Option A is correct.
Cathy needs to collect linear data . She should collect the data of option A-The height of a building for 20 years.
Explanation:
Linear data is that data whose slope is always same. Here lets assume, initially the building had 2 floors. Each year 2 floors are added above the previous floors. So our coordinate will be (0,2) (1,4) (2,6) (3,8) and so on.
So slope = [tex]\frac{difference in y}{difference in x}[/tex]
= [tex]\frac{4-2}{1-0} = \frac{2}{1}[/tex]
= [tex]\frac{8-6}{3-2}[/tex] = [tex]\frac{2}{1}[/tex]
So, here slope is 2 for all coordinates.
A toll collector on a highway receives $4 for cars and $9 for buses. At the end of a 2-hour period, she collected $188. How many cars and buses passed through the toll booth during that period? List all possible solutions.
One answer is 2 cars and 20 buses
The toll collector collected $188 in a 2-hour period. There are three possible solutions: 44 cars and 12 buses, 35 cars and 18 buses, or 26 cars and 24 buses.
Explanation:Let's assume the number of cars passing through the toll booth is 'x' and the number of buses is 'y'.
We can form the following equations based on the given information:
4x + 9y = 188 (total amount collected)
2x + 2y = 2 (total number of hours)
Now we can solve these equations simultaneously to find the values of 'x' and 'y'.
Using substitution or elimination method, we can find that 'x = 44' and 'y = 12', or 'x = 35' and 'y = 18', or 'x = 26' and 'y = 24'.
Therefore, there are three possible solutions:
44 cars and 12 buses35 cars and 18 buses26 cars and 24 busesLearn more about Toll booth collections here:https://brainly.com/question/33170235
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A street sign company is making street signs in the shape of equilateral triangles. The side length of each sign is 22 inches. What is the exact altitude length so that the company will be able to know what size box to ship them in?
Answer: 11 sqrt3
Well, since this is an equilateral triangle, you know that all of the sides have the same length: 22 inches. If you want to find the altitude (height), you would have to use the Pythagorean theorem: a^2 + b^2 = c^2
This means that the sum of the two legs squared is equal to the hypotenuse of the triangle squared.
We already know that the hypotenuse is 22 inches, so we can plug that in as c.
We also know that to make the triangle a right triangle, we will need to halve the bottom side, getting 11 inches, which we can plug in as b.
Lastly, we need to know a, so that is our variable to solve (the height). Here is the equation:
a^2 + (11^2) = (22^2)
This is equal to:
a^2 + 121 = 484
Now subtract 121 from both sides to get a^2 on its own:
a^2 = 363
Lastly, take the square root of both sides to solve for a:
a = 11 sqrt3
The altitude of an equilateral triangle with a side length of 22 inches is 11√3 inches.
Explanation:The altitude of an equilateral triangle can be found using the formula altitude = (side length * √3) / 2.
In this case, the side length of the street sign is 22 inches. Plugging this value into the formula, we get:
altitude = (22 * √3) / 2.
Simplifying, we have:
altitude = 11√3 inches.
Therefore, the exact altitude length is 11√3 inches.
how do you write seven thousand and 30 in numbers?
It's writen as 7,030
Which number is equivalent to 5*10+4*1+8*1/10+6*1/100+1*1/1,000
A. 54.861
B. 54.0861
C. 5.4861
D. 0.54861
The equivalent number to the given equation is 54.861, calculated by using the order of operations and understanding of place value.
Explanation:
To solve this problem, you need to understand the concept of place value and order of operations in mathematics. Given the equation 5*10 + 4*1 + 8*1/10 + 6*1/100 + 1*1/1,000, we can begin solving using the order of operations, which is often remembered as PEMDAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Here, we multiply before adding. The solution would look like this:
5*10 = 504*1 = 48*1/10 = 0.86*1/100 = 0.061*1/1,000 = 0.001Adding these results together, you get 50 + 4 + 0.8 + 0.06 + 0.001 = 54.861
So the equivalent number is 54.861, which corresponds to answer choice A.
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Given: △KPS m∠P=105°, m∠S=30° PS=12 Find: PK.
split ∠ P into a ∠45° and a ∠60° with altitude PO. ΔPOK is isosceles and ΔPOS is 30-60-90. PO=6=KO Pk=6√2
Answer:
6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Look at the pic below
Let me know if you have any questions
Also, if it's wrong will do my best to fix it
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One week anil earned $4 per hour. The next week he earned $4.50 per hour. What was the percent increased in his hourly rate?
The percent increase in Anil's hourly wage from $4 to $4.50, find the difference ($0.50), divide it by the original wage ($4), and multiply by 100, resulting in a 12.5% increase.
The student is asking how to calculate the percent increase in Anil's hourly wage from one week to the next. He was earning $4 per hour and then began to earn $4.50 per hour. The percentage increase is found by dividing the change in the quantity (the increase in pay) by the original quantity (the original pay) and then multiplying by 100 to get a percent.
To calculate the percentage increase:
Find the difference in pay: $4.50 - $4 = $0.50.
Divide this difference by the original pay: $0.50 / $4 = 0.125.
Multiply by 100 to get the percentage: 0.125 × 100 = 12.5%.
Therefore, the percent increase in Anil's hourly rate is 12.5%.
(-8 + 35) + |-16 + 4| A. 15 B. 31 C. 39 D. 55
Here is your equation:
[tex](-8+35) + |-16+4|[/tex]
Let's start with the equation in | |. ←These signs are used for absolute value. Absolute value is the distance between a number and 0. Absolute value is ALWAYS positive.
Here is the equation in the | |:
[tex]-16 + 4[/tex]
The negative number is greater than the positive number. That means your answer will be negative. When adding a greater negative number and a positive number, you can just subtract the positive number from the negative number and add the negative(-) sign.
[tex]16-4 = 12[/tex]
Add the (-) sign and it becomes:
[tex]12 \rightarrow -12[/tex]
Remember you have to find the absolute value of it, and absolute value is ALWAYS positive.
[tex]|-12| \rightarrow 12[/tex]
Here is your new equation:
[tex](-8+35)+12[/tex]
In the parentheses, the positive number is greater than the negative number. An easier way to do it is to subtract the negative number from the positive number.
[tex]35-8 = 27[/tex]
Here is your new(and last) equation:
[tex]27+12[/tex]
Add:
[tex]27+12=39[/tex]
The answer choice that matches is C, so that means your answer is C. 39
If you have any questions, feel free to ask in the comments! :)
Which is higher 214.7 or 214.275
easy 214.7 because if it was rounded it would be 214.700 an this is way bigger than 214.275
What is the value of a? a–2=3+6a over/divided by 3
Answer: A= -3
Step 1: Simplify both sides of the equation.
a−2=
3+6a
3
a+−2=2a+1(Distribute)
a−2=2a+1
Step 2: Subtract 2a from both sides.
a−2−2a=2a+1−2a
−a−2=1
Step 3: Add 2 to both sides.
−a−2+2=1+2
−a=3
Step 4: Divide both sides by -1.
−a
−1
=
3
−1
a=−3
How do you write an equation in slope- intercept form of the line passing through the given points ? (0,7), (1,9)
y = 2x + 7
the equation of a line in ' slope-intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the ' gradient formula '
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (1, 9)
m = [tex]\frac{9-7}{1-0}[/tex] = 2
given the point (0, 7 ) then c = 7
y = 2x + 7 ← in slope-intercept form
How can u use a number line to find the sum of -4 and 6
Find -4 on the number line.
Go to the right 6 place values (+6)
You will find your answer
-4 (+6) = 2
2 is your answer
hope this helps
The area of a circle with a diameter of 5cm
Answer:
19.625 cm² is your answer
Step-by-step explanation:
Area of the circle can be solved using the equation: Area = [tex]\pi r^2\\[/tex]
Solve for r (radius). To find radius, use Radius = [tex]\frac{diameter}{2}[/tex]
Solve for radius
[tex]\frac{5}{2} = 2.5\\[/tex]
Plug in 2.5 for radius. Remember that Area = [tex]\pi r^2\\[/tex]
Area = [tex]\pi 2.5^2\\[/tex]
Simplify
Area = [tex]\pi 6.25\\[/tex]
Area = [tex]\((3.14)(6.25)\\[/tex]
Multiply
Area = [tex]\ 19.625\\[/tex]
19.625 cm² is your answer
~Rise Above the Ordinary, Senpai
How to write 0.8 in words
Cell phone company charges $20 per month plus $.50 per text message. Write an equation that shows how your total bill depends on the number of text messages sent
a.which lines have positive slopes?
A
B
C
b. Which line has the steepest slope?
A
B
C
c. do any lines have an undefined slope?
Yes, line A has zero shape
No, a line with undefined slope is vertical and none
of the lines are vertical
No, a line with undefined slope is horizontal and none of the lines are horizontal
A positive slope is represented by an upward tilt, Line A has the steepest slope, and none of the lines have an undefined slope.
Explanation:In this case, line A represents a positive slope because it is a straight line that has an upward tilt or is increasing as we move from left to right. Line B represents a negative slope because it is a straight line that has a downward tilt or is decreasing as we move from left to right. Line C represents zero slope because it is a horizontal line without any tilt or change in y-values as we move along the x-axis.
To determine which line has the steepest slope, we need to look at the lines' tilt more closely. Line A has a steep positive slope as it increases quickly, while Line B has a less steep negative slope as it decreases slowly. Line C has a slope of zero, so it does not have any steepness. Therefore, Line A has the steepest slope.
None of the lines have an undefined slope. An undefined slope occurs when a line is vertical. Since none of the lines are vertical, they all have defined slopes.
Pls Help!!
What is the probability of a sum of 3 or 6 or 9?
If f(x)=2x, then f^-1(x)=
[tex]f(x)=2x\to y=2x\\\\\text{change x and y}\\\\x=2y\\\\\text{solve for y}\\\\2y=x\qquad|:2\\\\y=\dfrac{x}{2}\\\\Answer:\ f^{-1}(x)=\dfrac{x}{2}[/tex]
carlos estimates that he will need to earn at least $700 to take his girlfriend to the prom. carlos works two jobs as show in the table jobs main st. Deli $8 per hour and babysitting $6 per hour. A. write an inequality to represent this situation B. Graph the inequality. C. will he make enough money if he works 50 hours at each job?
Answer:
The required inequality is: [tex]8x+6y\geq 700[/tex]
The required graph is shown in figure 1.
Yes, he make enough money.
Step-by-step explanation:
Consider the provided information.
Part (A)
Carlos estimates that he will need to earn at least $700 to take his girlfriend to the prom.
Let the number of hours worked in Deli is x and the number of hours worked for babysitting is y.
Deli $8 per hour and babysitting $6 per hour. Carlos need to earn at least 700.
For at least use the inequity ≥
The required inequality is: [tex]8x+6y\geq 700[/tex]
Part (B)
Rewrite the inequity as an equation to find the the x and y intercept.
[tex]8x+6y=700[/tex]
Substitute x=0 in the above
[tex]8(0)+6y=700[/tex]
[tex]y=\frac{700}{6}[/tex]
[tex]y= 116.67[/tex]
Substitute y=0 in the above
[tex]8x+6(0)=700[/tex]
[tex]x =\frac{700}{8}[/tex]
[tex]x= 87.5[/tex]
Use the point (0,116.67) and (87.5,0) to draw the graph.
Since the sign of inequality is greater than equal to, so shade the graph above the line. Use solid line as the sign of inequality is ≥.
Thus, the required graph is shown in figure 1.
Part (C)
We need to find he make enough money if he works 50 hours at each job.
Substitute x=50 and y=50 in the inequality.
[tex]8(50)+6(50)\geq 700[/tex]
[tex]400+300\geq 700[/tex]
[tex]700\geq 700[/tex]
Which is true.
Hence, he make enough money.
Complete the pattern
5,10,30,60,180,__
Hi!
If the pattern starts off with 5 going to 10, then that would be multiplying by 2. Then, from 10 to 30 would be multiplying by 3. From 30 to 60 would be 2, and 60 to 180 would be 3. So, the pattern is multiply by 2, then multiply by 3, then by 2, then by 3, and so on. So, if we multiply 180 by 2, we get 360, the answer.
Hope this helps!
270 because you can realize it starts going up by 30 so you had to multiply 3 × 30 to get 90 then add 90 to 180 and get 270
The formula to find the velocity is given by V=d/t. Solve t in terms of V and d
To get d . you would do the opposite to move it to the other side..so you would multiply.. v×d=t
Evan said that the difference between two negative numbers must be negative. Was he right?
Ping's Ice Cream Palace offers a special sundae that contains over 2kilograms of ice cream plus any number of toppings.
Write an inequality that describes S, the weight of the special sundae in kilograms.
The inequality is [tex]\( S > 2 \),[/tex] indicating the special sundae weighs more than 2 kilograms of ice cream.
Sure, here's a detailed stepwise solution with explanation:
1. **Understand the problem**: We're tasked with writing an inequality that describes the weight [tex]\( S \)[/tex] of the special sundae in kilograms. The sundae contains over 2 kilograms of ice cream plus any number of toppings.
2. **Define the variables**: Let [tex]\( S \)[/tex] represent the total weight of the special sundae in kilograms.
3. **Write the inequality**: The problem states that the sundae contains over 2 kilograms of ice cream. Therefore, the weight of the sundae [tex](\( S \))[/tex] must be greater than 2 kilograms. This can be expressed as the inequality:
[tex]\[ S > 2 \][/tex]
4. **Explanation of the inequality**:
- The inequality [tex]\( S > 2 \) indicates that the weight of the special sundae (\( S \))[/tex] is greater than 2 kilograms.
- This inequality ensures that the sundae contains more than 2 kilograms of ice cream, as specified in the problem statement.
5. **Conclusion**: The inequality [tex]\( S > 2 \)[/tex] accurately describes the weight of the special sundae, confirming that it contains over 2 kilograms of ice cream plus any number of toppings.
write the standard form of the equation of the line described. through (3, -2) perp. to y=5x + 4
Since it is perp. to y = 5x +4, the slope would be the negative reciprocal of 5, which is -1/5. In order to find the y-in. you have to plug in the values you already know into y=mx+b.
-2 = -1/5(3) + b
b=-7/5
y = -1/5x -7/5
The equation of the line perpendicular to y = 5x + 4 and passes through the point (3, -2) is y = -1/5x - 7/5.
Explanation:The standard form equation of a line is y = mx + b, where m is the slope and b is the y-intercept. The question provides a line equation y = 5x + 4 and informs that the desired line is perpendicular to it. Two lines are perpendicular if the product of their slopes is -1. Hence, the slope of the perpendicular line will be the negative reciprocal of 5 which is -1/5.
Then to find the y-intercept, we use the point that the line passes through which is (3, -2). Insert these values into the equation:y = mx + b, so -2 = -1/5(3) + b, solve to find b = -7/5.
Therefore, the equation of the line in standard form is y = -1/5x - 7/5.
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Contains (0,1) and (5,2)
The volume of a rectangular prism can be computed using formula v = Iwh what is the height of a prism that has a volume of 2376 cubic cm a length of 18 cm and width of 11 cm
A. 12
B. 16
C. 726
D. 24
Answer:
Answer is A. 12
Step-by-step explanation:
Volume of a rectangular prism = Length * Width * Height
Volume of the rectangular prism = [tex]2376cm^{3}[/tex]
Length of the prism = 18cm
Width of the prism = 11cm
We need to find the Height of the Prism,
For that first make the Height as subject of the equation,
Height = [Volume of the rectangular prism/(Length * Width)]
=[tex]2376cm^{3}[/tex]/(18cm*11cm)
=[tex]2376cm^{3}[/tex]/[tex]198cm^{2}[/tex]
=[tex]12cm[/tex]
Therefore,
Answer is A. 12
please help, due tomorrow i really need help i’m scared
As triangles are similar therefore the ratio of their corresponding sides are equal . In this case
9/c = 7.5/d
Cross multiply
9d =7.5 c
Now arrange
d/c = 7.5/9
d/c = 75/90
d/c = 5/6
The value of d/c is 5/6
In order to find this, we need to simply replace the values of the triangles that match up. The d portion would match up with 7.5 and the c portion would match up with the 9. So, we can put them into the equation and simplify.
d/c = 7.5/9
d/c = 5/6
The product of 9 and the sum of three times a number and 8 is 180. What is the number? A) 4 B) 6 C) 12 D) 18
9(3x + 8) = 180
Distributive property.
27x + 72 = 180
Subtract 72 from both sides.
27x = 108
Divide both sides by 27.
x = 4
The value of x is equal to 4.
some one help me with problems 1,2,3 plz.thank you !
1. Straight lines are 180 degrees. That means 180-126=x. So, x=54.
You can then use x to find y. 180-54=y. y=126. OR You can use vertical angles to find y. Vertical angles are the same degree. So if y is vertical to the angle with 126 degrees, then y=126.
Either way, you will get x=54 and y=126.
2. You would solve problem 2 the same way as problem 1. I encourage you to try to do it yourself, but here's how you would do it.
180-103=y, so y=77. You can either use vertical angles or x=180-77 to find x. You will end up with x=103.
So y=77 and x=103.
3. Here you would use vertical angles. Remember, vertical angles have the same degree! So 2x+29=5x+20. Then all you have to do is solve it.
You would end up with x=3.
I hope that helps!
Elena has 20 apples and 35 crackers for making snack bags she wants to make as many snack bags as possible and wants each bag to have the same combination of apples and crackers what is the largest number of snackbags you can make
I'm pretty sure the answer is 5 because 5 is the greatest common factor. :)
Answer: I'm pretty sure the answer is 5 because 5 is the greatest common factor.
Step-by-step explanation:
500= 100e^(0.04t)
A. t= 25ln(5)
B. t= 25log(5)
C. t= 25ln(400)
D. t= 25log(400)
Answer:
A. [tex]t=25\ln(5)[/tex]
Step-by-step explanation:
We want to solve for t in [tex]500=100e^{0.04t}[/tex]
Divide through by 100
[tex]5=e^{0.04t}[/tex]
Take natural logarithm of both sides
[tex]\ln(5)=\ln(e^{0.04t})[/tex]
This simplifies to: [tex]\ln(5)=0.04t[/tex]
Divide both sides by 0.04
[tex]\frac{\ln(5)}{0.04}=t[/tex]
[tex]t=25\ln(5)[/tex]