1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.
2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:
a) Day 1: x
b) Day 2: 2x + 10
c) Day 3: x - 100
d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.
e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.
What is a mathematical expression?A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).
Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.
1) Multiplication:
(20x + 24) ÷ (5x + 6) = 4
Check:
4(5x + 6) = 20x + 24
2) Road Trip Expressions:
Day one driving distance = x miles
Day two driving distance = 2x + 10
Day three driving distance = x - 100
Total distance = x + 2x + 10 + x - 100
= 4x + 10 - 100
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To prevent deer from running across highways, researchers are investigating sound-emitting devices that would frighten deer before they reach the highway. As part of the investigation, the researchers set up 20 devices along a two-mile stretch of road. When a deer approached a device, the device would activate and emit a sound. The researchers recorded whether the deer moved toward the highway (positive response), away from the highway (negative response), or did not move (neutral response).
The researchers kept the loudness of the sound constant at 60 decibels. However, they varied the pitch of the sound. There were 6 treatment levels, all measured in kilohertz (kHz): 0, 0.28, 1, 8, 15, and 28. The order of the treatments was randomly assigned.
(a) The control in the experiment was 0 kHz, or no sound. What information is gained by using the control with no sound that could not be obtained if no control were used?
(b)(i) What is one advantage to keeping the loudness at a constant 60 decibels for all treatments?
(b)(ii) What is one disadvantage to keeping the loudness at a constant 60 decibels for all treatments?
(c) The results of the experiment are shown in the following bar chart.
Based on the results, would you recommend using a sound-emitting device to keep deer from running across highways? Explain your answer.
Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.
(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.
(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness
(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.
Step-by-step explanation:
The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.
Explanation:Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.
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100 PTS
Use the table to determine the appropriate model of the function,
x 0 1 2 3 4
f(x) 3 7 29 87 199
a. linear
b. quadratic
c. cubic
d. exponential
Answer:
The answer is D. An Exponential Function.
Step-by-step explanation:
So the table is setup as;
x : 0 1 2 3 4
f(x): 3 7 29 87 199
If you plot the points on the coordinate plane, the value of x increases, and value of y increases .
It is not linear, because slope between two points is not the same, so you can rule that one out.
It´s not quadratic or cubic, because it is not intercepting the x axis.
So, it can only be D, an exponential function since we ruled out every other option.
I hope this helps :))
Equations of Exponential Functions
Find the missing values for the exponential function represented by the table below.
a. 7.5
5
b. -16.875
25.3125
c. 16.875
25.3125
d. -16.875
-25.3125
Please select the best answer from choices provided
Answer:
C. 16.875
25.3125
Step-by-step explanation:
I calculated it logically
QUESTION 9 of 10: Mutual funds can be:
a) Purchased in any amount
b) Can be focused on a single asset class
c) Invested by sector
d) All the above
Submit
Answer: d) All of the above
Step-by-step explanation:
Pls help I’ll brainlest and add extra points
Answer:
26. D) $252
27. A) -6.7 + 6.8
Step-by-step explanation:
26. 400 * 0.3 = 120
400 - 120 = 280
280 * 0.1 = 28 (because the 10% is additional, cannot add it to the original 30%)
280 - 28 = 252
27. -4.5 + 4.4 = -0.1
- 6.7 + 6.8 = 0.1
-0.1 + 0.1 = 0
Can someone please help me with this algebra
Answer: d
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
6. Which fraction is equal to 30%
Answer:
3/10
Step-by-step explanation:
The product of two factors is 2,400. One of the factors is 30. What is the other factor
Answer:
80
Step-by-step explanation:
2400/30=80.
Answer:
another factor is 80
Step-by-step explanation:
2400 ÷ 30
= 80
for 20 please help TT
Answer:
a
Step-by-step explanation:
y=x+8 y=9x+72 substitution
Find the circumference of a circle with a diameter of 50 centimeters
Answer:
157.08 is the circumference. Hope it helps you
Step-by-step explanation:
A line goes through (-4,-5) and (2,-3). Write an equation that is perpendicular to the line above
9514 1404 393
Answer:
y = -3x
Step-by-step explanation:
The slope formula gives the slope of the segment between the given points.
m = (y2 -y1)/(x2 -x1)
m = (-3 -(-5))/(2 -(-4)) = 2/6 = 1/3
The slope of the perpendicular line is the opposite reciprocal of this, so is ...
m' = -1/(1/3) = -3
A perpendicular line is ...
y = -3x
is 3/8 bigger than 45/100
approximate v46 to the nearest hundredth
Answer:
6.78
Step-by-step explanation:
A sailfish can swim u to 68 miles per hour. At this rate, how far can a sailfish swim in 1/4 hour?
A. 34 mi.
B. 27.2 mi.
C. 17 mi.
D. 10.2 mi.
Answer:
C. 17 miles
Step-by-step explanation:
Divide 68 by 4 since it is a fourth of an hour
Tom's toy box is shown below. The toy box is shaped like a rectangular prism: It has 5 wooden faces and is open on the top.
What is the total surface area of the 5 fades of the toy box that are wooden?
O A 1,100 squares inches
O B 3,009 square inches
O C 900 square inches
O D 255 square inches
Don’t answer if you don’t know, and whoever answers correctly will get Brainliest. :)
Answer:
O C 900 square inches
Pyramid A is a right square pyramid with a height of 133m and a square base with a perimeter of 492m. Pyramid B has a square base with a perimeter of 592m and a height of 247m. Which pyramid has the greater volume and by how many times as great?
9514 1404 393
Answer:
Pyramid B is 2.6888 times the volume of pyramid A
Step-by-step explanation:
The volume is proportional to the height, and to the square of the linear measure of the base.
Then the ratio of volumes will be ...
B/A = (592²·247)/(492²·133) = 86564608/32194512 ≈ 2.6888
Pyramid B has the greater volume by a factor of about 2.6888.
_____
Additional comment
The actual volumes in cubic meters will be 1/48 of the numbers we used in the ratio above.
If you recall that the side length is related to the perimeter by ...
P = 4s ⇒ s = P/4
and the volume is ...
V = 1/3s²h
Then you have ...
V = 1/3(P/4)²h = 1/48·P²h . . . . . . P²h is the number we used above
PLEASE HELP, EXPLAIN HOW YOU GOT YOUR ANSWER AFTER PLEASE .
Answer:
Area = 288 m²
Step-by-step explanation:
The area of the shape given = area of the square + area of the triangle
= (side length)² + ½*base*height
side length = 16 m
base = 16 - 8 = 8 m
height = 8 m
Plug in the values into the equation
Area = 16² + ½(8)(8)
Area = 256 + 32
Area = 288 m²
Letters A, B, D and E represent numbers on the number line. The number line has evenly spaced marks
Question 12 (include your answers for part one and two in the space below)
Part 1. Find the value of |C|
Part 2. Describe where are you would place this value on the number line above and explain why
Answer:
0.5
Step-by-step explanation:
sjsbdir rievrjrvrjrbrhdbdjdbekebejebsjsbsirvrirvrjrrhirvrjrbrjr dry it said it had to be 20 characters long
There are 7 brown cars out of 35 cars. What is the ratio of brown cars to the cars?
Answer:
7:35 (can also be written as 7/35)
Step-by-step explanation:
A music store sells about 50 of a new model of drum per month at a price of $120 each. For each $5 decrease in price, about 4 more drums per month are sold. What prices of the drum will reach over $6500? And write the equation to this inequality?
The prices of the drum that will reach over $6500 are between $3 and $8
And the inequality expression is (50 + 4x) (120 - 5x) > 6500
What prices of the drum will reach over $6500?From the question, we have the following parameters that can be used in our computation:
Number of models = 50
Initial price = $120
Also from the question, we have:
Decrease in price by $5Increase in the number of drums by 4So, we have
Models = 50 + 4x
Price = 120 - 5x
This means that the revenue function is
R(x) = (50 + 4x) * (120 - 5x)
When the price reaches over $6500, we have
(50 + 4x) * (120 - 5x) > 6500
Using a graphing calculator, we have
2.911 <x < 8.5
Approximate
3 ≤ x ≤ 8
Hence, the model reaches $6500 between 3 and 8
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Number that appears the most in a given set of data
A) Mean
B.) Median
C) Mode
D) Range
I'll give brainliestttt
How many pints are needed for 2 3/4 pots of soup?
Answer:
1.38
Step-by-step explanation:
2 cups is one pint so if 3/4 is .38 then you would put it together to get 1.38
Which is not a factor pair of 300
Answer:
Step-by-step explanation:
So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. [Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300.
Tamara uses 8.5 of blue paint and white paint to paint her bedroom walls. Three fourths of this amount is blue paint, and the rest is white paint . How many pints of white paint did she used to paint her bedroom walls
The amount of white paint used by Tamara to paint the bedroom walls is 2.125.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Total amount of paint = 8.5
Three fourths of this amount is blue paint.
Amount of blue paint = (3/4) × 8.5 = 6.375
Rest is white paint.
Amount of white paint = Total paint - Amount of blue paint
= 8.5 - 6.375
= 2.125
Hence the amount of white paint used to paint bedroom walls is 2.125.
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the image point using the translation (x,y) (x + 4, y -1) for the point (3,3) is?
The image of the point (3, 3) after a translation 4 units right and one unit down is (7, 2)
What is transformation?Transformation involves moving an object from its original position to a new position on the coordinate plane. This can be a translation, dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size. Other types of rigid transformation are reflection, and rotation
The translation using the rule (x, y) ⇒ (x + 4, y -1) is a translation 4 units right and 1 unit down.
The image of the point (3, 3) using the rule (x, y) ⇒ (x + 4, y -1) is (7, 2)
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A cylindrical grain bin has a radius of 9 feet and a height of 30 feet. How many cubic feet of grain can the bin hold?
Answer:
7,630.2
Step-by-step explanation:
Cylinder Area = 2 x π x r x (r + h)
2 x π x 9 x (9 + 30) = 7,630.2
Answer:
7,630.2
Step-by-step explanation:
Do you find it easy or challenging to create your own rule to generate a pattern? Explain!
Answer:
yes but only because I don't do it often
which is best represented by the following equation 55x + 75.25 = 680.25
Answer:
11
Step-by-step explanation:
680.25-75.25=605
605÷55=11
Answer:
11
Step-by-step explanation:
Please Help Help Help
EDCB is a rectangle, so:
ED = BC = 12
DC = EB = 29
We know that,
= AB = AE + EB
= 34 = AE + 29
= 34 - 29 = AE
= 5 = AE
Now, in triangle EAD, by pythagonas theoram:
= H² = P² + B²
= H² = 5² + 12²
= H² = 25 + 144
= H = √169
= H = 13
So, AD = 13 cm
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