Gloria and Brad each left the same building at the same time to drive home in the same
direction. Gloria traveled at a rate of 54 mph and Brad's rate was 42 mph. In how many
hours were they 54 miles apart?
3.5 hours
4 hours
B
4.5 hours
3 hours
Answers
After 4.5 hours of travel, they will be 54 miles apart.
Let's assume that t is the time (in hours) they have been traveling.
The distance traveled by Gloria can be calculated as 54t (54 miles per hour multiplied by t hours), and the distance traveled by Brad can be calculated as 42t (42 miles per hour multiplied by t hours).
To find the time at which they are 54 miles apart, we need to solve the equation:
54t - 42t = 54
Simplifying the equation:
12t = 54
Dividing both sides by 12:
t = 4.5
Therefore, they will be 54 miles apart after 4.5 hours of traveling.
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Related Questions
Veronica is buying 6 ham sandwiches and 3 cheese sandwiches. Each sandwich
costs $4. The equation below can be used to find Veronica's total cost.
Veronica says all the sandwiches will cost more than $30. Use the drop-down
menus to explain if her statement is reasonable.
4×6+3=0
Answers
Answer: 36
Step-by-step explanation: 6 + 3 = 9.
4 * 9 = 36
Veronica's statement is reasonable because they cost more than $30.
The total amount of sandwiches is $36
Calculations and Parameters:Given that:
She buys 1 sandwich for $4
She buys 6 ham sandwiches and 3 cheese sandwiches
To find the total cost for Veronica would be:
6+3 = 9 total sandwiches
4 * 9= 36 total cost of the sandwiches.
Therefore, Veronica's statement is reasonable because they cost more than $30
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I'm not sure what to do about this problem, so please help me out.
Answers
Answer:
21
Step-by-step explanation:
Let the three consecutive integers be;
x , x + 1 and x + 2:
The sum of squares of the two smaller numbers:
The two smaller numbers are x and x+ 1
Sum of their squares:
x² + (x+1)²;
x² + x² + 2x + 1 = 2x² + 2x + 1
It is 45 more than the square of the larger number:
Larger number = x + 2
(x+2)² = x² + 4x + 4
45 more;
x² + 4x + 4 + 45 = x² + 4x + 49
Both are equal:
2x² + 2x + 1 = x² + 4x + 49
2x² - x² + 2x - 4x + 1 - 49 = 0
x² - 2x - 48 = 0
x² - 6x + 8x - 48 = 0
x(x - 6) + 8(x - 6) = 0
(x + 8)(x-6) = 0
x + 8 = 0 or x - 6 = 0
x = -8 or x = 6
We choose x = 6 because it makes the solution true as a positive integer
Sum of the three numbers:
x + x + 1 + x + 2 = 6 + 6 + 1 + 6 + 2 = 21
This one-dimensional figure goes on forever in two directions.
A. Line segment
B. line
C. Ray
Answers
X/6 = 8 what is the answer
Answers
Answer:
x = 48
Step-by-step explanation:
Multiply both sides by 6
x = 6 * 8
x = 48
Check:
48/6 = 8
8 = 8
Answer:
\( \frac{x}{6} = 8 \\ \\ x = 8 \times 6 \\ \\ x = 48\)
what sample size is necessary for a 90% confidence interval about the mean height of a shrub if we want a margin of error of 0.5 inches and the population standard deviation is known as 1.3 inches.
Answers
The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error = 0.5 inches
z = found by using a z-score table
SD = sample standard deviation = 1.3 inches
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values to the formula and solve for the sample size, n.
MOE = z x (SD / √n)
0.5 = 1.647 x (1.3 / √n)
√n = 1.647(1.3) / 0.5
n = 18.34
n = 18
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A biologist hypothesizes that the mean life expectancy of a mosquito is 14 days. Researchers believe the true mean is less than 14 days and they plan a hypothesis test at the 5% significance level on a random sample of 60 of these mosquitos. If the alternative hypothesis is correct, for which of the following values of μ is the power of the test greatest?
μ = 9
μ = 7
μ = 10
μ = 14
μ = 18
Answers
Based on the alternative hypothesis, the value of μ that will have the greatest test power is μ = 7.
Which value of μ will have the greatest power of test?The alternative hypothesis is that Hₐ : μ < 14.
For the alternative hypothesis to be right, μ will have to be less than 1.4.
μ will also give a greater test power the lower it is below 14. From the options therefore, μ with the greatest test power would be 7.
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Answer:
μ = 7
Step-by-step explanation:
Got this right on the segment exam. Good luck, my FLVS fellows!
simplify the ratio 84: 36: 108: 60
Answers
Answer:
A) 7 : 3
B) 7 : 4
Step-by-step explanation:
84 : 36
Simplified:
42 : 18 ( divided by 2)
21 : 9 ( divided by 2)
7 : 3 ( divided by 3)
7 : 3
108 : 60
35 : 20 ( divided by 3)
7 : 4 ( divided by 5)
7 : 4
the largest of the following integers which divides each of the numbers of the sequence $1^5 - 1,\, 2^5 - 2,\, 3^5 - 3,\, \cdots, n^5 - n, \cdots$ is:
Answers
The sequence's numbers are all multiples of 30. Every number can be divided by 30.
If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)
At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable
Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.
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round 8.456 to the nearest tenth
Answers
Answer:
It's 8.46 cause the preceding digit to 4=5
Hope it helps
Have a good day
Answer:
8.456 rounded to the nearest tenth = 8.5
Step-by-step explanation:
To round 8.456 to the nearest tenth consider the hundredths’ value of 8.456, which is 5 and equal or more than 5. Therefore, the tenths value of 8.456 increases by 1 to 5.
Find the slope of each line defined below and compare their values.
Equation of Line A:
5
y=-=x- 5
3
Submit Annua
Select values from Line B:
The slope of Line A is
of Line A is
X
-8
-6
-4
-2
0
0
-1
-2
-3
-4
and the slope of Line B is
the slope of Line B.
Therefore the slop
Answers
Answer: slope of A is -5/3 and the slope of B is -1/2
(20 Points) Write a program that calculates the sum for the following using a loop. The user will provide the values for i and k. Note: The value of i must always be smaller than or equal to the value of k. If the user provides a larger number first, the program must still work. If the user enters a value for k that is less than i, display an error message and continuously ask for proper values (using a loop). ∑ i
k
2x Example Program Run (red is user input): Enter value for i: 0 Enter value for k:3 Summation: 12 Explanation: 2(0)+2(1)+2(2)+2(3)=
0+2+4+6=12
The values for × go from i to k Another Example Program Run (red is user input): Enter value for i: 6 Enter value for k : 3 Error: i cannot be greater than k. Enter value for i: 5 Enter value for k : 2 Error: i cannot be greater than k.
Answers
The calculated summation value with the message "Summation: " preceding it. The program assumes that the user will provide valid numerical inputs (integers) when prompted.
Here's a Python program that calculates the sum using a loop based on the user's input values for `i` and `k`. The program handles cases where `i` is larger than `k` and continuously asks for proper values until valid inputs are provided.
```python
while True:
i = int(input("Enter value for i: "))
k = int(input("Enter value for k: "))
if i <= k:
break
else:
print("Error: i cannot be greater than k.")
summation = 0
for x in range(i, k+1):
summation += 2 * x
print("Summation:", summation)
```
In this program, we use a `while` loop to repeatedly prompt the user for values of `i` and `k`. We convert the inputs to integers using `int()` for numerical comparison. If the condition `i <= k` is satisfied, we break out of the loop; otherwise, an error message is displayed, and the loop continues.
Once we have valid values for `i` and `k`, we initialize the `summation` variable to 0 and use a `for` loop with `range(i, k+1)` to iterate through the values of `x` from `i` to `k` (inclusive). We accumulate the sum by adding `2 * x` to `summation` in each iteration.
Finally, we print the calculated summation value with the message "Summation: " preceding it.
Note: The program assumes that the user will provide valid numerical inputs (integers) when prompted.
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f(x) = 5x + 2x^2-7x+4
g(x) =3x-7
find (f+g)(x)
Answers
Answer:
(f+g)(x)=5x+2x²-7x+4+3x-7 = 2x²+x-3
Step-by-step explanation:
Answer:
=6x^3-20x^2+26x-28
Step-by-step explanation:
A confidence interval is constructed to estimate the value of O a statistic or parameter O a statistic. O a parameter
Answers
A confidence interval is constructed to estimate the value of a parameter.
In statistics, a parameter refers to a numerical characteristic of a population, such as the population mean or population proportion. When we want to estimate the value of a parameter, we construct a confidence interval.
A confidence interval provides a range of values within which we believe the true parameter value is likely to fall, based on our sample data. It is constructed using sample statistics and takes into account the variability and uncertainty in the estimation process.
A confidence interval is constructed to estimate the value of a parameter, not a statistic.
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find the sum of all multiples of 6 between 1 and 100.
Answers
Answer:
6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
Step-by-step explanation:
What is the mean of this data set?
Please help
Answers
Answer:
Step-by-step explanation:
Find the area of the circle with a circumference of
. Write your solution in terms of
.
Area in terms of
: ______
I need the answers to this: 3(2x-5)= 27
Answers
Answer: x=7
Step-by-step explanation: First, remove 3 from both sides by dividing. You will end up getting 9. Since 2x-5 = 9, add 5 from both sides by adding leaving you with 2x = 14. Divide 14 by 2 to get 7.
A 145 pound person burns 420 calories per hour riding an exercise bicycle at a rate of 15 miles per hour. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem related to the function
Answers
Answer: 580
Step-by-step explanation: i learned that just like 1 hour ago in school
how do I show work for 1/3 (y+7) = 3 (y-1)
Answers
Answer:
1/3(y+7)=3(y-1)
(y+7)/3=(3y-1)
by cross multiplying
3(3y-1)=(Y+7)
9y-3=y+7
take like terms
9y-y=7+3
8y=10
y=10/8
Evaluate. 3 x 2/3 x 1/8
Answers
Answer:
\( \frac{3}{8} \div \frac{2}{3} - \frac{1}{8} \)
Step-by-step explanation:
HOPE IT HELPS (^o^)/
#carryonlearning
Find DE, please help me
Answers
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
g Milk consumption and lactose digestion after weaning are exclusively human traits made possible by the continued production of the enzyme lactase in adulthood. In Europe and northwestern India, adult lactase persistence is considered a classic case of biocultural evolution since herders of Indian and European cattle share their predominant allele for lactase persistence and its presence in the human population appears to coincide with the presence of genes in the herded cattle for increased milk production. Multiple independent mutations in a 100-bp region-part of an enhancer-approximately 14-kb upstream of the LCT gene are associated with this trait in Europeans and pastoralists from Saudi Arabia and Africa. However, a single mutation of purported western Eurasian origin accounts for much of observed lactase persistence outside Africa. What is the dominant gene coding for adult lactase persistence in Europe and India? a. The south Asian -13910 C>T mutation has emerged as the dominant gene coding for adult lactase persistence in India and Europe. b. The west Eurasian -13910 C>T mutation accounts for nearly all the genetic variation observed in the 400- to 700-bp LCT regulatory region. c. None of the above. d. The north Atlantic -13910 C>T mutation is the basis for lactase persistence throughout the entire milk-drinking world. e. The east African -13910 C>T mutation diffused into Indian and then westward into Europe around 15 kya.
Answers
The dominant gene coding for adult lactase persistence in Europe and India is the east African -13910 C>T mutation diffused into Indian and then westward into Europe around 15 kya. The correct option is e.
In European popular and other areas population the lactase productions in body being continued throughout the life for lactase persistence. If we focus only on the European population a single -13,910×T genetic variant strongly associated with lactase persistence.
This genetic variant helps in natural adaptation. Enhancer region for the transcription of LCT is MCM6 which is upstream to LCT . In east Africa -13910 C>T mutation occurs which diffuse to India and western Europe. Option (a) is incorrect because this mutation indicate the high quantity of lactating animals and option (b) is incorrect because the mutation occurs in upstream region.
Therefore, option (e) is correct as mentioned above.
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samia needs to subtract 37 from 54 she cant subtract 7 from 4 so she subtracts 4 from 7 will she get the right answer? Explain how you know
Answers
If sum of the zeroes of the quadratic Polynomial k * x ^ 2 - 3x + 5 is '1', then write the
of k.
Answers
If sum of the zeroes of the quadratic Polynomial kx² - 3x + 5 is '1', then value of k is 3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
Given that If sum of the zeroes of the quadratic Polynomial kx² - 3x + 5 is '1'.
The sum of zeroes of a quadratic polynomial is given by -b/2a.
Now sum of the zeroes of the quadratic Polynomial kx² - 3x + 5 is '1',
Sum of zeros = -(-3)/K
Now equate sum of zeros with 1.
3/k=1
Three divided by k equal to one.
k equal to three.
Now k=3
Hence, if sum of the zeroes of the quadratic Polynomial kx² - 3x + 5 is '1', then value of k is 3.
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After his first month he had more than he expected to have due to interest the bank provided. this let rob come up with a better expression. where w is the number of weeks. how much will he have in 1 year?
Answers
He will earn 2603.16 dollar in one year.
What is expression?An expression is a collection of terms that have been joined together using the operations +, -, or x, such as 4 x 3 or x 2 - x y + 17.
Two expressions are said to be equal in value by an equation, such as 4 b 2 = 6.
Given:
A copy of the entire query is provided below:
45w+ 155
He will therefore save
=45*6+155
=270+155 =425 dollars
so, w=6.
Knowing that a year equals 52 weeks
Also,
w=52 and
w²/25+45w+155
Thus,
=52*52/25+45*52+155
=108.1602340+155
= $263.16
Hence, he will make $2603.16 in a year.
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Evaluate the expression for x = 8
7 x
Answers
Answer:
56 is the right answer
Step-by-step explanation:
7*8=56
While reading about a research study, which of the following would tell you that an association claim is being
made?
a. The presence of a scatterplot or bar graph
b. The measurement of two variables
c. The use of a correlation coefficient
d. The interrogation of internal validity
Answers
The answer to this question is c.The use of a correlation coefficient.
The use of a correlation coefficient would tell you that an association claim is being made in a research study. A correlation coefficient is a statistical measure that shows the strength and direction of a relationship between two variables. It ranges from -1 to 1, with 0 indicating no relationship and -1 or 1 indicating a perfect negative or positive relationship, respectively.
A scatterplot or bar graph may be used to visually display the relationship between two variables, but they do not necessarily indicate that an association claim is being made. The measurement of two variables is necessary for any type of research study, but it does not inherently imply that an association claim is being made.
Interrogation of internal validity is a process used to ensure that the study's results accurately reflect the relationship between the variables being studied. It is important for any research study but does not specifically indicate that an association claim is being made.
Therefore,the answer to this question is c.The use of a correlation coefficient.
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a(n) ____ is a mathematical representation of an object created by a special software
Answers
A(n) MODEL is a mathematical representation of an object created by a special software.
In computer science, a model is a mathematical abstraction of a system, process, or phenomenon that is intended to be simulated or executed on a computer system. A model is used to represent a system or process as a set of mathematical equations or logical rules in order to simulate or analyze it with a computer program.
It can be a physical object, such as a car or building, or an abstract concept, such as an economic system or a social network. In general, a model can be a simple or complex representation of a real-world object or process, and it can be used for a variety of purposes, such as predicting future outcomes, testing hypotheses, or designing new systems.
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What is 22 divided by 1,299?
Answers
Answer:
0.0169361047
Step-by-step explanation:
Answer:
0.01693610469
Step-by-step explanation:
PLEASE HELP IM FAILING GEOMETRY HELPPPP
Answers
Answer:
473.145 in squared
Step-by-step explanation:
Trick reminder: the top of the cylinder does not need to be calculated because it is the same as the negative part of the rectangle beneath.
20.25*3.14 = 63.585
6*28.26 = 169.56
10*10 = 100
10*3.5*4 = 140
63.585 + 169.56 + 100 + 140 = 473.145
3. Find the measure of each base angle in the figure below
A. 62
B. 28
C. 56
D. 124
Answers
Answer:
B
Step-by-step explanation:
Every triangle has 180 degrees.
so minus 124 you get 56. So you have 2 more angles so you divide that by 2 to get 28
The measure of each base angle in the figure, if The measure of an angle is 124°, and The side IH is equal to IJ, is 28°, so option B is correct.
What is the triangle?Triangles are basic three-sided polygons with three internal angles. The symbol represents one of the basic geometric shapes, which has three joined vertices.
Given:
The measure of an angle is 124°,
The side IH is equal to IJ,
As we know, the equal side makes the opposite angle equal then,
∠ IHJ = ∠ IJH
Assume the angle is x,
∠ IHJ +∠ IJH + ∠ HIJ = 180 (Triangle property)
2x + 124 = 180
2x = 180 - 124
x = 56 / 2
x = 28°
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