Answer:
The two triangles may be congruent, but additional information is needed about the third angle in each triangle
Answer:
If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
Step-by-step explanation:
What is the inverse of the following statement? If two triangles are congruent, then their corresponding angles are congruent.
Inverse of a statement means its opposite or negating both the hypothesis and conclusion of a conditional statement.
So, the inverse of the given statement will be :
If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
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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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
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 :)
What is 32% of 82 ?????????????????????????/
Answer: 26.24
32% of 82
0.32 • 82 = 26.24
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]
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.
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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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.
(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]
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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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]
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
Equivalent expression
Answer:
The answer is C. 9^-2
Step-by-step explanation:
Don’t know but not the first one
In the below system, solve for y in the first equation. x − 3y = −6 2x − 7y = 10
Answer:
[tex]y=\frac{1}{3}x+2[/tex]
Step-by-step explanation:
The given system of equation is;
[tex]x-3y=-6...(1)[/tex]
and
[tex]2x-7y=10...(2)[/tex]
To solve for y in the first equation; we add [tex]-x[/tex] to both sides.
[tex]-3y=-6-x[/tex]
We now divide through by -3;
This implies that;
[tex]y=\frac{1}{3}x+2[/tex]
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.
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
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:
The diameter of kitty's bicycle wheel is 24 inches what is the radius of the wheel
Diameter is the distance all the way across a circle (going through the center), and radius is the distance from the center to the edge. This means that the radius is always half of the diameter. If the diameter is 24, the radius is 24/2 = 12 inches.
Answer:
12
Step-by-step explanation:
it would be half of 24 which is half of the wheel
A bag of flour weighs 15 pounds. A shopkeeper has one bag of flour. She sells 1.065 pounds of flour every day. How much flour is left after 8 days?
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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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.
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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Wendy can ride her bike 0.7 miles in 6 minutes how many miles can she ride in 2.5 hours
Wendy can ride 17.5 miles in 2.5 hours
Answer:
17.5 miles
Step-by-step explanation:
[tex]\frac{miles}{min} = \frac{miles}{min} \\\\\\[/tex]
Convert hours to minutes
60 minutes = 1 hour
[tex]2.5*60=150[/tex]
2.5 hours = 150 minutes
[tex]\frac{0.7}{6} = \frac{x}{150} \\\\\\[/tex]
Cross multiply
[tex]0.7*150=6*x\\105=6x\\\frac{105}{6} =x\\17.5=x[/tex]
Identify the graph of the equation. What is the angle of rotation for the equation?
xy=-2.5
Answer:
It is B. hyperbola, 45 degrees.
SteIt is p-by-step explanation:
If we rotate the standard form x^2 - y^2 = 1 through 45 degrees we get xy = 1/2.
xy = -2.5 comes from x^2 - y^2 = -5 being rotated 45 degrees.
Answer:
The correct option is b
Step-by-step explanation:
The given equation is
[tex]xy=-2.5[/tex]
It can be written as
[tex]xy+2.5=0[/tex] .... (1)
The general forms of conic is
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] .... (2)
From (1) and (2), we get
[tex]A=0,B=1,C=0,D=0,E=0,E=2.5[/tex]
[tex]B^2-4AC=1-4(0)(0)=1>0[/tex]
Since the value of B²- 4AC > 0, then it is hyperbola.
The formula form angle of rotation is
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]
[tex]\tan 2\theta=\frac{1}{0-0}[/tex]
[tex]\tan 2\theta=\infty[/tex]
[tex]\tan 2\theta=\tan (90^{\circ})[/tex]
[tex]2\theta=90^{\circ}[/tex]
[tex]\theta=45^{\circ}[/tex]
The angle of rotation is 45°. Therefore the correct option is b.
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: 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
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
The sum of two numbers is 60. One number is four times as larger as the other. What are the numbers
The sum of two numbers is 60
The answer is
40 and 20
HELP URGENT 20 PTS!!!! Describe how to sketch a normal curve with a mean of 50 and a standard deviation of 2. Indicate how you would label the horizontal axis at 1, 2, and 3 standard deviations from the mean
Answer:
Step-by-step explanation:
Draw a generic normal curve. Subdivide the x-axis on each side of the center (mean) into four approx. = parts.
Label the mean with '50.'
1 std. dev. below the mean would be 50-2 = 48;
2 std. dev. would be 48-2= 46, and
3 std dev. would be 46 - 2 = 44
Do the same on the other side of the mean.
The 3 corresponding values will be 52, 54 and 56.
IF QR IS TANGENT TO O, FIND X.
[tex] \tan(60°) = \frac{x}{OR} \\ \Leftrightarrow x = OR \tan(60°) = OP \sqrt{3} = 12 \sqrt{3} [/tex]