Final answer:
To find out how many hours Suzette ran, we used a system of equations with the total distance and total time for running and biking. Solving the system, we determined that Suzette ran for 1.5 hours.
Explanation:
To determine how many hours Suzette ran, we can use the total distance and the total time given for running and biking activities, alongside her average speeds for each activity. We will then set up a system of equations that account for the distances and times and solve for the time Suzette spent running.
Let r be the time spent running and b be the time spent biking. We are given:
Total time: r + b = 3.5 hours
Total distance: 6r + 12.5b = 34 miles (6 mph is the running speed, 12.5 mph is the biking speed)
Now we'll solve this system of equations:
Substitute b from the first equation into the second equation: 6r + 12.5(3.5 - r) = 34.
Simplify and solve for r: 6r + 43.75 - 12.5r = 34.
This simplifies further to -6.5r = -9.75, hence r = 1.5.
Suzette ran for 1.5 hours.
58 people attend a banquet at Disney residents paid 13.00 and non residents paid 17.50. If Disney made 925.00 from ticket sales for the event how many residents and non residents attended
Answer:
$925.00
Step-by-step explanation:
A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of 9 centimeters. If the surface area of the pyramid is 140 4 square centimeters, what is the slant height of the pyramid
A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of [tex]9[/tex] centimeters. If the surface area of the pyramid is [tex]140.4[/tex]square centimeters, the slant height of the pyramid is [tex]Slant height= 2*(140.4-81\sqrt{3} )/27[/tex]
To find the slant height of the pyramid, we first need to determine the lateral area of one of the triangular faces of the pyramid.
Since all sides of the equilateral triangle have a length of [tex]9[/tex] centimeters, we can use the formula for the area of an equilateral triangle, which is:
[tex]A=\sqrt{3} /4*side length^{2}[/tex]
Substituting the given side length [tex]9[/tex] centimeters into the formula:
[tex]A=\sqrt{3} /4*9^{2} \\A=\sqrt{3} /4*81\\ A=81\sqrt{3}/4[/tex]
Now, since there are four equilateral triangular faces on the pyramid, the total lateral area of the pyramid is [tex]4*81\sqrt{3}/4=81\sqrt{3}[/tex] square centimeters.
Given that the total surface area of the pyramid is [tex]140.4[/tex] square centimeters, we subtract the area of the base (which is also an equilateral triangle) from the total surface area to find the lateral surface area:
[tex]Lateral surface area=Total surface area-Area of base\\Lateral surface area=140.4-81\sqrt{3}[/tex]
Now, the lateral surface area of a pyramid can be calculated using the formula:
[tex]Lateral surface area=12*perimeter of base*slant[/tex]
For an equilateral triangle, the perimeter is [tex]3*side length=3*9= 27[/tex]centimeters.
So, we have:
[tex]140.4-81\sqrt{3} =1/2*27*slant height\\140.4-81\sqrt{3} =27/2*slant height\\Slant height=2*(140.4-81\sqrt{3} )/27[/tex]
Calculating this expression gives us the value of the slant height of the pyramid.
COMPLETE QUESTION:
A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of [tex]9[/tex] centimeters. If the surface area of the pyramid is [tex]140.4[/tex]square centimeters, what is the slant height of the pyramid?
what term should be added to create a perfect square trinomial ??
x^2+18x
i think it’s +81 but i’m not positive.
Combine any like terms in the expression. If there are no like terms, rewrite the expression. 4s^2 + t^3 + 3s^2 – 7s^2
is 15\16 already in its simplest form?
While attending a college football game, you think you can guess the attendance within 10% of the actual value. If the announced attendance is 65,000, within what number of people would your guess have to be in order for you to support your claim?
Answer:
13,000 People
Step-by-step explanation:
65,000 (0.1) = 6500
6500 (2) = 13,000
You multiply by 2 to get 10% above or below the announced attendance.
Answer:
6,500
Step-by-step explanation:
If you think you can guess the attendance within 10% of the actual value, then your guess would have to be within 6,500 of the actual attendance of 65,000 in order for you to support your claim. This is because 10% of 65,000 is 6,500. So if your guess is within 6,500 of the actual attendance, then you can support your claim.
18m-9v+6v-7m hope you can help
PLEASE HELP ASAP!!!!!!!!!! I AM IN 7TH GRADE MATH FOR FLVS AND I NEED HELP ON Assignment 2.03 Rational Numbers in the Real World!!!!!!!! WHOEVER HELPS ME THE FASTEST GETS BRAINIEST!!!!!!!!!!!!!!
I did the chart just need help on these questions
1. What is the total cost of the entire bill (all four meals), including tip? Please show work
the sun of 3 times a number and 5 is 2 times the number plus 15. what is half the number
How much compound interest is earned on $2050 at 4% interest for 3 years, compounded annually? Give your answer in dollars and cents. Don’t forget to subtract P from A.
. ∠1 and ∠3 are complementary and ∠1 ≅ ∠2. Which one of these statements will always be true?
Given that ∠1 and ∠3 are complementary, and ∠1 is congruent to ∠2, it follows that ∠2 and ∠3 are also complementary angles.
Explanation:The student's question pertains to the properties of angles and triangles. When it is stated that
∠1 and ∠3 are complementary, this means that the sum of their measures is 90 degrees (
two right angles). And if
∠1
≅
∠2, then these two angles are congruent, having the same measure. Given these conditions, the following statement will always be true:
∠2 and ∠3 are also complementary angles. This is because the measure of
∠2 will be equal to the measure of
∠1 (since they are congruent), and thus their combined measure with
∠3 will also add up to 90 degrees, making them complementary as well.
Here is an interesting exponential function, Complete the table with integer values of x from 0 to 4. Then graph the function. Does the graph show exponential growth, exponential decay, or neither? Explain your thinking.
please show an example of your graph
456 000 has been rounded to the nearest thousand. What was the smallest possible number this could have been?
Answer:
The smallest possible number this could have been = 455500
Step-by-step explanation:
456000 has been rounded to the nearest thousand.
If the value is more than 456500 the value rounded to the nearest thousand is 457000.
If the value is less than 455500 the value rounded to the nearest thousand is 455000.
In between 455500 and 456500 the value rounded to the nearest thousand is 456000.
So, The smallest possible number this could have been = 455500
Which relation is a function
I’ve been looking at this for a while, and I can’t figure out the answers. Can someone walk me through it?
John participated in a science contest. He received 3 points for each correct answer but lost 2 points for each incorrect answer. After answering 50 questions, John's score was 95 points. How many questions did John answer incorrectly?
Answer:
11
Step-by-step explanation:
Checking account A charges a monthly service fee of $23 and a wire transfer fee of $7.50, while checking account B charges a monthly service fee of $14 and a wire transfer fee of $9.50. Which checking account is the better deal if four wire transfers are made per month?
Which of these might be used to determine common ancestry of two different species of plants? A. similar ecological niches B. fossil evidence C. the size of the population D. similar habitats
its science they wouldnt let me pick it so i had to put math
Final answer:
Fossil evidence, morphological, and genetic similarities are key factors in determining common ancestry of species, with fossil evidence being particularly definitive for extinct life forms.
Explanation:
To determine common ancestry of two different species of plants, scientists would most likely consider fossil evidence as a primary source. Fossils provide concrete evidence about extinct life forms and can give more accurate dates of divergence. Morphological (form and function) and genetic evidence are other crucial factors in establishing evolutionary connections among organisms. Similar physical features and genomes usually indicate a closer relationship, with homologous structures stemming from common evolutionary paths. Therefore, similar ecological niches or habitats may suggest a relationship, but they are not as definitive as morphological and genetic similarities and fossil evidence in determining a shared ancestry.
on monday, it took helen 3 hours to do a page of homework. the next day she did the same number of exercises in 2 hours. if her average rate on monday was P exercises per hour, what was her average rate the next day in terms of P
please don't just answer, explain HOW to set up equation
What happens when the smog lifts Los Angeles, California
A model of a volcano has a height of 12 in., and a diameter of 12 in. What is the approximate volume of the model? Use 3.14 to approximate pi, and express your final answer as a decimal. Enter your answer in the box. in³
Hello there!
Volume formula for cone: V=1/3(π)(b)(h)
First: you need to find the radius, we know that radius is half the diameter. The diameter is 12, so the radius is 6.
Second: Now we substitute b for 6 and h for 12, since the height is 12. We will substitute π for 3.14.
Third: V=1/3(3.14)(6)(12). When you simplify: 1/3x3.14x6x12=452.16
Final answer=452.16in³
I hope this helps! :)
The data below shows the average of text messages a group of students sends per day. Which histogram could represent the data?
If the diagonals of a quadrilateral are perpendicular, is the quadrilateral always a rhombus?
No, a quadrilateral with perpendicular diagonals is not always a rhombus. While a rhombus has perpendicular diagonals, other quadrilaterals like a square share this property.
While a rhombus does have perpendicular diagonals, other quadrilaterals, such as a square, also possess this property.
Therefore, if the diagonals of a quadrilateral are perpendicular, it does not exclusively imply that the quadrilateral is a rhombus.
Additional conditions, such as equal side lengths, are necessary to establish the quadrilateral as a rhombus.
Thus, perpendicular diagonals are a characteristic of both rhombuses and squares, but not solely indicative of a rhombus.
Mrs. Myles gave the same test to both her first and third period class. In first period, the median was 75 and the range was 30. In third period, the median was 80 and the range was 60. Which is a true statement? A) The lowest score was in third period. B) The highest score was in first period. C) On average, first period did better than third period. D) There is not enough information to know if any of these is true
if the pth , qth and rth terms of an A.P be a,b,c respectively, then show that a (q-r)+b (r-p)+c(p-q)=0
If the circumference of a circle measures 3/2 π cm, what is the area of the circle in terms of π?
The area of the circle with a circumference of 3/2 π cm is 9/16 π cm².
Explanation:The question is asking about finding the area of a circle when the circumference is given. The formula to find the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle. Given that the circumference is 3/2 π cm, we can use this information to find the radius.
From the circumference equation, r = C/2π = (3/2π)/ 2π = 3/4 cm. Having the radius, we can then use the formula for the area of a circle, which is A = πr². As a result, the area of the given circle is π(3/4)² cm² which simplifies to 9/16 π cm².
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On Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor’s lawn. You have $21 left. Use two methods to find how much money you started with that day.
The price of a house decreased from $200,00 to $150,000 in one year. What is the percent decrease?
A carpenter is creating a circular wooden table with a radius of 4 feet and needs to know the area of the table to purchase the correct amount of stain to finish it.
What is the area of the table?
Use 3.14 for π .
Enter your answer, as a decimal, in the box.
(?) ft²
Answer: The area of the circular wooden table = 50.24 ft²
Step-by-step explanation:
Given: The radius of the circular table = 4 feet
We know that area of a circle is given by :-
[tex]\text{Area}=\pi r^2[/tex]
Therefore, the area of circular wooden table is given by :-
[tex]\text{Area}=3.14(4)^2\\\Rightarrow\ 3.14\times16\\\Rightarrow\text{Area=}50.24\ ft^2[/tex]
The area of the circular wooden table = 50.24 ft²
Answer: 50.24
Step-by-step explanation:
We know: The radius = 4 feet and that the area of a circle = πr^2
Next: (π) 3.14 (4)^2
which we can simplify to be 3.14 * 16
= 50.24
(just took the test hope this helped)
The cost of 7 drinks is $16.38. What is the cost of each drink?
$1.54
$1.88
$2.34
$2.73
The cost of each drink if 7 drinks cost $16.38 is $2.34.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that the cost of 7 drinks is $16.38. Therefore, the cost of each of the drink will be:
Cost of each drink = Cost of all the drinks / Number of drinks
= $16.38 / 7
= $2.34
Hence, the cost of each drink is $2.34.
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