Bharat and Ingrid leave their building at the same time on their bikes and travel in opposite directions. If Bharat’s speed is 12 kilometers per hour and the Ingrid’s speed is 14 kilometers per hour, how long will it take until they are 78 kilometers apart?a. If Bharat rides a distance of `b` kilometers, write an expression to represent how far Ingrid rides.b. Write two equations in the table below.(Let `b` be the distance in kilometers, and `t` be time in hours)c. How long will it take until they are 78 kilometers apart?
Answers
We are given that Bharat travels with a speed of 12 km/h and Ingrid travels at a speed of 14 km/h.
Part a. Given that the distance that Bharat has traveled is "b" this means that the distance that Ingrid has traveled is:
\(d_I=d_0-b\)Where:
\(\begin{gathered} d_0=\text{ distance apart} \\ d_I=\text{ distance of ingrid} \end{gathered}\)We can see this in the following diagram:
Part b. We need to determine two equations to solve for the time when the distance apart is 78 kilometers. To do that we need to remember that distance is the product of velocity and time. Therefore, if the distance of Bharat is "b", then the first equation is:
\(b=12t,(1)\)Now, if "I" is the distance of Ingrid, then the second equation is
\(I=14t\)But, we already know the distance that Ingrid has traveled, therefore, we can substitute:
\(d_0-b=14t,(2)\)Part 3. Now, we are asked to determine the time. To do that we will add both equations:
\(b+d_0-b=12t+14t\)Now we can cancel out the "b":
\(d_0=12t+14t\)Adding like terms:
\(d_0=26t\)Since the distance apart is 78 kilometers, we can substitute:
\(78=26t\)Now we divide both sides by 26;
\(\frac{78}{26}=t\)solving we get:
\(3=t\)Therefore, after 3 seconds they will be 78 km apart.
Related Questions
Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Help math what is the equation of the line
Answers
HELP ME PLEASEEEE
Using the digits 1 - 9, at most one time each, create an improper fraction and a mixed number that are equivalent.
Answers
Answer: 5/4 = 1 2/8
Step-by-step explanation: That's the answer
Calcular los 3/5 de los 2/3 de las 3/4 de 560
Answers
For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.
How to solve fractions?To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:
Step 1: Calculate 3/4 of 560:
3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420
Step 2: Calculate 2/3 of the result from Step 1:
2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280
Step 3: Calculate 3/5 of the result from Step 2:
3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168
Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.
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Choose the answer to complete each statement.
Answers
Excuse me, sorry for using up your points, but what are the statements?
Suppose the coffee industry claimed that the average U.S. adult drinks 1.7 cups of coffee per day. To test this claim, a random sample of 34 adults was selected, and their average coffee consumption was found to be 1.95 cups per day. Assume the standard deviation of daily coffee consumption per day is 0.5 cups. Using a = 0.10, answer the following questions:
a. Is the coffee industryâs claim supported by this sample?
b. Determine the p-value for this test.
c. Verify your results using PHStat.
Answers
Answer:
a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.
b) p-value for this test = 0.006266
c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.
Step-by-step explanation:
a) Degree of freedom = n - 1 = 34 - 1 = 33
The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69
Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,
The rejection region is t < -1.69 and t > 1.69
So, we compute the t-statistic for this sample data to test the claim.
t = (x - μ)/σₓ
x = sample mean = 1.95 cups of coffee per day
μ₀ = The standard we are comparing against = 1.7 cups of coffee per day
σₓ = standard error = (σ/√n)
σ = standard deviation = 0.5 cups
n = Sample size = 34
σₓ = (0.5/√34) = 0.0857492926 = 0.08575
t = (1.95 - 1.70) ÷ 0.08575
t = 2.9154759464 = 2.92
This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.
b) Checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 34 - 1 = 33
Significance level = 0.10
The hypothesis test uses a two-tailed condition because we're testing in both directions.
p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266
c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.
The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.
The p-value obtained from PHstat = 0.0063
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.10
p-value = 0.0063
0.0063 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.
Hope this Helps!!!
Devon wants to build a ramp with the dimensions shown. How much wood does he need?
Answers
The image of the ramp with dimensions is missing, so i have attached it.
Answer:
680 in² of wood is needed.
Step-by-step explanation:
The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.
From the attached image,
Let's find the area of the 2 triangles first;
A1 = 2(½bh) = bh = 15 x 8 = 120 in²
Area of the slant rectangular portion;
A2 = 17 x 14 = 238 in²
Area of the base;
A3 = 15 × 14 = 210 in²
Area of vertical rectangle;
A4 = 8 × 14 = 112 in²
Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²
Mr. Marshal spent his salary of $8 400 in the following manner: Rental .....1/5 Food.......1/10 Bank ......1/4 Miscellaneous ......... the remainder. what fraction of the money was spent on miscellaneous. how much did he spend on rental. if marshal spent 4/9 of miscellaneous on a trip what fraction of his entire salary was spent on the trip ?
Answers
Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.
To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.
Rental: 1/5
Food: 1/10
Bank: 1/4
To find the fraction spent on miscellaneous:
Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)
Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40
Fraction spent on miscellaneous = 1 - 17/40 = 23/40
So, Mr. Marshal spent 23/40 of his salary on miscellaneous.
To find the amount spent on rental, we multiply the fraction spent on rental by his salary:
Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680
Therefore, Mr. Marshal spent $1,680 on rental.
If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.
Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90
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If f(x)= x^3 + 6x^2 - 9x + 14 and x-2 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answers
Answer
Write properties of function:
x intercept/zero: \(x_1=-7\); \(x_2=-1\); \(x_3=2\)
factorized form: \(f(x)=(x+1)(x-2)(x+7)\)
Explanation
Write properties of function: Write properties of function:
x intercept/zero: \(x_1=-7\); \(x_2=-1\); \(x_3=2\)
factorized form: \(f(x)=(x+1)(x-2)(x+7)\)
Answer: Write properties of function:
x intercept/zero: \(x_1=-7\); \(x_2=-1\); \(x_3=2\)
factorized form: \(f(x)=(x+1)(x-2)(x+7)\)
How many quarters in 4 quarters
Answers
Answer:
4 quarters in 4 quarters
Step-by-step explanation:
Which graph best represents the feasibility region for the system in the picture?See image for system.See image for possible graphs.
Answers
Given the system of inequalities:
\(\begin{gathered} x\ge0 \\ y\leq-\frac{1}{8}x+5 \\ y\ge\frac{5}{8}x-1 \end{gathered}\)Graph the inequalities.
First, shade the region of first inequality.
To shade the second inequality, draw the line
\(y=-\frac{1}{8}x+5\)When x = 0, y = 5 and when y = 0, x = 40.
Mark the points (0,5) and (40,0) and join the points to draw the line.
Shade the inequality.
Now, draw the next inequality.
To draw the third inequality, first draw the line
\(y=\frac{5}{8}x-1\)When x = 0, y = -1 and when y = 0, x = 8/5. Mark the points and join it to get the required line.
Shade the region correspondity to its inequality.
This is the feasible region. From the options, option C is correct.
A group of students uses a rope swing to cross back and forth over a stream. The motion of the students is modeled using a cosine function. What is the amplitude of the function? 4 feet 8 feet 16 feet 32 feet
Answers
Answer:
the answer is B.8.
Step-by-step explanation:
A function assigns the value of each element of one set to the other specific element of another set. The amplitude of the function is 8 meters.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Since the total displacement of the student during the motion is 16meters. Therefore, the amplitude of the function of the cosine function is.
Amplitude = Total Displacement/2
Amplitude = 16 meter / 2
Amplitude = 8 meters
Hence, the amplitude of the function is 8 meters.
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a landscaper is designing a park in the shape of a kite with a fountain in the center, F. AK = 28 ft, PF=48 ft and F=32 ft. He wants to install a walkway around the border of the park. The inside edge of the walkway will be edged with brick. The bricks are purchased in linear feet. How many linear feet of bricks should he purchaase?
Answers
Answer:
169.9
Step-by-step explanation:
what is the answer to: Mila bought 26 pounds of sausage for $65.what was the cost per pound of sausage?
Answers
Answer:
$2.50
Step-by-step explanation:
divide $65.00 by 26 pounds
Answer: $2.50 per pound
Step-by-step explanation: $65/26 pound = $2.5 per ponund
Find the open intervals on which the function f(x)= x+10sqrt(9-x) is increasing or decreasing.
Answers
The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).
To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.
Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.
f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)
= 1 - 5√(9 - x) / √(9 - x)
= 1 - 5 / √(9 - x).
To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.
Setting f'(x) = 0:
1 - 5 / √(9 - x) = 0
5 / √(9 - x) = 1
(√(9 - x))^2 = 5^2
9 - x = 25
x = 9 - 25
x = -16.
The critical point is x = -16.
We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.
Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).
For x < -16:
Plugging in a test value, let's say x = -17, into the derivative:
f'(-17) = 1 - 5 / √(9 - (-17))
= 1 - 5 / √(9 + 17)
= 1 - 5 / √26
≈ 1 - 0.97
≈ 0.03.
Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).
For -16 < x < 9:
Plugging in a test value, let's say x = 0, into the derivative:
f'(0) = 1 - 5 / √(9 - 0)
= 1 - 5 / √9
= 1 - 5 / 3
≈ 1 - 1.67
≈ -0.67.
Since f'(0) is negative, the function is decreasing in the interval (-16, 9).
For x > 9:
Plugging in a test value, let's say x = 10, into the derivative:
f'(10) = 1 - 5 / √(9 - 10)
= 1 - 5 / √(-1)
= 1 - 5i,
where i is the imaginary unit.
Since the derivative is not a real number for x > 9, we cannot determine the sign.
Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).
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Please look Below!!!!
(No links) Please explain.
Answers
Answer:
The surface area of the cylinder is about 954.56 square inches.
Step-by-step explanation:
The total surface area of a cylinder is given by the formula:
\(SA=2\pi r^2 + 2\pi rh\)
Here, we are given that the radius is 8 inches and that the height is 11 inches. We are also using 3.14 for π. So, substitute:
\(SA\approx 2(3.14)(8)^2+2(3.14)(8)(11)\)
Use a calculator:
\(SA\approx 954.56\text{ in}^2\)
The surface area of the cylinder is about 954.56 square inches.
The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to 17 years, given the household’s annual income, x.
Approximately how much would it cost to raise a child in a household with an annual income of $62,500?
$96,875
$146,288
$207,294
$216,542
Answers
Answer:
$207,294
Step-by-step explanation:
Since x equals annual income, we just plug in 62,500 in place of x in the given equation
y = 1.55(62,500) + 110,419
y = 96,875 + 110,419
y = 207,294
The average monthly income of three persons is rs. 3,600. If the income of the first is 1/5 of the combined income of the other two then his monthly income is
Answers
The monthly income of the first person is $600.
Given that, the average monthly income of three persons is RS 3,600.
The income of the first is 1/5 of the combined income of the other two.
Here, Let income of the first be A, let income of the second be B and let Income of the third be C.
A+B+C=3600 -----(i)
Income for the first person = 1/5(B+C) -----(ii)
Substitute equation (ii) in equation (i), we get
(B+C)/5 +B+C =3600
B+C+5B+5C=3600×5
6B+6C=18000
6(B+C)=18000
B+C=3000 ------(iii)
Substitute (iii) in equation (i), we get
A=$600
Therefore, the monthly income of the first person is $600.
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Question provided in attachment.
Answers
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.
How to calculate the valueSample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18
= 480 / 18
≈ 26.667
Sample Standard Deviation (s):
= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))
≈ ✓(319.778 / 17)
≈ ✓(18.81)
≈ 4.336
Confidence level = 99%
Sample Size (n) = 18
Sample Mean = 26.667
Sample Standard Deviation (s) = 4.336
Degrees of Freedom (df) = n - 1 = 18 - 1 = 17
Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.
Margin of Error (E) = 2.898 * (4.336 / ✓18))
≈ 3.748
Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)
= (22.919, 30.415)
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.
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Please Help!!!!
Using the slope formula, find the slope of the line through the given points. (12,0) and (2,-5)
Answers
Answer: The slope is 1/2
Step-by-step explanation:
Calculate the rise (change in y-component) divided by the run (change in x-component).
rise = 0 - (-5) = 5
run = 12 - 2 = 10
slope = 5/10 = 1/2
What is the value of n? Write your answer as a number only
Answers
Hey there!
The value of "n" is 10.
Since the lines on the sides represent congruency of those 2 sides, we also know that angle T is equal to angle S. Since a triangle's angles add up to 180°, we can use the following equation, and solve:
180 = 3.5n + 3.5n + 11n Add the "n"s
180 = 18n Divide both sides by 18
10 = n
Hope this helps! Good luck on your assignment! Have a great day!
Correct answer gets brainliest
Answers
Answer:
D. its a two dimensional object
Answer:
A. It is a polygon
C. It is a one-dimensional object
The shape is a polygon in two dimensions since a polygon must have at least three straight sides.
What are the coordinates of the vertices of the final image? A. P’(12, -6), Q’(8, -7), R’(4, -4), and S‘(7, -1) B. P’(12, 8), Q’(8, 9), R’(4, 6), and S‘(7, 3) C. P’(-12, 6), Q’(-8, 7), R’(-4, 4), and S‘(-7, 1) D. P’(12, 6), Q’(8, 7), R’(4, 4), and S’(7, 1)
Answers
Answer:
Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.
Now, let's find the new vertices of the dilated image:
Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).
Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).
Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).
Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).
Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).
Step-by-step explanation:
Hope this helps you!! Have a good day/night!!
Which measurements could NOT represent the side lengths of a right triangle?
O 8 cm, 15 cm, 17 cm
O 20 cm, 21 cm, 29 cm
O 36 cm, 77 cm, 85 cm
O 7 cm, 28 cm, 32 cm
Answers
Step-by-step explanation:
A. 8 cm, 15 cm, 17 cm => This is a right triangle.
B. 20 cm, 21 cm, 29 cm => This is a right triangle.
C. 36 cm, 77 cm, 85 cm => This is a right triangle.
D. 7 cm, 28 cm, 32 cm => This is not a right triangle.
a survyer was conducted amount 25 young adults to determine how many of them exercised during the week four people they exercised four days a week five people said they excersized five days a week what percentage exercised four or five days per week
Answers
The percentage of young adults who exercised four or five days a week is 36%
Out of the 25 young adults surveyed, a total of 4 people exercised four days a week and 5 people exercised five days a week. To calculate the percentage of young adults who exercised four or five days a week, we add the number of people who exercised four days a week to the number of people who exercised five days a week, which gives us a total of 9.
We then divide this by the total number of people surveyed (25) and multiply by 100 to get the percentage.
So the percentage of young adults who exercised four or five days a week is
(9/25) x 100 = 36%
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I have a difficult calculus question about maxima and minima, pic included.
Answers
The first thing we have to do is derivate the function in order to obtain the critical points of the function. Then we'll check which of them are inflection points, maximum or minimum.
So we have:
\(f(x)=12x^5+75x^4-120x^3+4\)Derivating:
\(f^{\prime}(x)=60x^4+300x^3-360x^2\)To obtain the critical points we equal this derivate to cero:
\(0=60x^4+300x^3-360x^2\)\(0=60x^2(x^2+5x-6)\)\(0=60x^2(x+6)(x-1)\)From this factor expression we can determinate the possible solutions is:
\(x=0,\text{ x=-6, x=1}\)Then we have 3 critical points.
To determinate what are they, if they are inflection, maximum or minimum and the concave of the intervales we have to do the cementery law, if you don't know about it don't worry, It is just evaluate the derivate:
Untill now we have this information:
As we said before, we have to evaluate in each intervale, if the values is negative then it means that the function is decreasing, if it is positive the function is increasing. We can use any value of each intervale.
To the first intervale we will use -10, to do the operation easier.
\(f^{\prime}(-10)=600\ast-4\ast-11=a\text{ positive number}\)To the second intervale we will use -1:
\(f^{\prime}(-1)=60\ast5\ast-2=\text{ a negative number}\)To the third intervale we will use 0.5:
\(f(0.5)=60\ast0.5^2\ast6.5\ast-0.5=\text{ a negative number}\)To the last intervale we will use 10:
\(f(10)=60\ast10^2\ast16\ast9=\text{ a positive number}\)From this we can conclude that the critical points are x=-6, x=-1, x=0.
And the direction of the function, if it is increasing or decreasing.
To get the concavity of the function we use the second derivate criterion:
\(f^{\prime}^{\prime}(x)=240x^3+900x^2-720x\)We equal to cero this time again:
\(0=240^3+900x^2-720x=60x(4x^2+15x-12)\)From this we obtain the inflection points:
\(x=0,\text{ x=0.68, x=-4.4}\)Now we evaluate in the intervarles:
To the first interval we will use -10:
\(f^{\prime\prime}(-10)=-600(4\ast10^2-150-12)=\text{ a negative number}\)To the second interval we will use -1:
\(f^{\prime}^{\prime}(-1)=-60(4-15-12)=\text{ a positive number}\)To the third interval we will use 0.5:
\(f^{\prime}^{\prime}(0.5)=30(1+7.5-12)=\text{ a negative number}\)To the last interval we will use 1:
\(f^{\prime}^{\prime}(1)=60(4+15-12)=\text{ a positive number}\)If the value of evaluate the second derivate is positve then the fuction is concave up, if the value is negative is concave down.
We can conclude:
The inflection points are:
x=-4.4
x=0
x=0.68
Concavity:
(-∞,-4.4)= concave down
(-4.4,0)= concave up
(0,0.68)= concave down
(0.68,∞)=concave up
Can someone help me with this question! Show work
Answers
Answer:
D. 72/100
Step-by-step explanation:
3/10 is equal to 30/100.
42/100 + 30/100 = 72/100
i hope that made sense. good luck!
Answer:
D, 72/100
Step-by-step explanation:
Ignore the extra two blocks for now
then add the four tens and the three ten together. 30 + 40 = 70
Then bring back the extra two blocks and add them to the end.
Hope this helps! :)
Is it true that all multiples of 5 end with 5 or 0?
Answers
Answer:
yes
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Divide and simplify. Give your answer using positive exponent. Leave your answer in exponential notation.
Answers
Answer:
14⁻⁵
Step-by-step explanation:
Dividing two exponents with the same base has the effect of subtracting the bottom exponent from the top one. Following that rule, we can simplify our fraction like this:
\(\dfrac{14^{-3}}{14^2}=14^{-3-2}=14^{-5}\)
Answer:
1/14^5
Step-by-step explanation:
14^-3 can be rewritten as 1/14^-3
When doing so you are left with 1/(14^2)(14^3)
Simplify: 1/(14^5) because when multiplying exponents with common bases, you add the exponents.
A terrarium is 9 inches wide, 16 inches long, and 10 inches high. The terrarium is filled halfway with dirt. How many cubic inches of dirt will be in the terrarium?
Answers
It’s that simple! Note, this equation is used for rectangular or cubic spaces,
ANSWER: 720