I believe the correct answer from the choices listed above is option D. The expression that could be used to determine the average rate at which the object falls during the first 3 seconds of its fall would be (h(3)-h(0))/3. Average rate can be calculated by the general formula:
Average rate = (change in y-axis) / (change in x-axis)
In this case,
Average rate = (change in height) / (change in time)
The average rate at which the object falls during the first 3 seconds can be calculated using the equation for average rate of change (h(3) - h(0))/3. Using the given function h(t) = 300 - 16t, this comes out to be -16 feet per second.
Explanation:In this problem, we are given a mathematical model of a falling object, as follows: h(t) = 300 - 16t. Here, the function h(t) represents the height of the object t seconds after it is dropped from a platform 300 feet above the ground.
To determine the average rate at which the object falls during the first 3 seconds, we should use the equation for average rate of change in functions. That is, the change in height divided by the change in time, or (h(3) - h(0))/3.
Let's calculate: h(3) = 300 - 16*3 = 252, and h(0) = 300. Then, the average rate = (252 - 300) / 3 = -48/3 = -16 ft/sec. This indicates that the object falls at an average rate of 16 feet per second during the first three seconds.
Learn more about Average Rate of Change here:https://brainly.com/question/34745120
#SPJ2
drag the tiles to the boxes to form the correct pairs. not all tiles will be used.
Expand or factor each of the following expressions to determine which expressions are equivalent.
Answer:
[tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]
Step-by-step explanation:
We need to drag the tiles and place them in boxes to form the correct pairs.
The given options are:-
1) [tex]9x^{2}+3x-20[/tex]
2) [tex](4x-3y)^{2}[/tex]
3) [tex](3x+5)(3x-4)[/tex]
4)[tex](3x+2)(9x^{2} -6x+4)[/tex]
First we simplify the all given factor and then compare with provided options
2) [tex](4x-3y)^{2}[/tex]
=[tex]16x^{2}+9y^{2}-24xy[/tex]
3) [tex](3x+5)(3x-4)[/tex]
[tex]9x^{2}-12x+15x-20[/tex]
[tex]9x^{2}+3x-20[/tex]
Here we can see equation (3) match with (1)
so, [tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]
Hence, the correct match is shown in figure-1
The expressions that are equivalent should be matched as follows;
9x² + 3x - 20 ↔ (3x + 5)(3x - 4)
How to match the equivalent expressions?In order to match the equivalent expressions, we would have to either expand or factor each of the given expressions as follows;
9x² + 3x - 20
By applying the sum-product pattern, we have:
9x² + 15x - 12x - 20
By writing the common factor from the two pairs, we have:
(9x² + 15x) + (-12x - 20)
3x(3x + 5) - 4(3x + 5)
(3x + 5)(3x - 4)
Next, we would expand the expression (4x - 3y)²;
(4x - 3y)(4x - 3y)
16x² - 12xy - 12xy + 9y²
16x² - 24xy + 9y²
9y² - 24xy + 16x²
Read more on factors here: https://brainly.com/question/26750554
#SPJ6
Solve 65x = 20.
Round to the nearest ten-thousandth.
Answer:
I think it's 0.30
Step-by-step explanation:
Multiply or divide as indicated. x^-8 • x^-2
ANSWER
[tex]\frac{1}{ {x}^{10} }[/tex]
EXPLANATION
The given exponentiial expression is
[tex] {x}^{ - 8} \bullet {x}^{ - 2} [/tex]
We simplify using the rule:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We apply this property to get:
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 8 + - 2}[/tex]
We simplify to get;
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 10}[/tex]
We rewrite as a positive index to get;
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = \frac{1}{ {x}^{10} } [/tex]
The Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits. Suppose your chosen number is 3079 .
(a) What is the probability that the winning number matches your number exactly?
(Enter your answer rounded to four decimal places.)
=
(b) What is the probability that the winning number has the same digits as your number in any order?
(Enter your answer rounded to four decimal places.)
Answer:
a) P(a)= 0.0001
b) P(b)= 0.0024
Step-by-step explanation:
Given:
Chosen number = 3079
Possible numbers that have chance of winning from 0000 to 9999= 10,000
Winning condition= if made choice matches the winning digits
Now
a)What is the probability that the winning number matches your number exactly?
From 0000 to 9999, only one time can the number 3079 can be the winning number, so
P(a)= 1/10000
= 0.0001
b)What is the probability that the winning number has the same digits as your number in any order?
Winning numbers from 0000 to 10000 that have same digits as 3079 are
4 x 3 x 2 x 1 = 24 ways
Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:
0379
0397
0973
0937
0793
0739
3079
3097
3970
3907
3790
3709
7039
7093
7930
7903
7390
7309
9073
9037
9370
9307
9730
9703
P(b)= 24/10000
=0.0024 !
20 POINTS PLZ HELP
Jack is doing an experiment to find the rate of water flow from a tap. He collects the water in a tub and records the height of the water level every five minutes. He then plots the data on a scatter plot. Which equation represents the line of best fit for Jack’s scatter plot?
A. y=14/45x
B. y=45x+15
C. y=45/14x
D. y=14x+45
Answer:
The correct option is C.
Step-by-step explanation:
If a line passing through two point then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the line of best fit passing through the points (0,0) and (14,45). So, the equation of line of best fit is
[tex]y-0=\frac{45-0}{14-0}(x-0)[/tex]
[tex]y=\frac{45}{14}x[/tex]
The equation of line of best fit is [tex]y=\frac{45}{14}x[/tex], therefore the correct option is C.
(1) 1 UU
15. Line segment RW has endpoints R(4, 5) and W6, 20). Point P is
on RW such that RP:PW is 2:3. What are the coordinates of point P?
(1) (2,9) (2) (0, 11) (3) (2, 14) (4) (10,2)
14
Answer:
P = (4.8, 11)
Step-by-step explanation:
P = 3R + 2W
RP + PW
= 3(4,5) + 2(6,20)
2 + 3
= (12,15) + (12,40)
5
= (24,55) = (4.8, 11)
5
Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is
on RW such that RP: PW is 2:3. the coordinates of point P would be (0, 11).
What is the coordinate of the point which divides a line segment in a specified ratio?Suppose that there is a line segment {AB} such that a point P(x,y) lying on that line segment{AB} divides the line segment {AB} in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
the coordinate of A is (x_1, y_1)
and the coordinate of B is (x_2, y_2)
Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is
on RW such that RP: PW is 2:3.
[tex](x,y) = \left( \dfrac{2(6) + 3(-4)}{2+3} , \dfrac{2(20) + 3(5)}{2+3} \right)\\\\(x,y) = \left( \dfrac{12- 12}{5} , \dfrac{40+15}{5} \right)\\\\(x,y) = \left( \dfrac{0}{5} , \dfrac{55}{5} \right)\\\\(x,y) = (0, 11)[/tex]
Learn more about a point dividing a line segment in a ratio here:
https://brainly.com/question/14186383
#SPJ2
what happens when you move a decimal point left or right?
Answer:
when you move a decimal point to the left you are increasing the number
when you move a decimal to the right you are decreasing the number
In a rectangle MPKN, the diagonals intersect each other at point O. A line segment OA is an altitude of a triangle MOP, and m∠AOP = 18°. Find the measure of ∠ONK.
To find the measure of ∠ONK in rectangle MPKN with given conditions, it's determined through the congruency of triangles and properties of a rectangle that ∠ONK is 72°.
The question involves finding the measure of ∠ONK in rectangle MPKN, where the diagonals intersect at point O, and a line segment OA is an altitude of triangle MOP with m∠AOP = 18°. Given the properties of a rectangle, we know that its diagonals bisect each other and are equal in length. Therefore, triangles MOP and NOP are congruent.
Because OA is the altitude to hypotenuse MP of triangle MOP, it creates two right triangles, OAM and OAP. The angle ∠AOP is given as 18°, which means ∠MOA = 90° - 18° = 72° since triangle OAM is a right-angled triangle. Because the diagonals of the rectangle bisect each other at O, triangle ONP is congruent to triangle OMP, and hence ∠ONK (which is also ∠ONP) is equal to 72° as angle ∠ONP is supplementary to ∠MOA in rectangle MPKN.
if the diameter of a circle is 50 yards ,the radius is
If the diameter of a circle is 50 yards the radius must be 25 yards.
This is because the radius is always half the diameter of the circle. Since we know the diameter is 50 yards, half of 50 is 25 so the radius must be 25 yards.
Have a great day!
The radius of the circle is 25 yards.
What is a Circle ?A circle is a round shaped figure which has all its points in one plane and the distance between all the points on its circumference to the center of the circle is equal .
It is given that
Diameter of a circle is 50 yards.
Radius of a circle = Diameter of circle / 2
Radius of the circle = 50/2 = 25 yards
Therefore the radius of the circle is 25 yards.
To know more about Circle
https://brainly.com/question/11833983
#SPJ2
What is the value of x?
Answer: Whats the whole question?
Step-by-step explanation:
The price of a watch was increased by 20% to 198. What was the price before the increase?
To find the original price before the increase, divide the new price by 1 + the percent of increase.
198 / 1.20 = 165
The original price was $165
The price before the increase was $ 165
What is percentage?Percentage can be said as a part of a whole expressed in hundredths .
How to know what was the price of the watch before the increase?Let the price of the watch be $ x
According to the problem,
The price of a watch was increased by 20% to $ 198.So, we can write x + 20x/100 = 198
⇒ 6x/5 = 198
⇒ x = 165
∴ The price before the increase was $ 165
Find more about "Percentage" here: https://brainly.com/question/24304697
#SPJ2
PLEASE HELPPPP i will give brainliest to whoever answers first please and thanks
The first term of a geometric sequence is 3, and the common ratio is 4. What is the 5th term of the sequence?
a) 768
b) 3,072
c) 192
d) 81
Answer: I got A. 768 as the answer
What is the mean of the set of data?
6, 7, 10, 12, 12, 13
6
7
10
11
Answer:
10
Step-by-step explanation:
Mean is all the given numbers in the set added together then divided by the total amount of numbers
6+7+10+12+12+13= 60
60÷6=10
Answer:10
Step-by-step explanation: Mean is all the given numbers in the set added together ,then divided by the total amount of numbers
6+7+10+12+12+13= 60
60÷6=10
Example: 1, 6, 2, 3
Proportion is 1:2=3:6
25) 3, 6, 7, 14
Proportion is _________________
26) 2, 6, 5, 15
Proportion is _________________
27) 7, 2, 14, 4
Proportion is _________________
28) 2, 2, 1, 4
Proportion is _________________
29) 10, 5, 8, 4
Proportion is _________________
30) 3, 12, 8, 2
Proportion is _________________
25) proportion is 3:6=7:14
26) proportion is 2:6=5:15
27) proportion is 2:4=7:14
28) proportion is 1:2=2:4
29) proportion is 4:8=5:10
30) proportion is 2:8=3:12
26% of animals at the animals shelter are dogs. About what fraction of animals at the shelter are dogs
Answer:
The answer is 26/100
Can someone pls help me with this
there is 1 solution of the equation represented on the graph because the line only cuts the graph at one point
Answer:
none
Step-by-step explanation:
The solutions to an equation given graphically are the points where the graph crosses the x- axis.
This graph has no points of intersection with the x- axis and therefore no solutions are shown.
The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
Answer:
44, 46
Step-by-step explanation:
The integers are both even, so if the smaller one is x, then the larger one is x+2.
Therefore:
((x) + (x+2))² = 4048 + (x)² + (x+2)²
(2x + 2)² = 4048 + x² + x² + 4x + 4
4x² + 8x + 4 = 2x² + 4x + 4052
2x² + 4x - 4048 = 0
x² + 2x - 2024 = 0
(x + 46) (x - 44) = 0
x = -4+, 44
Since x must be positive, x = 44. And x+2 = 46. So the numbers are 44 and 46.
Let's check:
(44 + 46)² = 8100
4048 + 44² + 46² = 8100
Weights of Andrews cats are 8 pounds, 15 pounds, 18 pounds, 15 pounds, and 12 pounds. Which statements are true about the weights of Andrews cats? Select the four that apply.
A. The mean is 13.6 pounds
B. The median is 16 pounds
C. The range is 10 pounds
D. The mode is 15 pounds
E. The mean is greater than the median
F. The median and the mode are the same
Answer:
a,b,d,f
Step-by-step explanation:
The body of a soda can (in between the lid and the bottom) is a cylinder. If the body is about 4.5 inches tall with a diameter of about 2.6 inches, what is the volume of soda the body of the can is able to hold?
Answer: V=7.605π
Step-by-step explanation:
The cylinder formula is V=πr^2h
Substitute the values into the equation.
V=π(1.3)^2(4.5)
V=π(1.69)(4.5)
V=7.605π
Hope this helps!
2. Simplify
(1) 41
5a 2a
(u)
4x-4
*+2x-3
a-5b
2a+b
(iii)
2
5
Answer:
Can you take a pic of the problem if you can't type it out?
Step-by-step explanation:
Answer:
3/10a
Step-by-step explanation:
4/5a - 1/2a
4 × 2a - 1 × 5a/5a × 2a
8a - 5a/10a²
3a/10a²
3/10a
-TheUnknownScientist
which of the following best describes the word postulate
Answer:
Statements that are true with out any given proof
Step-by-step explanation:
There is no information needed for you to get your answer
Answer:
Statements that are true with out any given proof
Step-by-step explanation:
its basicly the def of it
Subtract: (2x3+7x2−4)−(2x2+4x−10)
To subtract the given expressions, first, simplify each expression separately by combining like terms. Then subtract the second expression from the first expression by distributing a negative sign and adding it to the first expression.
Explanation:To subtract the given expressions, (2x^3+7x^2-4) - (2x^2+4x-10), we need to simplify each expression separately and then subtract them. First, combine like terms within each expression. Then, subtract the terms of the second expression from the first expression. This can be done by distributing a negative sign to each term in the second expression and then adding it to the first expression.
So, (2x^3+7x^2-4) - (2x^2+4x-10) = 2x^3+7x^2-4 - 2x^2-4x+10.
Combining like terms, we get 2x^3+(7x^2-2x^2)+(-4-4x)+(10). Simplifying further, we have 2x^3 + 5x^2 - 4x + 6. Therefore, the result of the subtraction is 2x^3 + 5x^2 - 4x + 6.
Learn more about Subtracting expressions here:https://brainly.com/question/17538351
#SPJ2
the length is 4cm, the width is 3cm. find the area
547663
Step-by-step explanation:
Answer:
12 cm²
Step-by-step explanation:
To find the area of a rectangle, you multiply all of its dimensions together, which is length and width. That is A = l * w
Plug in: A = 4 cm * 3 cm
Multiply: A = 12 cm²
Simplify the following expression log(x^4)-log(x^3)
Answer:
log x
Step-by-step explanation:
Using the rule of logarithms
• log [tex]x^{n}[/tex] ⇔ n log x
Hence
log [tex]x^{4}[/tex] - log x³
= 4 log x - 3 log x
=log x
The value of logx⁴ - logx³ will be logx.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
If you want to write 1 in logarithm then it will be log(base).
The first method →
Given,
⇒ logx⁴ - logx³
By log property that loga7 = 7loga
⇒ 4logx - 3 logx
⇒ logx
The second method →
This question can also be solved by another log property that
logm - logn = log(m/n)
Since given,
logx⁴ - logx³ = log(x⁴/x³) = logx
Hence, The value of logx⁴ - logx³ will be logx.
For more about logarithm,
https://brainly.com/question/20785664
#SPJ2
Which of the following points satisfies the inequality 2x - 3y < 1?
(-2, 1)
(, 0)
(2, -1)
I'm not sure about the second point you posted, but I believe the answer is (-2, 1). Here is my work:
Answer:-2,1
Step-by-step explanation:
The intersection of the prism and the plane is a _______
cross section.
Trapezoid
Rectangle
Square
Answer:
Rectangle
Step-by-step explanation:
The cross-section will result in a face, that looks just like the top face, since the cut + face are parallel. And because that face is rectangular, so will the cross-section.
Answer:
Rectangle
Step-by-step explanation:
Given : A prism and a plane
To Find : The intersection of the prism and the plane is a _______ cross section.
Solution:
We are given a rectangular prism
Let length be l , breadth be b and height be h
When the prism is intersected by plane , The height becomes 0 .
Length and breadth will remain same
So, the obtained figure is rectangle
So, Option B is true .
Hence The intersection of the prism and the plane is a rectangle cross section.
Which expression represents the number of ways that a president and vice president can be chosen out of a group of 15 people?
Answer: The answer is 15 * 14
Step-by-step explanation:
You start with 15 people to choose from to select a president, so you have 15. After removing one person 15-1,=14 you have fourteen people to choose from, to select a vice president. This gives you 15*14.
The expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.
What is Permutation?Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
[tex]^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
The number of people that are available for the post of the president is 15, while the number of people that are available for the post of vice-president after the president is selected is 14. Therefore,
Number of ways in which president and vice-president can be selected
= ¹⁵P₂
= 15 × 14
Hence, the expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.
Learn more about Permutation:
https://brainly.com/question/11732255
#SPJ2
The lateral area of a right cylinder which has a base diameter of 12 cm and a height of 8 cm is?
Answer:
[tex]A = 301.59\ cm^2[/tex] or [tex]A=96\pi\ cm^2[/tex]
Step-by-step explanation:
The lateral area of a cylinder is calculated by the following formula
[tex]A = 2\pi r * h.[/tex]
Where r is the radius of the right cylinder and h is the height
In this case we know that the diameter d of the cylinder is
[tex]d=2r\\\\r=\frac{d}{2}\\\\r=\frac{12}{2}\\\\r=6\ cm[/tex]
[tex]h=8\ cm[/tex]
Therefore the lateral area is:
[tex]A = 2\pi*6 * 8.[/tex]
[tex]A = 96\pi[/tex]
[tex]A = 301.59\ cm^2[/tex]
Answer:
The lateral area of a right cylinder = 96π cm²
Step-by-step explanation:
Points to remember
The lateral area of a right cylinder = 2πrh
Where r - Radius of cone and
h - Height of cone
To find the lateral surface area
Here diameter d = 12 cm
then radius r = d/2 = 12/2 = 6 cm
And h = 8 cm
Lateral surface area = 2πrh
= 2 * π *6 * 8 = 96π cm²
Therefore the lateral area of a right cylinder = 96π cm²
You sell an automobile part for $9.98, which includes a $.40 sales tax. The article cost you $8.75.
What percentage markup are you charging (to the nearest tenth)?
Answer:
9.5%
Step-by-step explanation:
Buying price of the part= $ 8.75
Selling price of the part= $ 9.98
sale tax= $0.40
Selling price before sale tax= $9.98-$ 0.40 = $ 9.58
Make-up amount charged= $9.58- $8.75 = $ 0.83
As a percentage= (0.83/ 8.75) ×100
=9.5%
I need help with this question
ANSWER
Option D
EXPLANATION
The given function is
[tex]y = \sqrt{16x - 32} - 3[/tex]
We factor 16 under the radical.
[tex]y = \sqrt{16(x - 2)} - 3[/tex]
[tex]y = \sqrt{16} \times \sqrt{(x - 2)} - 3[/tex]
[tex]y = 4 \sqrt{x - 2} - 3[/tex]
This is the graph of
[tex]y = 4\sqrt{x } [/tex]
translated 2 units right and 3 units down.
The last option is the correct choice.