20 PTS!!!David's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $60 a day for food and lodging and $0.65 for each mile traveled. David drove 600 miles and was reimbursed $3,390. Part A: Create an equation that will determine the number of days on the trip. (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many days did David spend on this trip? (1 point)
Answer:
The company pays $60 a day for food and lodging and $0.65 for each mile traveled.
David drove 600 miles and was reimbursed $3,390.
Part A:
Let the number of days of trip be = x
Equation forms:
[tex]600(0.65)+60x=3390[/tex]
=> [tex]390+60x=3390[/tex] .......(1)
Part B:
Solving (1) for x.
[tex]390+60x=3390[/tex] (given)
Applying subtraction property of equality;
[tex]60x+390-390=3390-390[/tex]
Now simplifying this we get;
[tex]60x=3000[/tex]
Applying division property by dividing 60 on both sides, we get
x = 50
Part C:
We get x = 50, so David spent 50 days on the trip.
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
Not in words
The picture below shows a container that Sue uses to freeze water:
What is the minimum number of identical containers that Sue would need to make 2,000 cm3 of ice? (Use π = 3.14.)
Answer:
The number of identical containers are 27
Step-by-step explanation:
The picture below shows a container that Sue uses to freeze water.
We need to make 2000 cm³ of ice using small identical container.
Volume of cylinder [tex]=\pi r^2 h[/tex]
Where,
r = radius of cylinder (r=2 cm)
h = height of cylinder ( h=6 cm)
Volume of small cylinder [tex]=\pi (2)^2\cdot 6 = 75.39\text{ cm}^3[/tex]
We need to find number of small cylinder.
[tex]\text{Number pf small cylinder }=\dfrac{\text{Volume of ice}}{\text{Volume of each cylinder}}[/tex]
[tex]\text{Number pf small cylinder }=\dfrac{2000}{75.39}\approx 27[/tex]
Hence, The number of identical containers are 27
How many different triangles can be formed from four rods with lengths of 1 meter, 3 meters, 5 meters, and 7 meters?
Since there is no angle restriction in this case, therefore the one rule that is applicable to this is that in forming a triangle, the sum of the lengths of the two smaller sides (A + B) should be larger than the length of the biggest side (C):
Triangle length rule: Side A + Side B > Side C
We can see that no matter how we combine the rods, the only combination of rods that satisfies this rule is:
Triangle formed by rods 3 meters, 5 meters, and 7 meters
Therefore, there is only 1 triangle that can be formed from these four rods.
how do you write 10 X 3 ten's in standard form?
Find x. The units are in feet.
If r is the radius of the circle and d is it diameter ,which of the following is an equivalent formula for the circumference c=2pir
to calculate circumference you can either use
2 x PI x r
or
pi x d
Answer:
PI X D
Step-by-step explanation:
Have a nice day :)
The numbers 1 through 9 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random.
What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?
The probability of drawing the slips '1', '2', '3', and '4' in that order is 1/126 or approximately 0.0079.
Explanation:The probability that the drawn slips are '1', '2', '3', and '4', in that order, can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.
There are 9 slips in the box, so the total number of possible outcomes is 9 choose 4, which is denoted as C(9,4) or 9!/(4!(9-4)!), which simplifies to 126.
Since we want the slips to be drawn in a specific order, the number of favorable outcomes is 1, because there is only 1 way to arrange the slips in the order '1', '2', '3', and '4'.
Therefore, the probability is 1/126, which simplifies to approximately 0.0079 or 0.79%.
If you choose a card at random from a well shuffled deck of 52 cards, what is the probability that the card chosen is not a heart
The probability that the card chosen is not a heart is 0.75
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
Sample space ={13 H + 13 D + 13 S + 13 C}
= 52 cards
The total number of cards in a deck is 52
Number of cards with hearts = 13
Therefore, P(getting one heart) = 13/52 = 1/4
P( getting NO heart) = 1-1/4 = 3/4 = 0.75
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ2
On a cross-country trip, a couple drives 500 mi (miles) in 10h on the first day, and 400 mi in 8h on a second day. the average speed for the whole trip is:
How many different 7-digit numbers can be formed using the digits in the number 5,474,575?
Integration of (cosec^2 x-2005)÷cos^2005 x dx is
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 96t-16t^2 . After how long will it reach its maximum height? Do not round your answer.Time: ___ seconds
The time taken to reach the maximum height = 3 s
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + cwhere a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²
The maximum value of the function is obtained if the first derivative of the function h (t) = 0
96-32t = 0
96 = 32t
t = 3 s
Learn more
The maximum height
https://brainly.com/question/12298041
the fencing
https://brainly.com/question/7190180
domain of the function
brainly.com/question/4135536
Final answer:
The ball reaches its maximum height after 3 seconds. This is determined by finding when the derivative of the height function h(t) = 96t - 16t² equals zero and solving for t.
Explanation:
To determine the time at which the ball reaches its maximum height, we need to analyze the function h(t) = 96t - 16t². Here, h(t) represents the height of the ball after t seconds. The ball achieves its maximum height when the derivative of the height function with respect to time is zero (i.e., when its upward velocity is zero).
To find this, we can take the derivative of h(t) and set it equal to zero to find the critical points:
h'(t) = d/dt (96t - 16t²) = 96 - 32t.
Setting the derivative equal to zero:
96 - 32t = 0
32t = 96
t = 96/32 = 3 seconds.
Therefore, the ball reaches its maximum height after 3 seconds.
A new surgery is successful 75% of the time. if the results of 10 such surgeries are randomly sampled, what is the probability that fewer than 9 of them are successful
This is a binomial probability problem where we calculate the probability of fewer than 9 successful surgeries out of 10, given a success rate of 75% for each surgery. The probabilities of 0 to 8 successful surgeries are calculated and summed up.
Explanation:The question asks for the probability that fewer than 9 out of 10 surgeries are successful, given that each surgery has a 75% chance of being successful. This is a binomial probability problem since each surgery can result in either success (75%) or failure (25%), and we are dealing with a fixed number of independent trials (10 surgeries).
To solve this, we first calculate the probability of exactly 8 successes, exactly 7 successes, and so on down to 0 successes, then sum these probabilities. The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and nCx is the combination of n items taken x at a time.
However, calculating each probability individually and summing them can be tedious, and tools or calculators designed for binomial distributions are often used to compute this more efficiently. For a result of fewer than 9 successes, we would add the probabilities of getting 8, 7, ..., down to 0 successful surgeries.
what is 2500g converted to kg
17.16 is 62.4% of what
divide them
17.16/0.624 = 27.5
27.5 is the answer
double check by multiplying 27.5 by 62.4%
27.5*.624 = 17.16
Write a complete c program that finds the square roots of all elements of type double in an array of size 8. your program should display the original array as well as the array of square roots.
#include< stdio.h;
// #include< math.h;
int main() {
int I = 0;
double value[8];
for(I = 0; I < ;8; i++){
printf(“Enter value at index %d: “; (i +1 ));
Please note, always use %lf and not %f when reading double data from the user. double is %lf, while float is %f. That is the difference.
In this problem, we use two headers, stdio.h and math.h. The math.h defines a lot of mathematical functions. It returns double as a result since all functions in this library takes double as an argument.
The stdio.h header defines 3 variable types, namely size_t, FILE, and fpos_t.
what is the axis of symmetry of y=3x^2+6x+5
Liz is using the distributive property to evaluate the expression 27(36) by using friendlier numbers. Her work is shown below.
Liz’s Work
27(36)
Step 1
27(3 + 12)
Step 2
27(3) + 27(12)
Step 3
81 + 324
Step 4
405
What was the first error that Liz made?
Step 1 should have been 27(6 + 30).
Step 2 should have been 27(3) + 12.
Step 3 should have been 27(30)(12).
Step 4 should have been 16,244.
Answer:
A
Step-by-step explanation:
what are 3 different ways to make tbe number 15638 with only hundreds tens and ones
Answer:
156 hundreds, 3 tens and 8 ones.155 hundreds, 12 tens and 18 ones155 hundreds, 10 tens and 38 onesStep-by-step explanation:
The easiest way is to divide the number by 100, 10 and 1 in that order so:
15638/100=156.38 <- From this number you take only the integer (or the number without decimals), and that would be your hundreds, for this case 156 is the integer part, so 156 hundreds.
Next we take take the 38 we had left from the above division, and we divide it by 10.
38/10=3.8 <- we apply exactly the same steps as before but with the tens, working only with the integer, meaning 3, so you end up with 3 tens.
Last but not least, the rest, that is 8, will be your ones. In this case, just 8 ones.
Your first answer would be 156 hundreds, 3 tens and 8 ones.Now, the combinations are infinite, if you take one from the hundreds it becomes 10 tens or 100 ones, and if you take 1 from the tens you get 10 ones. So you could have
155 hundreds (155-1), 12 tens (3+10-1), and 18 ones. Or any permutation you prefer.
For quick studies, it is easier to round down to the nearest 5 or 0, so another way to see this would be:
155 hundreds, 10 tens, and 38 ones.
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. the value of the test statistic in this problem is approximately equal to
The value of the test statistic in this problem is approximately equal to [tex]\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex]
Explanation:Aspirin also known as acetylsalicylic acid, is a medication used to reduce pain, fever, or inflammation. A test statistic is the random variable that calculated from sample data it used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis or not. The test statistic can compare the data with what is expected under the null hypothesis
A survey (a general view, examination, or description of someone or something) claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. the value of the test statistic in this problem is approximately equal to [tex]\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex] where
a = People who indicate that they recommend aspirin = 0.83
b = the actual proportion of doctors who recommend aspirin = 0.9
c = the actual proportion of doctors who not recommend aspirin = 1-0.9 = 0.1
d = a random sample = 100
[tex]\frac{a-b}{\sqrt{\frac{(b)(c)}{d} } } =\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex]
Learn more about the test statistic https://brainly.com/question/13017916
#LearnWithBrainly
a rectangle has a length of 7 meters longer than double the width. the perimeter is 134 meters. find the dimensions of the rectangle.
There are 50 competitors in the men’s ski jumping. 30 move on to the qualifying round. How many different ways can the qualifying round be selected?
To calculate the number of different ways 30 qualifiers can be selected from 50 competitors in a ski jumping event, use the combination formula C(n, k) = n! / (k!(n - k)!), where in this case n=50 and k=30.
Explanation:The question here is focused on finding the number of different combinations in which the qualifying round can be selected from a group of competitors in a sport event, specifically men’s ski jumping. This falls under the category known as combinatorics, which is a part of mathematics that deals with counting, both in a concrete and abstract way, as well as finding certain properties of finite structures.
The total number of different ways 30 competitors can be chosen from a group of 50 can be found using the combination formula, which is expressed as C(n, k) = n! / (k!(n - k)!), where "n" is the total number of competitors, "k" is the number of competitors to choose, "n!" signifies the factorial of "n", and "(n - k)!" is the factorial of the difference between "n" and "k".
In this situation, to find the number of different ways to select the 30 qualifiers from 50 competitors, we plug the values into the formula to calculate C(50, 30).
Final answer:
To find the number of different ways the qualifying round can be selected, you need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.
Explanation:
To find the number of different ways the qualifying round can be selected, we need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.
In this case, n = 50 and r = 30. Plugging these values into the formula, we get C(50, 30) = 50! / (30!(50-30)!). Simplifying this expression, we find that C(50, 30) = 211915132760.
Therefore, there are 211,915,132,760 different ways the qualifying round can be selected.
A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. for a sample of 49, the probability that the sample mean will be larger than 82 is
The Perimeter of a rectangle is 66 feet and the width is 7 feet. What's the length in feet?
Please explain how to solve this problem-a)26;b)52;c)40;d)20
simplify sin(2x+7y)+sin(2x-7y)
20 points PLEASE HELP WITH THIS QUESTION,, I WILL RANK HIGHEST TOO
Directions: Three families have purchased a large lot in the country and have built new homes on it. They plan to install a satellite dish on their lot. Locate the point on their lot that is equidistant (equal distance) from their 3 homes. Find the best location of the satellite dish. .
The best location for the satellite coordinates is
(Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3).
We have,
From the figure given,
Assume that the coordinates of the three families are:
Sanchez = (a, b)
Perez = (c, d)
Reyes = (e, f)
The point equidistant from all three families' coordinates can be calculated using the formula.
Midpoint = ((m + o) / 2, (n + p) / 2)
Where (m, n) and (o, p) are the coordinates.
Midpoint between Sanchez and Perez:
Midpoint(SP) = A = ((a + c) / 2, (b + d) / 2)
Midpoint between Perez and Reyes:
Midpoint(PR) = B = = ((c + e) / 2, (d + f) / 2)
Midpoint between Sanchez and Reyes:
Midpoint(SR) = C = ((a + e) / 2, (b + f) / 2)
Equidistant Point
= (Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3)
Where "Ax" represents the x-coordinate of the midpoint between Sanchez and Perez, Bx" represents the x-coordinate of the midpoint between Perez and Reyes, and Cx" represents the x-coordinate of the midpoint between Sanchez and Reyes. Similarly, Ay, By, and Cy" represent the y-coordinates of the respective midpoints.
Thus,
The best location for the satellite coordinates is
(Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3).
Learn more about coordinates here:
https://brainly.com/question/13118993
#SPJ3
Two buses leave at the same time traveling in opposite directions. One bus travels at 63mph and the other at 62mph. How soon will they be 187.5
miles apart?
What is the value of s and the length of side BC if ABCD is a rhombus?
Step 1
Find the value of s
we know that
In a Rhombus all sides are congruent
so
[tex]AB=BC=CD=DA[/tex]
[tex]AB=9s+29\\CD=10s-16[/tex]
equate AB and CD
[tex]9s+29=10s-16\\[/tex]
Combine like term
[tex]10s-9s=29+16\\[/tex]
[tex]s=45\ units[/tex]
The answer Part a) is
the value of s is [tex]45\ units[/tex]
Step 2
Find the value of side AB
[tex]AB=9s+29[/tex]
substitute the value of s
[tex]AB=9*45+29=434\ units[/tex]
Remember that the sides are congruent
[tex]AB=BC=CD=DA[/tex]
therefore
the answer Part b) is
The length of the side BC is [tex]434\ units[/tex]
The value of s is 45 and the length of side BC is; 434.
What is a Rhombus?A rhombus is a plane shape of the form given I'm the attached image with all its sides equal.
Hence,
AB = BC = CD = DATo determine the value of s;
10s - 16 = 9s + 2910s-9s = 29+16s = 45.The length of side BC = CD = 10(45) - 16 = 450 - 16
The length of side BC = 450 -16 = 434
Read more on Rhombus;
https://brainly.com/question/20627264
what is the answer to simplify 10y-7y