Answer:
The average rate of change of the height over the interval [1, 2.5] is - 56 feet per second.
Step-by-step explanation:
Let [tex]s(t) = -16\cdot t^{2} + 150[/tex]. Geometrically speaking, average rate of change over a given interval ([tex]\bar v[/tex]), measured in feet per second, is determined by definition of secant line, which is defined:
[tex]\bar v = \frac{s(t_{2})-s(t_{1}) }{t_{2}-t_{1}}[/tex] (1)
Where:
[tex]s(t_{1})[/tex], [tex]s(t_{2})[/tex] - Initial and final position of the object, measured in feet.
[tex]t_{1}[/tex], [tex]t_{2}[/tex] - Initial and final times, measured in seconds.
If we know that [tex]t_{1} = 1\,s[/tex] and [tex]t_{2} = 2.5\,s[/tex], then the average rate of change over the interval [tex][1,2.5][/tex]:
[tex]s(1) = -16\cdot (1)^{2}+150[/tex]
[tex]s(1) = 134[/tex]
[tex]s(2.5) = -16\cdot (2.5)^{2}+150[/tex]
[tex]s(2.5) = 50[/tex]
[tex]\bar v = \frac{50\,ft-134\,ft}{2.5\,s-1\,s}[/tex]
[tex]\bar v = -56\,\frac{ft}{s}[/tex]
The average rate of change of the height over the interval [1, 2.5] is - 56 feet per second.
I need help part d of this question
Answer:
D is 50,230,000,000
Step-by-step explanation:
explanation
510,000,000
9,600,000,000
244,000
50,230,000,000
You are trying to increase your monthly savings to buy a used car. Your boss allows you to work one hour of overtime at time-and-half 5 days per week. Your regular wage is $12.00 per hour. You want to save $3,000 for your car. Approximately how many weeks must you work with the extra hour per day to reach your goal?
Answer:
34 weeks
Step-by-step explanation:
As given,
Wage of 1 hour = $12
⇒1$ = [tex]\frac{1}{12}[/tex] hour
⇒$3000 = [tex]\frac{3000}{12}[/tex] = 250 hour
As given,
1 week = 5 days
And he works
[tex]1\frac{1}{2} = \frac{3}{2}[/tex] hour in 1 day
⇒5 days = 5×[tex]\frac{3}{2}[/tex] = [tex]\frac{15}{2}[/tex] hours
⇒1 week = [tex]\frac{15}{2}[/tex] hours
⇒1 hour = [tex]\frac{2}{15}[/tex] week
⇒250 hour = [tex]\frac{250 . 2}{15}[/tex] = 33.34 weeks ≈ 34 weeks
∴ we get
He has to Approximately work for 34 weeks with the extra hour per day to reach your goal.
A loan of $2,000 dollars is being paid off over time. You have automatic payments set up to pay $50 towards the loan each month. You also work and save money in your bank account. You currently have $500 in the bank and save an additional $100 per month. What is the earliest you could pay off you loan?
Answer:
10 months
Step-by-step explanation:
2000 - 500 = 1500.
You can pay 100 + 50 = 150 per month
1500 / 150 = 10 months
For every 7 grams of protein in a cup of yogurt, there are 10 grams of carbohydrates. How many grams of protein are there for every gram of
carbohydrates?
Answer:
0.70 grams of protein are there for every gram of carbohydrates
Step-by-step explanation:
10/10 = 1
7/10 = 0.7
Maia's garden is made of rectangular regions, as shown below. She wants to cover her garden with plastic muluch to warm the soil. What is the area of the garden?
*check figure 1 for the diagram of the garden
Answer:
2,400 cm²
Step-by-step explanation:
The area of the garden has been decomposed into 3 rectangles, rectangles 1, 2, and 3 (see figure 2 in the attachment below).
To find the area of the garden, calculate the area of each of the 3 rectangles and sum them together.
Thus:
Rectangle 1:
Area = length × width = 20 × 20 = 400 cm²
Rectangle 2:
Area = length × width = 60 × 10 = 600 cm²
Rectangle 3:
Area = length × width = 70 × 20 = 1,400 cm²
✔️Area of the garden = 400 + 600 + 1,400 = 2,400 cm²
A bit confused on what to do. Can someone help?
Answer: the answer is on a calculator
Step-by-step explanation:
If your aboe to do that you can so anything
How many atoms of element X with one valence electron will combine with one oxygen atom?
A.) 2
B.) 1
C.) 3
D.) 5
The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x and also the value of the observation in the data.
Answer:
x = 9
Number of observations = 6
Sum of observations = 54
Step-by-step explanation:
Number of observations, n = 6
Mean = ΣX / n
(6 + 8 + x + 2 + 10 + 2x - 1 + 2) / 6 = 9
(27 + 3x) / 6 = 9
27 + 3x = 6 * 9
27 + 3x = 54
3x = 54 - 27
3x = 27
x = 27 / 3
x = 9
Solve: 3a - 2.4 = 5.1 a = _____
Answer:
a=2.5
Step-by-step explanation:
3a-2.4=5.1 Add the like terms ( plus 2.4 cancels out -2.4)
+2.4 +2.4
3a=7.5 Now divide by 3
/3 /3
a=2.5
An item is regularly priced at $95. It is on sale for 80% off the regular price. How much (in dollars) is discounted from the regular price?
Answer:
76??
Step-by-step explanation:
95×0.20=19
95-19=76
PLEASE HELP WILL MARK BRAINLIEST!!! A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost, in dollars, for a passholder to watch n movies.
1. Is function C a piecewise function? Explain your reasoning.
2. Draw a graph to represent C.
3. Describe, as completely as possible, the domain of C.
4. Describe, as completely as possible, the range of C.
The equation to describe this will be y = 8x. It is assumed that Pass holders pay $8 each movie for the first five films. After five films, up to fifteen films, additional films are free. This will be represented by the function y = 40.
What is meant by equation?When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth.To learn more about equation, refer to:
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A blank is a fraction with a denominator of one
Answer:
Whole Number
Step-by-step explanation:
Answer:
A whole is a fraction with the denominator of one.
Step-by-step explanation:
i'll mark you brainlist <3
Solve the compound inequality
3t-8/5 and 4-t<-7
Answer: -2.8
Step-by-step explanation:
3t-(8/5) * 4-t < -7
(15t-8)/5 * 4-t < -7
((15t-8)(4-t))/5 < -7
(15t^2)-28t-32< -7
(15t^2)-28t-32-7< 0
(15t^2)-28t-39< 0
Using the quadratic/almighty formula
t= (-b +- ((b^2)-4ac)^(1/2)/2a)
a=15, b=-28, c=-39
t= (-(28) +- (((-28)^2)-4(15)(-39))^(1/2))/2(15))
t= -2.8 or t= 0.9
Since
t<0, then t= -2.8
pls help me with this multiple choice ! (Actually try).
Answer:
B
Step-by-step explanation:
[tex] \sin(30) = \frac{y}{68} \\ y = 34 \\ \cos( 30) = \frac{ x }{68} \\ x = 34 \sqrt{3} [/tex]
Please help will mark brainliest
Answer:
-19
Step-by-step explanation:
Answer:
-19
Step-by-step explanation:
Plz, mark me brainliest ;)
Can someone help me plzzzzzz :(
Answer:
y = 12
Step-by-step explanation:
Please help I will give brainiest I’m struggling on this no funny answers please!!!!!!
Answer:
B.) You don't really have to worry about finding the slope. You just have to look for the y intercept, which is (0, -2)
Hope this helps! :)
someone give the worked solution for this please!!!!
Answer:
The scale Myra should use is one graph unit = 400 km or;
←--→ = 400 km
Step-by-step explanation:
The question relates to the representation of scale drawing
The actual distance between Perth and Sydney = 3294 kilometers
The given coordinates of Perth on the grid = (1.3, 3.4)
The given coordinates of Sydney on the grid = (9.2, 3.3)
The measure of the distance between Perth and Sydney, 'd', is given by using the following formula for finding the distance between two points given their 'x', and 'y' coordinates;
[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]
Therefore, by substitution, we have;
[tex]d = \sqrt{\left (9.2-1.3 \right )^{2}+\left (3.3-3.4 \right )^{2}} = \sqrt{\left (7.9 \right )^{2}+\left (-0.1 \right )^{2}} = \dfrac{\sqrt{6242} }{10} \approx 7.9[/tex]
d ≈ 7.9 units
Therefore, we have;
7.9 units of the graph = 3294 kilometers
1 unit of the graph ≈ 3294/7.9 km = 416.962025316 km ≈ 416.96 km
Therefore, the scale Myra should use for her map is 1 unit = 400 km.
solve for x
(3x-1)
71
Answer:
3x+1=71
3x=71+1
3x=72
x=24
There is a cube that is 1 unit long, 1 unit wide,
and 1 unit deep. What is the volume of this
cube?
a. 4 cubic units
b. 3 cubic units
c. 2 cubic units
d. 1 cubic unit
Answer:
D
Step-by-step explanation:1x1x1=1
Pls help I hate math
A water container in the shape of a rectangular prism has a length of 2 meters, a width of 3/4 meter, and a height of 1/2 meter. If a cubic meter of water costs $1.20, what is the cost to fill the container?
Answer:
look below!
Step-by-step explanation:
For the length I think you meant 32, and if you did it is $14.40
If not and you meant length of 2 it is $0.90
Answer:
lxwxh for volume.
2x.75x.5 = .75 cubic meters.
.75 percent of 1.20 = .90.
90 cents is the answer.
Find the value of two numbers if their sum is 21 and their difference is 5
Answer: x = 13 and y = 8
Step-by-step explanation:
Two numbers must add to 21. We don't know them yet, so let's just use a placeholder for both of them for now.
x + y = 21
Their difference is five, meaning that if we subtract one from the other, we get five. Again, we don't know the numbers yet, so we'll add a placeholder for now.
x - y = 5
We can now solve a system of equations for x.
x = y + 5
y + 5 + y = 21
2y + 5 = 21
2y = 16
y = 8
x - 8 = 5
x = 13
So x = 13 and y = 8
what is x
5 (x-2)= 45
Answer:
11
Step-by-step explanation:
5(x-2)=45
x-2=45/5
x-2=9
x=9+2
x=11
Maria bought G gallons of gasoline for $2.75 per gallon and see cans of oil for $3.15 per can a what expression can be used to determine the total amount Maria spent on gasoline be if she bought 7.4 gallons of gasoline and eight cans of oil how much do you spend in all
Answer: $20.35 on gallons of gas and $25.2 on cans of oil
If elimination is the method used to solve this system of equations, what is the result of the first step?
S 4x + 3y = 6
4x - y = 2
Answer:
a
Step-by-step explanation:
In terms of the water lily population change, the value 3.915 represents:
Answer:
he initial number of water lily’s :the value 1.106 represents the population increase rateedge
Step-by-step explanation:
The value 3.915 represents the initial population in the exponential equation of water lilies.
What are exponential functions?When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function.
There usual form is specified below. They are written in several such equivalent forms.
The standard exponential equation is given as; y = ab^x
where;a is the initial population b is the rate (growth or decline)
We have been Given the exponential equation; y = 3.915(1.106^x)
On comparison, we can see that,
a = 3. 915
Hence, This shows that the value 3.915 represents the initial population of water lilies.
Learn more on exponential equation here:
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what is the measure of
Answer:
The measure or what?
Step-by-step explanation:
Answer:
we need a measure
Step-by-step explanation:
Question 9 of 10
Solve the system of equations:
y= 2x + 1
y = x2 + 2x - 8
A. (0.1) and (2,5)
B. (-4,0) and (2,0)
C. (-3, -5) and (3,7)
O D. (-3,5) and (3, 2)
Answer:The answer is =3,7
Step-by-step explanation:
The scale of the room design shows that 1" = 3 feet. How big is the actual room if the design shows a square that is 6 inches wide?
Answer:
arah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:
1 inch=30 feet.
If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?
In this concept, you will learn how proportions are used to find actual and scale dimensions using a scale ratio.
Using Proportions to Find Dimensions
A scale is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.
A scale drawing is a drawing that is used to represent and object that is too large to be drawn in its actual dimensions. If a drawing is to scale, you can use proportions to determine the actual dimensions of the scale drawing.
Let’s look at a scale drawing of a sculpture. In the drawing, the sculpture is 4 inches tall. The scale is 1 inch : 4 feet. It scale can be written as
1 in4 ft
(Note: Inch is abbreviated “in.” or with the double prime mark, ″. Foot/feet is abbreviated “ft” or with the single prime mark, ′.)
A drawing with this scale tells you that 1 inch on paper is equal to 4 feet in real life. If the drawing is 4 inches tall, use the scale to find the actual height of the sculpture.
First, create a proportion using equivalent ratios. Remember to write the corresponding units in the numerator and in the denominator. The actual height of the sculpture is represented by the variable x.
1 in.4 ft.=4 in.x ft.
Then, cross multiply and simplify the equation to find the value of x.
xx==4(4)16
The sculpture will be 16 feet tall.
Let’s make a scale drawing. Use the scale 1′′=2′. Draw a room that is 8′×12′.
First, write a proportion to find the measurement of the width.
1′′2′=x′′8′
Next, cross multiply and simplify the equation to find the value of x.
2x2xx===1(8)84
The drawing will be 4