The transformed parallelogram P'Q'R'S' is smaller than the original parallelogram PQRS, due to a scale factor of less than 1 (0.75) being applied in this dilation.
Explanation:The given transformation (x, y) → (0.75x, 0.75y), the scale factor is 0.75, indicating a reduction in size. This means that the transformed parallelogram P'Q'R'S' is smaller than the original PQRS. The scale factor of 0.75 signifies that both the x and y coordinates of every point in the original parallelogram are multiplied by 0.75, leading to a proportional reduction in dimensions. Therefore, option B) stating that Parallelogram P'Q'R'S' is smaller than parallelogram PQRS due to the scale factor being less than 1, accurately describes the transformation, illustrating the diminished size of the transformed figure in comparison to the original one.
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The correct answer is B: Parallelogram P'Q'R'S' is smaller than parallelogram PQRS because the dilation scale factor is 0.75, which is less than 1.
The question asks about the effect of a given dilation on a geometric figure, specifically a parallelogram named PQRS, which is transformed into parallelogram P'Q'R'S'.
This transformation is performed using the dilation rule (x, y) → (0.75x, 0.75y), which indicates that every point on the original parallelogram is multiplied by the scale factor of 0.75 when creating the new parallelogram.
Since the scale factor is less than 1, each coordinate is reduced to 75% of its original value, resulting in a figure that is proportionally smaller than the original.
Therefore, the correct statement about the relationship between the original parallelogram PQRS and the dilated parallelogram P'Q'R'S' is Option B: Parallelogram P'Q'R'S' is smaller than parallelogram PQRS, because the scale factor is less than 1.
Lines a and b are perpendicular. The slope of line a is −2. What is the slope of line b?
b= 1/2
perpendicular slopes are those that are opposite signs and reciprocal of the original given slope
Answer:
1/2
Step-by-step explanation:
When two lines whose scopes are m₁ and m₂ are perpendicular, then the product of the scopes of both lines is -1.
Therefore,
If m₁ is the scope of line a and m₂ is the scope of line b then,
m₁m₂ = -1 and m₁ = -2
-2m₂ = -1
m₂ = -1/-2 = 1/2
The slope of line b is 1/2.
Shelly biked 21 miles in 4 hours (part A) what is Shelly's average speed in miles per hour (part B) at the same rate how many hours will it take Shelly to bike 42 miles.
A) Divide total miles by total time:
21 miles / 4 hours = 5.25 miles per hour.
B) Divide miles by miles per hour:
42 miles / 5.25 miles per hour = 8 hours.
a normal distribution with a mean of 15 and standard deviation 0f 5.95% its area is within ?
Answer:
Step-by-step explanation:
B
The normal distribution describes how the values of a variable are distributed. Given a mean of 15 and standard deviation of 5.95, the area within which values lie could be found using the properties of a normal distribution, which state that ~68% of data falls within one standard deviation of the mean, ~95% within two standard deviations, and ~99.7% within three standard deviations.
Explanation:This question is related to the normal distribution in statistics. The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely.
Given a normal distribution with a mean of 15 and a standard deviation of 5.95, we are asked to find the area within which the values lie. Using the properties of a normal distribution, we know that:
Approximately 68% of the data falls within one standard deviation of the mean (mean ± 1*standard deviation). Approximately 95% falls within two standard deviations (mean ± 2*standard deviation). Approximately 99.7% falls within three standard deviations (mean ± 3*standard deviation).
So, if we wanted to find the area within one standard deviation of the mean, for instance, we would calculate the values of (mean - standard deviation) and (mean + standard deviation), which would represent the range within which approximately 68% of the data lies.
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(3Q) Evaluate the logarithm.
Answer:
a. 5/3
that's your answer
ANSWER
[tex]a. \: \frac{5}{3} [/tex]
EXPLANATION
The given logarithm is
[tex] log_{8}(32) [/tex]
Rewrite both the base and the number as a power to base 2.
[tex]log_{8}(32) = log_{ {2}^{3} }( {2}^{5} ) [/tex]
Use the following property:
[tex] log_{ {a}^{q} }( {a}^{p} ) = \frac{p}{q} [/tex]
This implies that,
[tex]log_{8}(32) = log_{ {2}^{3} }( {2}^{5} ) = \frac{5}{3} [/tex]
Which of the following describes a situation in which a soccer player ends up 0 m from his starting point? The player runs 7 meters forward and then runs 7 meters in the opposite direction The player runs 3 meters forward and then runs 7 meters in the opposite direction The player runs 0 meters forward and then runs 7 meters in the opposite direction The player runs 7 meters forward and then runs 0 meters in the opposite direction
Answer:
Seven forward, seven opposite. It's like saying a footballer runs from 0 yd line to 50 yd line then turns around and runs 50 yards again, ends up right back at the 0.
Answer:
a
Step-by-step explanation:
got it right on test
Identify the area of the rhombus. The answer with the red arrow is incorrect!
Answer:
[tex]\large\boxed{A=240\ cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
The formula of an area of a rhombus:
[tex]A+\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonals
We have d₁ = 30 cm.
Use the Pythagorean theorem to calculate d₂ = 2x.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2+225=289[/tex] subtract 225 from both sides
[tex]x^2=64\to x=\sqrt{64}\\\\x=8\ cm[/tex]
d₂ = (2)(8) = 16 cm.
Substitute:
[tex]A=\dfrac{(30)(16)}{2}=(30)(8)=240[/tex]
PLZ HELPPPP
GREATLY APPRECIATED!!
Your answer’s 5! If not, message me, I’ll be happy to help.
The answer is 5! Hope this helps :)
You roll a number cube numbered from 1 to 6. What is the probability that the number is a composite number?
it had a 50 &#>#*(@?'ndhdjeke
Condense the following logs into a single log:
[tex]5log_{b} x - 6log_{b} y[/tex]
Answer:
[tex]logb(X^5 / Y^6)[/tex]
Step-by-step explanation:
Given in the question an expression
5logbX - 6logbY
To Condense the following logs into a single log we will use logarithm rules
1) log power rule5logbX = logbX^5
6logbY = logbY^6
2)log qoutient ruleln(x/y) = ln(x)−ln(y)
logbX^5 - logbY^6 = [tex]logb(X^5 / Y^6)[/tex]
Answer:
[tex]5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})[/tex]
Step-by-step explanation:
The given logarithmic expression is [tex]5\log_b(x)-6\log_b(y)[/tex]
We apply the rule: [tex]n\log_b(M)=\log_b(M^n)[/tex]
This implies that;
[tex]5\log_b(x)-6\log_b(y)=\log_b(x^5)-\log_b(y^6)[/tex]
We now apply the rule; [tex]\log_a(M)-\log_a(N)=\log_a(\frac{M}{N} )[/tex]
[tex]5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})[/tex]
The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Critical Reading 502 Mathematics 515 Writing 494 Assume that the population standard deviation on each part of the test is = 100. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.
Answer:
For the Critical Reading part: P = 0.6578
For the Math part: P = 0.6578
Step-by-step explanation:
See attached photo for solutions
The probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population means of 502 (Critical Reading) and 515 (Mathematics) on the SAT is approximately 68.26% for both.
Explanation:To calculate the probability for each section of the SAT, we use the formula for the z score: z = (X - μ) / (σ / sqrt(n)). In this case, X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
For the Critical Reading section, μ = 502, X is between 492 and 512 (502 ±10), σ = 100, and n = 90. When we input these values into the formula, we get a z value of -1 (for 492) and 1 (for 512) approximately. We then use a z-table to find the probability associated with these z-values. The probability for z = -1 is 0.1587 and for z = 1 is 0.8413. To find the probability that the sample mean lies within these z values, we subtract the lower probability from the higher one, which gives us 0.6826 or 68.26%.
The same steps are applied to the Mathematics section where μ = 515. The resulting probability also comes to around 68.26% that a sample mean test score will be within 10 points of the population mean.
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How do you do this problem?
Answer:
Step-by-step explanation:
Remarks
They want only the exponential equation, here's the point.
You need to be dividing by a number barely over one. You need to reflect the idea that every 500 ft. the % is going to go down by approximately 1.8%. The model for an exponential result is not as good as a linear one (this is really better done a s a linear result, but I will be obedient to what is asked for).You ought to try so values just to see if the equation works.Equation
[tex]\text{Amount the pressure becomes} = \dfrac{101 kpa}{(1+\dfrac{ 1.8}{100} )^\frac{h}{500} }[/tex]
What this gives you is the equation for a rise every 500 feet. To figure out the %
Use
[tex]\text {\% =} \frac{\text{101 - answer from above equation}}{101}*100\%[/tex]
Example
Let h = 1000 feet
101 / (1 + 1.8/100) ^ (1000/500)
101 / (1.018)^2
101 / 1.036324
97.46
Now take this number and use the second formula
% = (101 - 97.46)/101 * 100%
% = 3.54%
The answer should be 3.6% (2 * 1.8%)
This is close enough. The question does say approximately.
1500 feet will give you 5.2% which is close to 5.4 (1.8 * 3). The higher you go, the more it is going to be out, but the results will always be close.
Mars inc. says that until very recently yellow candies made up 20% of it's milk chocolate m&m's, red another 20%, and orange, blue, and green 10% each. the rest are brown. on his way home from work the day he was writing these exercises, one of the authors bought a bag of plain m&m's. he got 29 yellow ones, 23 red, 12 orange, 14 blue, 8 green, and 20 brown. is this sample consistent with the company's stated proportions? test an appropriate hypothesis and state your conclusion.
No.The company ratio is yellow:red:(orange+blue+green):brown as 2:2:1:5 while the packet's ratio is 29:23:34:20
Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 74% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.) yr
Answer: 2500 years
Step-by-step explanation:
I'm not quite sure if I'm doing this right myself but I'll give it a shot.
We use this formula to find half-life but we can just plug in the numbers we know to find t.
[tex]A(t)=A_{0}(1/2)^t^/^h[/tex]
We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For [tex]A_{0[/tex] let's just assume that there are 100 original atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. h is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.
[tex]74=100(1/2)^t^/^5^7^3^0[/tex]
Now, solve. First, divide by 100.
[tex]0.74=(0.5)^t^/^5^7^3^0[/tex]
Take the log of everything
[tex]log(0.74)=\frac{t}{5730} log(0.5)[/tex]
Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the t and get
[tex]5730\frac{log(0.74)}{log(0.5)} =t[/tex]
Use your calculator to solve that giant mess for t and you'll get that t is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.
Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.
PLEASE HELP! I WILL MARK AS BRAINLIEST!! I REALLY NEED SOMEONES HELP!
Error analysis: describe the error in the way the difference of the two polynormials is set up and/or solved. Please be specific.
(6x^2 - 5x) - (2x^2 + 3x - 2)
= 6x^2 - 5x - 2x^2 + 3x - 2
= 4x^2 - 2x - 2
Solve the problem in the question above correctly. Please show your work!
Since this is subtraction, everything must be turned negative in the second polynomial.
(6x^2 - 5x) - (2x^2 + 3x - 2)
6x^2 - 5x - 2x^2 - 3x - (-2)
6x^2 - 5x - 2x^2 - 3x + 2
Now, reorder the terms to make it easier.
6x^2 - 2x^2 - 5x - 3x + 2
Now, just combine like terms.
4x^2 - 5x - 3x + 2
4x^2 - 8x + 2
There’s the answer!
Please consider marking this answer as Brainliest to help me advance.
In a chemistry lab experiment, you use the conical filter funnel shown at the right. How much filter paper do you need to line the funnel?
Answer:
[tex]7,561.12\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a cone is equal to
[tex]LA=\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=80/2=40\ mm[/tex] ----> the radius is half the diameter
[tex]h=45\ mm[/tex]
To find the slant height apply the Pythagoras theorem
[tex]l^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]l^{2}=40^{2}+45^{2}[/tex]
[tex]l^{2}=3,625[/tex]
[tex]l=60.2\ mm[/tex]
Find the lateral area
assume [tex]\pi=3.14[/tex]
[tex]LA=(3.14)(40)(60.2)=7,561.12\ mm^{2}[/tex]
The average annual costs for owning two different refrigerators for x years is given by the two functions: f(x) = 850 + 62x /x and g(x) = 1004 + 51x /xIn the long run, the cost of the refrigerator modeled by will be the cheapest, averaging $ per year.
Answer:
part 1: After one year, the cost of the refrigerator modeled by f(x) is cheaper.
part 2: 14 years
part 3: g(x)
part 4: 51
hope this helps :)
To find the cheapest refrigerator in the long run, calculate the limit of the cost per year as x approaches infinity for both given functions and compare the results. The cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.
Explanation:The average annual costs for owning two different refrigerators for x years can be calculated using the given functions: f(x) = 850 + (62x / x) and g(x) = 1004 + (51x / x). To determine which refrigerator will be cheaper in the long run, we need to find the limit of the cost per year as x approaches infinity for both functions. Taking the limit as x approaches infinity for f(x), we get 62. Therefore, the cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.
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Given: 2x + 11 = 15 Prove: x = 2 Statements Reason 1. 2x + 11 = 15 1. Given 2. 2x = 4 2. 3. X = 2 3. Division Property of Equality
Answer:
Statements Reasons
1. 2x + 11 = 15 1. Given
2. 2x = 4 2. Subtraction Property of Equality
3. X = 2 3. Division Property of Equality
Step-by-step explanation:
An equation can be solved and its solution proven using algebraic theorems and properties. To create a proof, form two columns. Label one side Statements and the other Reasons.
Begin your proof listing the any information given to you. List as the reason - Given.
Then list the next step which here would be to subtract by 11 on both side. The reason is Subtraction Property of Equality. Subtraction is the inverse of addition. Inverse axiom is another acceptable reason.
Then divide both sides by 2. The reason is Division Property of Equality or Inverse axiom once again. See the proof below.
Statements Reasons
1. 2x + 11 = 15 1. Given
2. 2x = 4 2. Subtraction Property of Equality
3. X = 2 3. Division Property of Equality
An office manager needs to decide between two tables for the conference room. One is rectangular, 5 feet wide by 10 feet long. The other is a circle with an 8-foot diameter. Which table can seat more people? Explain your answer be sure to support your answer using facts about the tables.
Answer:
The rectangular 5 x 10 table.
Step-by-step explanation:
To find which table the office manager needs to get so he can sit more people at it is decided by one factor, the perimeter. The rectangular one, which is 5 x 10 the perimeter is (5 x 2) + (10 x 2) = 10 + 20 = 30. The circular one can be calculated by the equation[tex]\pi * d[/tex] where d = 8. Putting [tex]/pi[/tex] x 8 in my calculator and it comes out approximately at 25.132, having a less amount of perimeter space to work with, making the rectangular table the way to go.
The rectangular and circular tables offer roughly the same area, approximately 50 square feet. However, due to space utilization, traditionally, rectangular tables can seat more people as it allows seating around the sides and ends instead of wasting some space at the edges, a common issue with circular tables.
Explanation:Determining which table can seat more depends on how much space each person needs. However, as a basic comparison, we can calculate the area of each table as a starting point.
The rectangular table is 5 feet wide and 10 feet long. Therefore, its area is 5 * 10 = 50 square feet.
For the circular table, we can use the formula for the area of a circle, which is pi * r^2, where r is the radius. The radius is half the diameter, so it is 4 feet here. Thus, the area is about 3.14 * 4^2 = 50.24 square feet.
Both tables have very similar areas. However, people can sit around both the sides and ends of a rectangular table, while some space might be wasted around the edges of the circular one. Therefore, the office manager might find that the rectangular table can seat more people comfortably.
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our football team won 3/4 of the game that you played it was 12 games how many games did it play
Answer:
24
Step-by-step explanation:
Find the area of the rhombus. Check answer please
Answer:
128 m²
Step-by-step explanation:
The area of the rhombus can be calculated using the diagonals
area = [tex]\frac{1}{2}[/tex] diagonal × diagonal
= [tex]\frac{1}{2}[/tex] × 16 × 16 = 8 × 16 = 128 m²
Final answer:
The area of a rhombus can be found using the formula (diagonal1 * diagonal2) / 2.
Explanation:
To find the area of a rhombus, you can use the formula:
Area = (diagonal1 * diagonal2) / 2
Where diagonal1 and diagonal2 are the lengths of the diagonals of the rhombus.
For example, if one diagonal is 8 meters and the other diagonal is 6 meters, the area would be:
Area = (8 * 6) / 2 = 24 square meters
Find a reasonable estimate of the limit
Answer:
The answer is (c) ⇒ the value is 6.6667
Step-by-step explanation:
∵ [tex]\lim_{x\to \2} _2\frac{x^{5}-32}{x^{3}-8}[/tex]
∵ 32 = 2^5 , 8 = 2³
∴ [tex]\lim_{x \to \2}_2 \frac{x^{5}-2^{5}}{x^{3}-2^{3} }[/tex]
* by using the rule:
[tex]\lim_{x\to\a}_a \frac{x^{n}-a^{n}}{x^{m}-a^{m}}=\frac{n}{m}(a)^{n-m}[/tex]
∴ [tex]\frac{5}{3}(2)^{5-3}=\frac{5}{3}(2)^{2}=\frac{20}{3}[/tex]
∴ 20/3 = 6.6667 ⇒ answer (c)
Answer:
The correct option is c.
Step-by-step explanation:
The given limit is
[tex]lim_{x\rightarrow 2}\frac{x^5-32}{x^3-8}[/tex]
It is can be written as
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}[/tex]
According to the property of limits,
[tex]lim_{x\rightarrow a}\frac{x^n-a^n}{x^m-a^m}=\frac{n}{m}(a)^{n-m}[/tex]
In the given limit, a=2, n=5 and m=3. Using the above property of limits we get
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{5-3}[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{2}[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(4)[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{20}{3}[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=6.6667[/tex]
Therefore the correct option is c.
If the length of each leg of an isosceles triangle is 13 and the base is 24 the length of the altitude to the base is
Answer:
The altitude to the base is [tex]5\ units[/tex]
Step-by-step explanation:
we know that
To find the length of the altitude apply the Pythagoras Theorem
Let
h-----> the altitude
[tex]h^{2}=13^{2}-(24/2)^{2}[/tex]
[tex]h^{2}=13^{2}-(12)^{2}[/tex]
[tex]h^{2}=169-144[/tex]
[tex]h^{2}=25[/tex]
[tex]h=5\ units[/tex]
Answer:
The Answer C
Step-by-step explanation:
I just did the test
Issac has 21 marbles and 7 blue marbles he wants to place them in identical group without any marbles left
Answer:
It would be 3 groups because 21/7 = 3
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The less role game uses a number cube with the number 2,4,6,8,10 and 12 there are prices for rolling any number less than 6 how likely is it to role a number less than 6
Answer:
1/3.
Step-by-step explanation:
To roll a number less than 6 it must be 2 or 4 (2 numbers). There are 6 numbers on the cube.
So the probability = 2/6
= 1/3.
Timmy has a box which is 3" wide, 4" long, and 2" high. Paul has a box whose dimensions are three times as wide, long, and high. How much more volume does Paul's contain?
The volume of a rectangular box is calculated by multiplying its dimensions. Timmy's box has a volume of 24 cubic inches. Paul's box, with dimensions three times larger, has a volume of 5832 cubic inches which is 5808 cubic inches more than Timmy's.
Explanation:The volume of a rectangular box is found by multiplying its length, width, and height. In Timmy's case, the volume is 3" * 4" * 2" which equals to 24 cubic inches. Paul's box has dimensions that are three times larger, which means the volume is (3 * 3") * (3 * 4") * (3 * 2") = 27 * 36 *6 = 5832 cubic inches. The difference in volume is 5832 - 24 which equals to 5808 cubic inches, so Paul's box has 5808 cubic inches more volume than Timmy's.
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Alyssa wants to tile a room with an área of 480 square feet.The width of the room is 12 feet.What is the length of the room?
Answer:
40
Step-by-step explanation:
You do 480 divided by 12
To find the length of the room Alyssa wants to tile, given its area is 480 square feet and its width is 12 feet, divide the area by the width. The length is found to be 40 feet.
The question asks to find the length of a room given its area is 480 square feet and its width is 12 feet. To find the length, you use the formula for the area of a rectangle, which is Area = Length × Width. Since we're given the area and the width, we can rearrange the formula to solve for the length by dividing the area by the width.
Therefore, Length = Area / Width = 480 sq ft / 12 ft = 40 feet.
This means that the length of the room Alyssa wants to tile is 40 feet.
In a town’s study of its stray cats, a sample of stray cats had a mean weight of 7.3 lb. The study had a margin of error of 1.1 lb.
What is the interval estimate for the mean weight of the town’s stray cats in the form (lower limit, upper limit)?
Show your work:
Answer:
(6.2, 8.4)
Step-by-step explanation:
Mean weight of the cats = u = 7.3 lb
Margin of Error = E = 1.1 lb
The interval estimate is calculated by subtracting and adding the margin of error to the mean value as shown below:
( u - E, u + E)
Using the given values, we get:
(7.3 - 1.1, 7.3 + 1.1)
(6.2, 8.4)
Thus, the interval estimate for the mean weight of the town’s stray cats is (6.2, 8.4)
Given that the measure of ?x is 60°, and the measure of ?y is 90°, find the measure of ?z
Answer:
The measure of angle z is 30
Step-by-step explanation:
The angles of a triangle all add up to 180. So we can set these measures equal to 180 and solve for the unknown.
60 + 90 + z = 180
150 + z = 180
z = 30
Algebra 2, please help asap
A box contains 4 black shirts, 8 blue shirts, 4 black pants, and 10 blue pants. Determine the probability of randomly selecting a blue piece of clothing or a pair of pants. Use P(A or B) = P(A)+P(B)-P(A and B) to explain your answer
Answer: P(A or B) = 22/26 or 11/13
Step-by-step explanation:All in all there are 26 pieces of clothing available. The probability of randomly selecting a blue piece is equal to 18/26. Also, the probability of picking up a pants is 14/26. There are 10 blue pants and the probability of picking up one of those is 10/26. The answer can be computed as follows:
P(A or B) = (18/26) + (14/26) - (10/26) = 22/26
P(A or B) = 22/26 or 11/13
HELP ASAP PLEASE
A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bill was $53.50. Write and solve an equation to find the price of each shrub.
4p + $17.50 = $53.50; p = $11.25
4(p + $17.50) = $53.50; p = $4.00
4p + $17.50 = $53.50; p = $9.00
4p + 17.5 p = $53.50; p = $2.49
You would need to multiply the quantity of shrubs bought by the price of each one, so 4p and add that to the price of the soil to get the total cost
The equation becomes 4p + 17.50 = 53.50
Now solve for p:
4p +17.50 = 53.50
Subtract 17.50 from both sides:
4p = 36
Divide both sides by 4:
p = 36/4
p = 9
The answer would be: 4p + $17.50 = $53.50; p = $9.00