
Answer:
c
Step-by-step explanation:
What is the length of the missing leg?
15 m/
9 m
meters
Answer:
The length of the missing leg is approximately 17.49 meters.
Explanation:
To find the length of the missing leg in a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, if one leg(hypotenuse) is 15 meters and the other leg(base) is 9 meters, and we denote the missing leg as [tex]\(x\)[/tex] meters, we have:
[tex]\[x^2 + 9^2 = 15^2\][/tex]
[tex]\[x^2 + 81 = 225\][/tex]
[tex]\[x^2 =144 \][/tex]
Now, to find [tex]\(x\)[/tex] , we take the square root of both sides:
[tex]\[x = \sqrt{144}\][/tex]
[tex]\[x = 12\][/tex]
Question:
A right triangle's leg is 9 and the hypotenuse is 15, what is the other leg s length?
what is the answer to this?
The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A=1700e^0.062t When will the account be worth $2466?
Answer:
The value of the investment will be worth $2466 in the year 2017
Step-by-step explanation:
In this question, we are tasked with finding the specific year in which an amount invested in a money market account reaches a particular value
To get this year, what we need to do is to get the value of t from the exponential equation given in the question. To get t, we simply make the value of A set to the particular value in the question.
Hence, we use [tex]A = 1700e^{0.062t} \\[/tex]
Now, we plug the value of A = 2466 and take the natural logarithm of both sides i.e [tex]Log_{e}[/tex] or simply ln
From;
[tex]2466 = 1700e^{0.062t}[/tex]
ln 2466 = ln[tex]1700e^{0.062t}[/tex]
ln 2466 = 0.062t ln1700
7.81 = 0.062t × 7.44
t = 7.81/(0.062 × 7.44)
t = 16.93 approximately 17 years
This means that the value of the investment will have that worth in the year 2000+17 = year 2017
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
If interest rates stay at 4% APR and I continue to make my monthly $50 deposits into my retirement plan, I should have at least $30 comma 000 saved when I retire in 25 years.
The statement ___________ because I will have $ ___________ nothing in my retirement account when I retire in 25 years.
(Round to the nearest cent as needed.)
Answer:
False
$25,706.48
Step-by-step explanation:
The annual percentage rate (APR) is 4%, so the monthly rate is 4%/12 = ⅓%.
25 years = 300 months.
The monthly deposit (annuity) is $50.
The future value of the annuities is:
F = A [(1 + i)ⁿ − 1] / i
Given i = 1/300, A = 50, and n = 300:
F = 50 [(1 + 1/300)³⁰⁰ − 1] / (1/300)
F = 25,706.48
The statement is false. The amount after 25 years is less than $30,000.
The statement doesn't make sense because if you make $50 monthly deposits at a 4% APR for 25 years, you will have approximately $41,981.86 in your retirement account, not only $30,000.
Explanation:The statement does not make sense or is clearly false. Let's add up the total deposits over 25 years and calculate the interest gained using the given annual percentage rate (APR) of 4%.
Total deposits = $50/month * 12 months/year * 25 years = $15,000Using formula for compound interest, Final Value = P (1 + r/n)^(nt) where P is principal amount (initial investment), r is annual interest rate (decimal), n is number of times that interest applied per time period, t is time the money is invested for. In this case, P=$50, r=4%/12/100%=0.003333, n=1 (monthly), t=12*25=300. After calculations, the final value comes to approximately $41,981.86Therefore, if you continue to make $50 monthly deposits with a 4% APR for 25 years, you will have just under $41,981.86 in your retirement account, not $30,000 as stated. So, the statement is inaccurate.
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factor the expression 3x^2 - 6x
Answer:
3x(x-2)
Step-by-step explanation:
1. find out the common factor in each components which is 3x
2. done.
A three-character code uses the letters D and Q. Either of the letters may be repeated.
Find the probability of a code with exactly two D’s.
Answer:
1/1 x 1/2 x 1/2 = 1/4
One times One-Half times One-Half Equals One-Fourth
The Probability is 1/4 or One-Fourth.
Step-by-step explanation:
There is a One-Half possibility on two of them for choosing D.
Multiply that by each other and than by 1.
Write an equation with slope of 2/3 and y intercept of -3
Answer:
y = [tex]\frac{2}{3}[/tex]x - 3
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
You know:
m = 2/3
b = -3 So substitute/plug it into the equation
y = mx + b
[tex]y=\frac{2}{3}x-3[/tex]
QUESTION 16 The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.5° F. Hint: You will need to use the sampling distribution of the sample mean.
Answer:
34%
Step-by-step explanation:
The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F.
We want to find the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F.
The mean of the sampling distribution of the sample means is the same as the population mean,
[tex] \mu = 98.6 \degree[/tex]
The standard error of the mean becomes the standard deviation of the sampling distribution of the means.
[tex]SE= \frac{ \sigma}{ \sqrt{n} } [/tex]
[tex]SE= \frac{0.6}{ \sqrt{36} } = 0.1[/tex]
By the Central Limit Theorem, the distribution of mean of means is approximately normal
The z-score of 98.5° F
[tex] z= \frac{98.5 - 98.6}{0.1} = - 1[/tex]
By the empirical rule 68% of the distribution is within one standard deviation (-1 to 1).
Therefore from (-1 to 0), it will be approximately 34%
Final answer:
To calculate the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F, you'd use the z-score formula after finding the standard error. The final probability is found by subtracting the z-score probability corresponding to a score of -1 from 1. The correct distribution for calculation is the z-distribution due to the known standard deviation.
Explanation:
The question pertains to calculating the probability that the mean body temperature of a randomly selected sample of 36 adults is greater than 98.5° F. Given that the mean is 98.6° F and the standard deviation is 0.60° F, one would first calculate the standard error of the mean (SE) using the formula SE = σ/√n, where σ is the standard deviation and n is the sample size. In this case, SE = 0.60/√36 = 0.10° F.
To find the probability, we can use the z-score formula, which is z = (X - μ) / SE, where X is the value we are finding the probability for, μ is the mean, and SE is the standard error. Plugging in the values, we get z = (98.5 - 98.6) / 0.10 = -1. When we look up the z-score of -1 in the z-tables or use a statistical software, we find the probability to the left of z=-1. However, since we want the probability that the mean temperature is greater than 98.5° F, we need to subtract this value from 1.
The final step will give us the probability that the mean of the selected sample is greater than 98.5° F. It's important to note that while the question hints at using the t-distribution due to not knowing the population standard deviation, since we're using the provided standard deviation of 0.60° F, we're actually using the z-distribution. If we were dealing with smaller sample sizes or truly didn't know the population standard deviation, we would use the t-distribution as suggested.
5x - y ÷ 8 when x = 5 and y = 8
Answer:
24
Step-by-step explanation:
5x - y ÷ 8
Let x=5 and y=8
5(5) -8÷8
PEMDAS
multiply and divide from left to right
25 -8÷8
25 -1
Then add and subtract
24
24
Step-by-step explanation:
First I replaced x and y so the equation was:
5(5)-8/8
multiply 5*5
25-8/8
25-1
When you subtract the answer is 24
And I solved this equation using PEMDAS!
Hope that helps!!
What is the length of side AB of parallelogram ABCD?
units
Answer:
8 units
Step-by-step explanation:
did the assignment
Answer:
8
Step-by-step explanation:
A bag contains 5 red balls 3 green beads and 2 blue beads if three beads are picked from the bag at radnom without replacement what is the probability that the beads that are picked are all different colors?
Answer:
1/4 or 0.25
Step-by-step explanation:
please kindly check the attached files for details
6c + 14 = -5c + 4 + 9c solve for c
Answer:
-5
Step-by-step explanation:
6c + 14 = -5c + 4 + 9c
6c + 14 = 4c + 4
- 4. - 4
--------------------------
6c + 10 = 4c
- 6c - 6c
-----------------------
10 = -2c
--------------
-2. -2
C = -5
Answer:
-5 = c
Step-by-step explanation:
Step 1
6c + 14 = -5c + 4 + 9c
subtract 4 to the other side, then subtract 6c to the opposing side
ex: 14-4 = -5c -6c +9c
then combined.. 10= -2c
Step 2
divide -2 from 10 to solve for c.
ex: 10/-2 = c
solve... -5 = c
To the nearest tenth percent, how many students played for exactly 4 hours?
how do i calculate the height of a parallelogram?
Answer:
A/b = Area/base
Step-by-step explanation:
1)If area of the parallelogram has been given :
Area of a parallelogram = bxh
Area of a parallelogram/b = h
2) And if the measure of the sides is given then use Pythagoras theorem to find the height
Hope this will help u mate
can someone help me find x pleaseeee
Yol drove 390.25 miles back home to surprise his brother for his birthday. The drive took 7 hours. What was Yol's average speed for the trip, in miles per hour?
Answer:
55.75 miles/hour is the average speed
Step-by-step explanation:
In this question, we are asked to calculate the average speed attained by Yol if he traveled a certain distance within a given time frame.
To calculate his average speed, what we do is to divide the distance travelled by Yol by the number of hours he traveled.
mathematically what we are saying is that
Average speed = Total distance/ Total time
From the question, the distance is 390.25 miles while the time is 7 hours
we now input these values
Average speed = 390.25/7 = 55.75 miles per hour is the average speed
CB is tangent to ⊙A at point C. Find the radius.
Circle A is shown. Line segment A C is a radii. Line segment B C is a tangent and it intersects with the circle at point C. A line is drawn from point B to point A and a point is drawn where the line intersects with the circle. The length of the radius is r, the length of C B is 8, and the length of B to the circle is 5.
CB ⊥ AC by the radius-tangent theorem, so ∠C is a right angle.
ΔABC is a right triangle, so apply the Pythagorean theorem.
Use the steps and solve for the radius.
r2 + 82 = (r + 5)2
r2 + 64 = r2 + 10r + 25
Answer:
The Answer is 39/10! I Did The Assignment!
Step-by-step explanation:
The radius is 3.9 units
What is radius of circle?In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the image of a circle given below showing the relationship between radius and diameter.
given:
As, CB ⊥ AC by the radius-tangent theorem.
In ΔABC, applying the Pythagoras theorem
r² + 8² = (r+ 5)²
r² + 64= r² + 25 + 10 r
64 - 25 = 10 r
39 = 10r
r= 39/10
r= 3.9 units
Hence, the radius is 3.9 units.
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A submarine dives as shown in the diagram.
To the nearest degree, determine the dive angle whose measure is x.
Answer:
Tan x = 125/500= 0.25
so x = arctan (0.25)
=14 degree
The measure of the diving angle is 14°.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
Sea level and 500 ft are parallel.
This means,
x° and end drive angles are alternate angles.
So,
tan x = 125/500
tan x = 0.25
x = [tex]tan^{-1}[/tex] (0.25)
x = 14°
Thus,
The measure of the diving angle is 14°.
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The art and science of gathering, analyzing, and making inferences (predictions) from numerical information obtained in an experiment is called
Answer:
Statistics
Step-by-step explanation:
Statistics is the science of collecting and analysing numerical data in large quantities from a sample.
What is the x axis label what is the y axis label the order pair ????? Is found in the scatter plot
Answer:
AA BB CC DD EE FF GG HH II JJ KK LL MM NN OO PP QQ RR TT UU VV WW XX YY ZZ
Step-by-step explanation:
Answer:
height goes on the x–axis and, arm span goes on the y-axis, and the order pair is (30,27)
Step-by-step explanation:
The tiles below represent the polynomial, what is the factorization of 2x2 + 7x + 6
Answer:d
Step-by-step explanation: just factor it out
The factorisation of the given polynomial is (x+2)(2x+3). Therefore, option D is the correct answer.
The given polynomial is 2x²+ 7x + 6.
We need to factorise the given polynomial.
How to factorise the quadratic polynomials?In order to factorise a quadratic algebraic expression in the form ax² + bx + c into double brackets:
Multiply the end numbers together ( a and c ) then write out the factor pairs of this new number in order.We need a pair of factors that + to give the middle number ( b ) and x to give this new number.Group the terms and take common factors out.Now, 2x²+ 7x + 6=2x²+ 4x +3x+ 6
=2x(x+2)+3(x+2)
=(x+2)(2x+3)
Therefore, option D is the correct answer.
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Chef Selena is making her special dish that requires pasta, sauce, and onions.
She has 5 1/8 pounds of pasta, 6 pounds of sauce, and 47/8 pounds of onions.
How many servings of her dish can she make if each serving is 12 pounds?
Which two equations are needed to solve the problem?
Answer:
4/3 servings or her dish can be made
These are the 2 equations:
Total = 5 and 1/8 pounds + 6 pounds + 4 and 7/8 pounds
N = Total / 10
Step-by-step explanation:
We know 1 serving = 12 pounds
We want the number of servings able to make. call it N
N = (Total pounds)/ (12 pounds/serving)
P = pasta per serving
S = sauce per serving
O= onions per serving
It appears that
P*N = 5 and 1/8 pounds
S*N = 6 pounds
O*N = 4 and 7/8 pounds
5 and 1/8 + 6 + 4 and 7/8 = Total
16 pounds total.
N = 16/12 = 4/3 servings
Total = 5 and 1/8 pounds + 6 pounds + 4 and 7/8 pounds
N = Total / 10
7 3/4 divide 1/3 kjkgcccccccccccccccffffffhhhhhhhhhhhhhhhhhhhhhhffffffffffffffhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhg
Answer:
23 1/4
Step-by-step explanation: