Answer:
t = 54 seconds
Step-by-step explanation:
The equation that models the path of a rocket into the air is given by :
[tex]h(t)= -16t^2+864t[/tex]
It is required to find the time after which the rocket will hit the ground. When it hits the ground, the height of the rocket will becomes zero. It means,
h(t) = 0
i.e.
[tex]-16t^2+864t=0\\\\16t(-t+54)=0\\\\16t=0, -t+54=0\\\\t=0\ and\ t=54\ s[/tex]
It means after 54 seconds, the rocket will hit the ground.
In the table, x represents every mile driven in a cab and y represents the cost. A 2-column table with 5 rows. Column 1 is labeled x with entries 1.25, 2.50, 3.75, 5, 6.25. Column 2 is labeled y with entries 7.50, 10.0, 12.5, 15.0, 17.5. Is the slope increasing or decreasing? What is the slope for this scenario?
The slope for this scenario of X (every mile driven in cab) and Y (cost ) is 2 and the slope is increasing.
X 1.25 2.50 3.75 5 6.25
Y 7.50 10.0 12.5 15 17.5
[tex]x_{1}= 1.25 \\ x_{2} = 2.50 \\ y_{1}=7.50 \\y_{2}=10[/tex]
What is the Slope?
The slope or gradient of a line is a number that describes both the direction and the steepness of the line. It is represented by m.
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
Substitute all the required values in Slope formula, we get
[tex]m =\frac{10-7.50}{2.50-1.25}[/tex]
[tex]m = \frac{2.50}{1.25}[/tex]
[tex]m=2[/tex]
Thus, the slope of the given scenario is 2 and X and Y are increasing simultaneously as well as slope is positive. So, we can say it is a increasing slope.
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Answer: In the table, x represents every mile driven in a cab and y represents the cost.
A 2-column table with 5 rows. Column 1 is labeled x with entries 1.25, 2.50, 3.75, 5, 6.25. Column 2 is labeled y with entries 7.50, 10.0, 12.5, 15.0, 17.5.
Is the slope increasing or decreasing?
✔ increasing
What is the slope for this scenario?
✔ 2
Step-by-step explanation:
Given f(x) = 5x – 3, find f(2).
Answer:
f(2) = 7
Step-by-step explanation:
To figure this out you just have to plug in 2 wherever x is in the equation.
f(2) = 5(2) - 3
Multiply 5 by 2
f(2) = 10 - 3
Subtract
f(2) = 7
Which inequality is true if p= 3.4?
A. 3p < 10.2
B. 13.6 < 3.9p
C. 5p > 17.1
D. 8.5 > 2.5p
The correct inequality is B. 13.6 < 3.9p.
Explanation:To determine which inequality is true if p = 3.4, we can substitute the value of p into each inequality and see which one is satisfied. Let's do this for each option:
A. 3p < 10.2:
Substituting p = 3.4, we get 3(3.4) = 10.2 < 10.2, which is not true.
B. 13.6 < 3.9p:
Substituting p = 3.4, we get 13.6 < 3.9(3.4) = 13.26, which is true.
C. 5p > 17.1:
Substituting p = 3.4, we get 5(3.4) = 17 < 17.1, which is not true.
D. 8.5 > 2.5p:
Substituting p = 3.4, we get 8.5 > 2.5(3.4) = 8.5 > 8.5, which is not true.
Therefore, the correct inequality is B. 13.6 < 3.9p.
How does f(x) = 6x change over the interval x = 3 to x = 4?
Answer:
I assume the answer would be that f(x) = 6(x) increases over the interval x = 3 to x = 4
Step-by-step explanation:
6 x 3 is 18 and 6 x 4 is 24, so over the interval x = 3 to x = 4 f(x) would increase.
**Use Pie Graph for Projected Percentage
Category Total Projected
Difference
Housing
$575
(Type Here)
Budget Busters #2- Bella
($28,000 annual salary at 18% tax rate)
Amount of Taxes: (Type Here)
Net Annual Income:
Net Monthly Income:
(Type Here (Type Here)
Actual
(Type Here)
$478.25 (Type Here)
Debt
(Type Here)
Groceries
S320
(Type Here)
Category
Total
Percent
Transportation
S250
(Type Here)
(Type Here)
(Type Here)
(Type Here)
Housing
$575
$100
Charity
(Type Here)
(Type Here)
Debt
$189.75
$478.25
Savings
(Type Here)
(Type Here)
(Type Here)
Groceries
$320
(Type Here)
Transportation
$250
(Type Here)
1. What is the most significant difference between Bella's actual
spending and her budget?
(Type Here)
Charity
$100
(Type Here)
Savings
$189.75
(Type Here)
Answer:0.0
Step-by-step explanation:
To find the most significant difference in Bella's budget, calculate the difference for each category and compare them. For Mary Ann, by subtracting her expenses from her net income of $2,589.10, we determine she can save more than 10% of her income, exceeding her savings goal.
Explanation:The most significant difference between Bella's actual spending and her budget can be determined by comparing the projected expenses to the actual expenses in each category. You'll first calculate the difference for each category by subtracting the actual amount from the projected amount. These differences should be compared to determine which one is the largest. For Mary Ann's scenario, we can construct a budget table and calculate the possibility of saving 10% of her after-tax monthly income by deducting her monthly expenses from her net income. To do this, you'll start with her net monthly income and subtract each of her monthly expenses to check if there's at least 10% of her income left for savings.
If Mary Ann's net monthly income is $2,589.10, her goal is to save 10% of that amount, which would be $258.91. Once you subtract her expenses which total $2,145 (the sum of rent, cell phone, utilities, cable TV and internet, groceries, entertainment, car payment, and gasoline) from her net income, you're left with $444.10. Therefore, she can meet her savings goal since $444.10 is more than $258.91. You can use similar steps and considerations for creating and managing a budget based on the cost of living in your area.
5 less than 18 times the number x, is less than of equal to -45. write and inequality for this statement
Answer:
18x-5≤-45
Step-by-step explanation:
The statement '5 less than 18 times the number x is less than or equal to -45' translates to the inequality '18x - 5 ≤ -45'. This can be solved to yield 'x ≤ -20/9'.
Explanation:The phrase '5 less than 18 times the number x' can be written as an expression '18x - 5'. The complete inequality saying this is less than or equal to -45 can thus be written as '18x - 5 ≤ -45'.
To clarify, this means that if you were to multiply a number 'x' by 18, and then subtract 5, the resulting number should be less than or equal to -45.
This is a type of linear inequality and can be solved in a similar way to a linear equation. Subtracting 5 from both sides yields '18x ≤ -40', and then dividing by 18 gives the solution 'x ≤ -40/18' or 'x ≤ -20/9' in simplified form.
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The figure shows the dimensions of the couch cushion find the surface area of the cushion 35 inches 20 inches 30.25 inches 4 inches 14.5 inches
Answer:
1,787.75
Step-by-step explanation:
The sum of the areas of the 10 rectangles gives the surface area of the cushion:
A = 140 sq. in. + 80 sq. in. + 121 sq. in. + 2(605 sq. in.) + 22 sq. in. + 2(68.875) sq. in +19 sq. in. + 58 sq. in.
= 140 sq. in. + 80 sq. in. + 121 sq. in. + 1,210 sq. in. + 22 sq. in. + 137.75 sq. in +19 sq. in. + 58 sq. in.
= 1,787.75 sq. in.
The surface area of the cushion is 1,787.75 square inches.
write an expression to represent 6 less than 8 times c
Answer:
(8*c)-6
Step-by-step explanation:
Answer:
8c - 6.
Step-by-step explanation:
8 times c = 8c.
Now 6 less than this is 8c - 6.
] Mr. Santiago received a job with an annual salary of $51,000. He will receive a 1.5% increase every year. How much will Mr. Santiago make in 3 years?
Answer:
He will make $53,330
Step-by-step explanation:
In this question, we are tasked with calculating how much Mr Santiago will make in three years.
To calculate the future value of his earnings, we can use the formula for the future value of the salary
Mathematically, the FV = I(1 + r)^t
Where I is the initial amount of $51,000
r is the interest rate which is 1.5% = 1.5/100 = 0.015
t is the time in years which is 3 years
We plug these values into the equation above;
FV = 51,000(1+0.015)^3
FV = 51000(1.015)^3
FV = 53,329.59 which is $53,330 to the nearest whole dollars
How can I factorize the next equation?
[tex]f(x)=x^4+2x^3-9x^2+18x[/tex]
Step-by-step explanation:
Use grouping.
f(x) = x⁴ + 2x³ − 9x² + 18x
f(x) = x³ (x + 2) − 9x (x + 2)
f(x) = (x³ − 9x) (x + 2)
f(x) = x (x² − 9) (x + 2)
f(x) = x (x − 3) (x + 3) (x + 2)
How do I solve for the value of csc0 ?
Answer:
Step-by-step explanation:
X=y
[tex]\[ \csc(\theta) = \frac{15}{12} = \frac{5}{4} \][/tex] Option C. 15/12 is the Right Choice.
In a right triangle, the cosecant ([tex]\(\csc\)[/tex]) of an angle is the ratio of the length of the hypotenuse to the length of the side opposite the angle. In this scenario, we're given an angle [tex]\( \theta \)[/tex] and the side opposite to it measures 12 units. The length of the hypotenuse is denoted as [tex]\( r \)[/tex], and the length of the other side is 9 units.
To find the length of the hypotenuse ([tex]\( r \)[/tex]), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, we have:
[tex]\[ r^2 = 12^2 + 9^2 \][/tex]
[tex]\[ r^2 = 144 + 81 \][/tex]
[tex]\[ r^2 = 225 \][/tex]
Taking the square root of both sides, we get [tex]\( r = 15 \)[/tex].
Now that we have the length of the hypotenuse ([tex]\( r = 15 \)[/tex]), we can find the cosecant ([tex]\(\csc\)[/tex]) of angle [tex]\( \theta \)[/tex]. The definition of [tex]\(\csc\)[/tex] in a right triangle is:
[tex]\[ \csc(\theta) = \frac{r}{\text{opposite side}} \][/tex]
Substituting the values we have, we get:
[tex]\[ \csc(\theta) = \frac{15}{12} \][/tex]
Simplifying this expression, we find that:
[tex]\[ \csc(\theta) = \frac{5}{4} \][/tex]
Therefore, the value of [tex]\( \csc(\theta) \)[/tex] is [tex]\( \frac{5}{4} \)[/tex]. Hence, the correct answer is C. 15/12.
Amar and his friends went to a movie at 4:45 p.m. The movie ended at 6:20 p.m. PART A How long was the movie in hours and minutes?
Answer:
The movie was 1 hour and 35 minutes long. (Or 95 minutes long)
Step-by-step explanation:
Well let's see:
It will take 15 minutes from the start to reach 5:00 PM
4:45+0:15=5:00
Now it will be 1 hour and 20 minutes from 5:00 PM to reach the end time of the movie.
Adding the minutes and hours together:
1 hour + 20 minutes + 15 minutes = 1 hour and 35 minutes
Answer:
1:35
Step-by-step explanation:
4:45 is where you start. If you go an hour at would be 5:45. Then count to 6:20. if it's tough go to a silent place and try not to think of anything else just of what your counting to. Hope this helps!
The city zoo has an equal number of visitors on Friday, Saturday, and Sunday. In all, 48,144 people visited the zoo that weekend. How many visited each day
Answer:
16,048 visitors per day.
Step-by-step explanation:
To solve for this answer, you will simply need to divide the total amount of visitors (48,144) by the amount of days given, which in this instance, is 3.
48,144÷3= 16,048 visitors per day.
Bethany has a circular table that she needs to carry inside her house to paint. Her front door is a rectangle and has a width of 36 inches and a height of 80 inches
Answer: 1440
Step-by-step explanation:
36 * 80 = 2880 * ½ = 1440 so the answer of the triangle is 1,440
The area of circular table top is greater than the area of rectangular front door, circular table top will not fit through front door.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, front door is a rectangle and has a width of 36 inches and a height of 80 inches.
We know that, area of a rectangle is length×breadth
Now, area of front door is 80×36
= 2880 square inches
Here, radius of circular table top is 43 inches
Area of circle = πr²
= 3.14×43²
= 5805.86 square inches
Since, the area of circular table top is greater than the area of rectangular front door, circular table top will not fit through front door.
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"Your question is incomplete, probably the complete question/missing part is:"
Bethany has a circular table that she needs to carry inside her house to paint. Her front door is a rectangle and has a width of 36 inches and a height of 80 inches. If the table top has a diameter of 86 inches, will it fit through her front door?
If ABCD is a rhombus AD=4x+2 DC=7x-13 and BD=34 find AE (E is in the middle)
Answer: Line AE equals 14 units (approximately)
Step-by-step explanation: If you have a rhombus given, it is important to begin by highlighting the properties of a rhombus. A rhombus first of all is four-sided shape with all sides congruent, then the two opposite sides are parallel and congruent. Also, the diagonals bisect each other into two equal halves each.
Therefore, we shall examine a rhombus labelled ABCD, with side AD measuring 4x + 2, and side DC measuring 7x - 13. Then BD is a diagonal from point B to point D, and it measures 34 units. Also a diagonal is drawn halfway from point A and stops at point E (E is in the middle), where it bisects diagonal BD into two halves. Remembering that all sides of a rhombus are equal, then note that AD equals DC, that is;
4x + 2 = 7x - 13
2 + 13 = 7x - 4x
15 = 3x
Divide both sides of the equation by 3
5 = x
If AD = 4x + 2, then when x = 5
AD = 4(5) + 2
AD = 20 + 2
AD = 22
Therefore triangle ADE can now be isolated with side AD measuring 22 units and side ED measuring 17 units (midpoint between points B and D). Line AE can be calculated using the Pythagoras theorem which states as follows;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the two other sides
Substituting for values as given in the question, we now have;
AD² = ED² + AE²
22² = 17² + AE²
484 = 289 + AE²
484 - 289 = AE²
195 = AE²
Add the square root sign to both sides of the equation
√195 = √AE²
13.96 = AE
Therefore line AE ≈ 14 units (to the nearest whole number)
The distance between (9,10 and (9,3)
The volume of the triangular prism is 54 cubic units.
What has to happen for a disease to become a pandemic?
Answer:
its the second one
Step-by-step explanation:
I want brainliest
Answer:
it has to spread over a large portion of the world
Explanation:
That's what a pandemic is.
27.9 divided by 0.3.
Answer:
93
Step-by-step explanation:
Answer:
Step-by-step explanation:
93
How much interest is earned in 2 years on an investment of $2,000? The interest rate is 3%
Sin 74 to nearest tenth
Answer:
sin(74º) = 0.96
Step-by-step explanation:
answer is 70
When rounding to the nearest tenth like 74 we:
Round the number to the nearest tenth if the last digit of the number is 5678 or 9
Then we do the same rounding it down
Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below:
Baseball Scores
Based on the table, what is the mean baseball score?
Answer:
Correct answer is 4.1
Step-by-step explanation:
You have to list all scores, total them and then divide by the total count:
0,1,1,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6
The sum is 134 divided by the total values in the data set, 33 = 4.1
To calculate the mean baseball score, add up all the scores and then divide by the number of scores. The example provided demonstrates this process with hypothetical scores.
Explanation:The mean is calculated by adding up all the scores and then dividing by the number of scores. Let's say the scores are 10, 20, 30, and 40. Here's how you calculate it:
Add up the scores: 10 + 20 + 30 + 40 = 100Count the number of scores. In this case, there are 4 scores.Divide the total by the number of scores: 100 ÷ 4 = 25. Therefore, the mean baseball score is 25.This method applies to any group of numbers, whether they are baseball scores or other data sets.
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Which statement is true of data in a line graph?
It is discrete.
It can only have certain values.
It is given in data pairs.
It is continuous.
Answer:
the last one i think
Step-by-step explanation:
What is the simplified base for the function f(x) = 2RootIndex 3 StartRoot 27 EndRoot Superscript 2 x?
2
3
9
18
Answer:c
Step-by-step explanation:
twice a number decreased by 20 is 50.
Answer:
The number is 35.
Step-by-step explanation:
Let the number be x
Twice the number: 2*x = 2x
Twice the number decreased by 20: 2x - 20
2x - 20 = 50
Add 20 to both sides
2x - 20 +20 = 50 + 20
2x = 70
Divide both sides by 2
2x/2 = 70/2
x = 35
Lauren determined that the difference in the medians is greater than the difference in the interquartile ranges. Which
explains Lauren's error?
Lauren made her first error in step 1 because the median is 85 for chemistry and 80 for biology
Lauren made her first error in step 1 because the median is 60 for chemistry and 60 for biology
Lauren made her first error in step 3 because she should have used 90-55 = 35 for chemistry and 90-50 - 40 for
biology
Lauren made her first error in step 3 because she should have used 85-60-25 for chemistry and 80-60-20 for
biology
Answer:
D: Lauren made her first error in step 3 because she should have used 85-60 = 25 for chemistry and 80-60 = 20 for biology
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Got it right on ed 2020
A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 75,000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 8% each year. How many total fish did the company catch over the first 7 years, to the nearest whole number?
Answer:
The total amount of fishes caught is 414,519 fishes
Step-by-step explanation:
Here, given the percentage decrease in the population of fishes, we want to know the total amount of fishes caught by the company in the first 7 years.
First year, we have 75,000 fishes
Second year, we would have 75,000 - (8% of 75,000) = 75,000 - (0.08 × 75,000) = 75,000 - 6,000 = 69,000
Third year, we would have 69,000- (0.08 × 69,000) = 69,000 - 5520 = 63,480
Fourth year, we would have 63,480 - (0.08 × 63,480) = 58,401.6
Fifth year, we would have 58,401.6 - (0.08 × 58,401.6) = 58,401.6 - 4,672.18 = 53,729.472
Sixth year, we would have 53,729.472 - (0.08 × 53,729.472) = 53,729.472 - 4,298.3578 = 49,431.114
Seventh year, we would 49,431.114 - (0.08 × 49,431.114) = 45,476.625
The addition of all these values will give the total number of fishes caught = 75,000 + 69,000 + 63,480 + 58,401.6 + 53,729.472 + 49,431.114 + 45,476.625 = 414,518.8 = 414,519 fishes to the nearest whole number
Final answer:
Learn how to calculate the total fish caught by a fishing company over 7 years with decreasing catches.
Explanation:
A major fishing company caught 75,000 fish in the first year. Each year, the number of fish caught decreased by 8%. To find the total fish caught over 7 years:
Calculate the number of fish caught each year by multiplying the previous year's catch by (100% - 8%).
Add up the catches for 7 years.
Round the final total to the nearest whole number.
Therefore, the fishing company caught approximately X fish over the first 7 years.
Kelsey graphed the equation y = 3x + 1 as shown below. On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3). Which describes Kelsey’s error?
Answer: Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.
Step-by-step explanation:
Answer: D on edg
Step-by-step explanation:
Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.
Plzzzzz help im giving 50 pts if u help me and ill mark brainliest
Solve the system of equations.
–5x – 12y – 43z = –136
–4x – 14y – 52z = –146
21x + 72y + 267z = 756
Question 4 options:
a. x = 6, y = 9, z = –6
b. x = 1, y = 3, z = 4
c. infinite solutions
d. no solution
Answer:
no solution
Step-by-step explanation:
–5x – 12y – 43z = –136
–4x – 14y – 52z = –146
21x + 72y + 267z = 756
Every coefficient of the second equation is a multiple of 2, so divide both sides by 2.
Every coefficient of the third equation is a multiple of 3, so divide both sides by 3.
–5x – 12y – 43z = –136
–2x – 7y – 26z = –73
7x + 24y + 89z = 252
Let's call the above system the "simplified original system."
Using the simplified original system, multiply the first equation by -2 and the second equation by 5. Then add them.
10x + 24y + 86z = 272
(+) -10x - 35x - 130z = 365
------------------------------------------
-11y - 44z = 637
Now we have an equation with only y and z.
Now, using the simplified original system, multiply the second equation by 7 and the third equation by 2. Then add them.
–14x – 49y – 182z = –511
(+) 14x + 48y + 178z = 504
-------------------------------------------
-y - 4z = -7
Now we have a system in 2 unknowns, y and z.
-11y - 44z = 637
-y - 4z = -7
Multiply the second equation by -11 and add to the first equation.
-11y - 44z = 637
(+) 11y + 44z = 77
-----------------------------
0 = 714
Since 0 = 714 is false, this system has no solution.
If a car can drive 62 miles on 3 gallons of gas, how many gallons of gas will it use to travel 231 miles?
Answer:
x =11.17741935 gallons
Step-by-step explanation:
We can use a ratio to solve
62 miles 231 miles
--------- = -----------
3 gallons x gallons
Using cross products
62x = 231 *3
62x =693
Divide each side by 62
62x/62 = 693/62
x =11.17741935 gallons
Answer: 11.1774194 gallons of gas
Explanation: To solve this problem, our first step is to write down the unit ratio that is involved. In this case, it's miles traveled/gallons of gas.
Next, we set up a proportion based
on the information in the problem.
We know that a car gets 62 miles for every 3 gallons so we have 62/3 and we're asked how many gallons of gas
will it use to travel 231 miles so that's 231/x.
Notice that the 231 miles must go on top in the second ratio
because our unit ratio tells us that we put miles over gallons.
Solving from here, we use the means-extremes property which states that the product of the extremes, (62)(x) equals the product of the means, (3)(231).
So we have the equation 62x = 693.
Now, dividing both sides of the equation
by 63, we find that x = 11.1774194.
This means that the car will use 11.1774194
gallons of gas to travel 231 miles.