the lines are perpendicular (option B)
Explanation:
For L1 and L2 to be parallel, their slopes must be equal
That is: M1 = M₂
The given slope: M1= 4/7, M₂= -7/4
Hence, they are not parallel as they are not equal
For the lines to be perpendicular, one of the the slope will be the negative reciprocal of the other one:
M1 = 4/7
Reciprocal of M1 = 7/4
Reciprocal means inverse. For
Negative Reciprocal of M1 = -7/4
This is equal to M₂
Hence, the lines are perpendicular (option B)
using pascals triangle, find the 5th power of 25
The image below shows the pascal triangle.
The pascal triangle shows until the fifth power, where a = 25 and b = 0.
[tex]25^5=25^5+5\cdot25^4\cdot0+10\cdot25^3\cdot0^2+10\cdot25^2\cdot0^3+5\cdot25\cdot0^4+0^5=9,765,625[/tex]Hence, the answer is 9,765,625.Convert 0.03 inches to days to grow 3 inches
Answer: 700
Step-by-step explanation:
i am smart
In ADEF below, mZD=3x+5, mZE = 4x-15, and mZF = 2x+10. Which statement is1) DF=FE2) DE = FE3) m
Therefore:
[tex]DF=FE[/tex]I need help breaking it down to understand the answer.
SOLUTION
Each amount in the situation with the expression that represents it will be shown below
Situation Expression
The centimeters of rain on Thursday r
How many more centimeters of rain fell on Saturday 0.15r
than on Thursday
The centimeters of rain on Saturday 1.15r
what is the error and how do I explain it
When we do multiplications of polynomials we have to multiply every term of the first expression with every term of the second expression, then:
[tex]\begin{gathered} (k+4)^2=(k+4)(k+4) \\ =k\cdot k+4k+4k+4\cdot4 \\ =k^2+8k+4^2 \\ =k^2+8k+16 \end{gathered}[/tex]Now, the error in the expression given is that they did not do all the possible multiplications, they only squared the two terms.
Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.Write the explicit equation for f (n) that represents the number of llonfish in the bay after in years. Show all necessary math work.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Lionfish:
growth rate: 65%
time = 1 year
amount (1) = 7000
Step 02:
explicit equation:
f(1) = 7000
n = time
r = 65% = 0.65
f(n) = f(1) * r ^ (n - 1)
f(n) = 7000 * (0.65) ^ (n - 1)
[tex]f(n)\text{ = 7000 }\cdot(0.65)^{(n-1)}[/tex]The answer is:
f(n) = 7000 * (0.65) ^ (n - 1)
Stella is a scientist. She observes and counts 210 bacteria in a culture. Later, Stella counts again and finds the number has increased by 30%. How many bacteria are there now? There are bacteria now.
Answer:
273
Step-by-step explanation:
you just need to find 30% of 210 which is 63
Then you do 210 + 63 which is 273 bacteria
A can of beans has surface area 329 cm². Its height is 14 cm. What is the radius of the circular top?
One option in a roulette game is to bet $20 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) Ifthe ball lands on red, you get to keep the $20 you paid to play the game and youare awarded $20. If the ball lands elsewhere, you are awarded nothing and the $20that you bet is collected. Find the expected payback for this roulette game if you bet $20 on red.The expected payback is $ (Round to the nearest cent as needed.)
In order to calculate the expected value, we need to calculate the sum of products of every possibility (the product of its pr
Type the correct answer in the box. Use numeral instead of words. If nessary, use / for fraction bar. The data set represents the number of cups of coffee sold in a Cafe
Calculate the value of the limit to the indicated values of x then draw the graphf (x) = (x² -1 ) / (x-1,) with x = 1
Given:
The function is,
[tex]\lim _{x\to1}\frac{(x^2-1)}{(x-1)}[/tex]Take the limit as x tends to 1,
[tex]\begin{gathered} \lim _{x\to1}\frac{(x^2-1)}{(x-1)} \\ \text{Applying the limit as x=1 it will give }\frac{0}{0}\text{ form } \\ So,\text{ simplify the function.} \\ \lim _{x\to1}\frac{(x^2-1)}{(x-1)}=\lim _{x\to1}\frac{(x^{}-1)(x+1)}{(x-1)}=\lim _{x\to1}(x+1)=1+1=2 \end{gathered}[/tex]The limit of the function is 2.
The graph of the function is,
A mail order company has a 6% success rate. If it mails advertisements to 538 people, find the probability of getting less than 28 sales. Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places.
Solution
- This is a binomial probability problem because we have multiple trials.
- The formula for calculating the Z-value is:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ where, \\ \mu=\text{ The mean} \\ \sigma=\text{ The standard deviation} \\ X=\text{ The value we are testing} \end{gathered}[/tex]- This value of Z can be used to calculate the probability we need using a Z-score calculator or a Z-distribution table.
- Before we proceed, we need to find the mean and the standard deviation as follows:
[tex]\begin{gathered} \mu=np \\ n=\text{ Number of subjects} \\ p=\text{ The probability of success} \\ \\ \mu=\frac{6}{100}\times538 \\ \\ \mu=32.28 \\ \\ \sigma=\sqrt{np(1-p)} \\ \sigma=\sqrt{538\times\frac{6}{100}(1-\frac{6}{100})} \\ \\ \therefore\sigma=5.5085 \end{gathered}[/tex]- Now that we have both the mean and the standard deviation, we can proceed to find the value of the Z-score as follows:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ \\ Z=\frac{28-32.28}{5.5085} \\ \\ \therefore Z=-0.78\text{ \lparen To 2 decimal places\rparen} \end{gathered}[/tex]- Now that we have the Z-score value, we can proceed to find the corresponding probability for values less than X = 28 sales using a Z-distribution table or a Z-score calculator.
- Using a Z-score calculator, we have:
- Since we are looking for the probability of having sales lower than 28, we have:
[tex]P(X
Follow the instructions below..Write (20)4 without exponents.+(2a)* = 0Х5?Fill in the blanks.(zla)* = 120
Given the indices expression shown below;
[tex](2a)^4[/tex]This can be simplified as:
[tex]\begin{gathered} (2a)^4=2^4a^4 \\ (2a)^4=2^2\times2^2\times a^4 \\ (2a)^4=4\times4\times a^4 \\ (2a)^4=16a^4 \end{gathered}[/tex]This gives the resulting expression on expansion
solve the literal equation for x.v= x• y•zx=
v = x• y•z
v/(y•z) = x• y•z/(y•z) (dividing by (y•z) on both sides of the equation)
v/(y•z) = x (simplifying)
The answer is x=v/(y•z)
10 POINTS
The given table of values represents a linear equation. What is the slope?
x 3 4 5 6
y 1 5 9 13
Responses
2,
3,
5,
4
The slope of the linear equation is 4.
We are given a table which has the values of the "x" column and the corresponding "y" column.The values in the "x" column are 3, 4, 5, and 6.The values in the "y" column are 1, 5, 9, and 13.The values represent the linear equation as given.We need to find the slope of the linear equation.We can form the data into coordinate form.The points are (3, 1), (4, 5), (5, 9), and (6, 13).Let us consider the first (3, 1) and the last point (6, 13) to cover the whole range of the data that is given to us.The slope is given by the ratio of the change in the y-coordinates to the change in the x-coordinates.The slope is Δy/Δx.The slope is (13 - 1)/(6 - 3).The slope is 12/3.The slope is 4.To learn more about equations, visit :
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Find the variance and the standard deviation of the following set,(5,6,7,8,9)
To find the variance, and standard deviation, calculate first for the mean.
[tex]\begin{gathered} \mu=\frac{\sum x_i}{n} \\ \mu=\frac{5+6+7+8+9}{5} \\ \mu=\frac{35}{5} \\ \mu=7 \end{gathered}[/tex]Now that we have the mean, we can now solve for the variance.
[tex]undefined[/tex]3. Which equation correctly shows the relationship between the numbers 4p2,560 and 256?
748,917 has 8 in the thousands place
The value of the digit in the hundreds place in the number 653,841 is 800
Now, out of the options, we want to get a digit that is multiplied by 10 of this
The digit multiplied will be 8,000
So, we want to select a number out of the options which has a value of 8,000 in the thousands place
The correct number here is 748,917
This is because the digit in the thousands place here is 8,000
How many liters each of a 55% acid solution and a 80% acid solution must be used to produce 50 liters of a 60% acid solution? (Round to two decimal places if necessary.)
Given:
Let x denote the number of liter solutions.
[tex]\begin{gathered} \text{acid}+\text{acid}=\text{acid} \\ 55\text{ \%x+80 \%( 50-x)=}60\text{ \%}\times50 \end{gathered}[/tex]Solve the equation for x,
[tex]\begin{gathered} 55\text{ \%x+80 \%( 50-x)=}60\text{ \%}\times50 \\ \frac{55}{100}x+\frac{80}{100}(50-x)=\frac{60}{100}\times50 \\ 0.55x+0.8(50-x)=30 \\ 0.55x+40-0.8x=30 \\ -0.25x=30-40 \\ x=-\frac{10}{-0.25} \\ x=40 \end{gathered}[/tex]It gives,
[tex]\begin{gathered} 40\text{ liters of 55 \% acid will be n}eeded \\ (50-x)=(50-40)=10\text{ liters of 80 \% acid will be n}eeded \end{gathered}[/tex]Answer: 40 liters of a 55% acid solution and 10 liters of 80% acid solution must be used to produce 50 liters of a 60% acid solution
Eliminate factors equivalent to 1 and rewrite the right side of this equation
which which mixture tastes saltier explain how you know. PLEASE HELP ME WITH THIS I'm not good at math sorry
The saltier mixture will have more teaspoons of salt per cups of water.
For mixure B, we have 2.5 cups of water per teaspoons of salt this is 1/2.5 = 0.4 teaspoons of salt per cups of water.
Now, we need to calculate the relation between teaspoons of salt per cups of water for mixture A, so:
[tex]\begin{gathered} \text{We calculate the relation for the thr}ee\text{ rows in the table:} \\ 1)\frac{4}{5}=0.8\text{ teaspoons of salt/cups of water} \\ 2)\frac{7}{8\frac{3}{4}}=0.8\text{ teaspoons of salt/cups of water} \\ 3)\frac{9}{11\frac{1}{4}}=0.8\text{ teaspoons of salt/cups of water} \end{gathered}[/tex]So, mixture A has the greater relation of teaspoons of salt per cups of water, so it's saltier than mixture B.
A map of Levi's property is being made with a scale factor of 2 centimeters: 3 meters. Whats the scale factor
As a result, if 2 centimeters on the map equals 3 meters, you might express that as a fraction and convert it to a standard unit of meters: 0.02 / 3, which you could then multiply by 50 / 50 to get the fraction 1 / 150. The scale factor 1 is 150.
What is Scale Factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.Scale factor = Dimension of the new shape Dimension of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.
To learn more about Scale Factor refer :
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Clara scores 24 points per coin. In all, how many coins does Clara have to collect to score a total of 48 points?
I need help in math two please
a reflection over the y-axis an then a traslation
Corbin begins calculating the volume of a cylinder, in cubic meters, using the following steps. V = Bh V = (113.04) x 20 Which model could represent Corbin's cylinder? 120 m 113.04 m 20 m 36 m A 20 m 6 m 20 m *50.52 m
Given the following expression:
[tex]\begin{gathered} V=Bh \\ \Rightarrow V=(113.04)\cdot(20) \end{gathered}[/tex]Notice that the value of the area of the base is the following:
[tex]B=\pi\cdot r^2=113.04[/tex]with pi = 3.14, we can solve for r to find the radius of the cylinder:
[tex]\begin{gathered} 3.14r^2=113.04 \\ \Rightarrow r^2=\frac{113.04}{3.14}=36 \\ \Rightarrow r=\sqrt[]{36}=6 \\ r=6 \end{gathered}[/tex]therefore, the cylinder has radius 6 and height 20 (the correct model is C)
Find S20 given -4,8,20,32, ... Precalc Series and sequences, will give brainliest.
Solution
Step 1
Given -4, 8, 20, 32....
Common difference
8- (-4)=12
20 -8= 12
32- 20= 12
The common difference (d) is 12
Step 2
We are finding the sum of the first 20th term
[tex]S_{20}=\frac{n}{2}(2a+(n-1)d)[/tex]where n is 20
d is 12
a is -4
[tex]\begin{gathered} S_{20}=\frac{20}{2}(2\times-4\text{ +(20-1)12)} \\ S_{20}=10(-8+(19)12) \\ S_{20\text{ }}=10(-8+228) \\ S_{20}=10(220) \\ S_{20}=2200 \end{gathered}[/tex]solve for y y - 2x = 15
Starting with the equation:
[tex]y-2x=15[/tex]Add 2x to both sides of the equation:
[tex]y-2x+2x=15+2x[/tex]Since -2x+2x=0, then:
[tex]y=15+2x[/tex]Can someone help me asap
Answer:
A) 670
B) 192 and 670
C) 192
Solve quadratic equations by finding square roots (2r-5)^2=81
r
=
7
r
=
−
2
Explanation:
(
2
r
−
5
)
2
=
81
or
2
r
−
5
=
±
√
81
or
2
r
−
5
=
±
9
or
2
r
=
5
±
9
or
r
=
5
±
9
2
or
r
=
5
+
9
2
or
r
=
14
2
or
r
=
7
-------------Ans
1
or
r
=
5
−
9
2
or
r
=
−
4
2
or
r
=
−
2
------------Ans
2
https://socratic.org/answers/295715
Joseph raced his control car 600 feet in 24 seconds. He said the speed of the remote control car was 20 feet per second during the race. Assuming the car raced at a constant speed. A. Joseph is correct the car was traveling 20 feet per second because 600÷24=20 per second B. Joseph is correct the car traveling 20 feet per second because 600÷25=20 feet per second C. Joseph is incorrect the car was traveling 24 feet per second because 600÷25=24 feet per second D. Joseph is incorrect the car was traveling 25 feet per second because 600÷24=25 feet per second
D. Joseph is incorrect the car was traveling 25 feet per second because 600÷24=25 feet per second
Explanations:Distance raced in 24 seconds = 600 Feet
Distance raced in 1 second = 600 / 24
Distance raced in 1 second = 25 feet
Therefore, the speed of the car = 25 feet per second
Joseph said the speed = 20 feet per second
Joseph is incorrect because the car was travelling 25 feet per second
Sole the following problem by using the 4 measurements given
The symbol Σ (called sigma) means "sum up". So, in this case, the expression indicates the sum of the (xᵢ)², where i goes from 1 to 4, which is 1, 2, 3 and 4. Then, we have:
[tex]\sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2[/tex]From the word problem, we know the value of each xᵢ.
[tex]\begin{gathered} x_1=5 \\ x_2=13 \\ x_3=19 \\ x_4=16 \end{gathered}[/tex]Finally, we operate.
[tex]\begin{gathered} \sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=(5)^2+(13)^2+(19)^2+(16)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=25+169+361+256 \\ \sum_{i\mathop{=}1}^4(x_i)^2=811 \end{gathered}[/tex]AnswerThe result of computing the given expression is 811.
