Answer:
f(3) = (-∛150)/10
Step-by-step explanation:
Put 3 where x is and evaluate. If you don't want the decimal, you can rationalize the denominator to get an exact form.
f(3) = ∛(3/(-7·3+1)) = ∛(-3/20)
= -∛(3·50/(20·50)) = (-∛150)/10 ≈ -0.5313292845913...
_____
Multiplying numerator and denominator by 50 makes the denominator 1000, a perfect cube.
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.
Simplify 13 2
the 2 is tiny so I think it's 13 to the power of 2
Answer: 169
Step-by-step explanation:
You just multiply 13 by 13
When simplifying 13 to the power of 2, you multiply 13 by itself, resulting in 13 x 13, which equals 169. This is known as squaring a number.
The question you've asked involves exponents, which is a way to express repeated multiplication of the same number. When you write 13 with a tiny 2 next to it, you're indicating that 13 should be multiplied by itself once, which is what squaring a number means. In other words, 13 to the power of 2 is 132, which is 13 × 13.
Let's simplify 132:
Multiply 13 by itself: 13 × 13.Calculate the product: 169.So, 132 equals 169. This process is using an integer power, which involves multiplying the base (in this case, 13) by itself as many times as indicated by the exponent (in this case, 2). This can apply to any number, where for example 53 (5 cubed) equals 5 × 5 × 5, which is 125.
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 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
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
(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]
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)
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.
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.
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]
What is 32% of 82 ?????????????????????????/
Answer: 26.24
32% of 82
0.32 • 82 = 26.24
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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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
MARK AS BRAINIEST PLEASE
You roll a die and flip three coins. The number of possible outcomes in the sample space is.
Answer:
48
Step-by-step explanation:
We assume that the die and coins are non-bias.
If you roll a die once, you have 6 possible outcomes (anything from 1-6).
If you flip 3 coins once, you have 2 possible outcomes for each coin (either heads or tails). Multiply those 3 possibilities (2x2x2), you get 8.
Multiply 8 with 6, and you get 48 possible outcomes in sample space.
*In the sample space shown below, do the same combinations to all roll die outcomes to get the whole sample space (i.e., 2TTT, 3TTT, 4TTT etc.).
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]
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?
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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If you were to create a histogram from the data shown in this stem-and-leaf plot, how many data points would be contained in the bar from 95-105?
A) 3
B) 4
C) 5
D) 6
Answer:
the answer is A, 3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Stem Leaf Plot : A special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
So, In the Given Stem leaf plot the numbers are :
100,101,90,93,94,94,95,81,86,87,89,70,72,76,69,56,58,49
Arrange in ascending order
49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101
Now we are supposed to find how many data points would be contained in the bar from 95-105
49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101
So, we can see there are 3 data points are contained in bar from 95 -105.
Hence 3 data points are contained in bar from 95 -105.
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]
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
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.
samantha purchased an automobile for 4,200. her state charged 4% tax for the car, $47 for the license plate, and $35 for the state safety and emission inspection. how much does samantha need to pay for the extra charges , not including the price of the car
The amount that need to be pay is $250.
The calculation is as follows;= 4% of 4,200 + $47 + $35
= $168 + $47 + $35
= $250
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Samantha needs to pay a total of $250 in extra charges, which includes $168 for the state tax, $47 for the license plate, and $35 for the state safety and emission inspection.
Explanation:Calculation of Extra Charges for Automobile PurchaseTo determine how much Samantha needs to pay in extra charges for her automobile purchase, we need to calculate each component separately and then sum them up. Firstly, we calculate the state tax by multiplying the purchase price by the tax percentage:
Tax = Purchase Price × Tax Rate
Tax = $4,200 × 0.04 = $168
Next, we add the fixed costs for the license plate and state safety and emission inspection:
Total Extra Charges = Tax + License Plate Fee + Inspection Fee
Total Extra Charges = $168 + $47 + $35 = $250
Therefore, Samantha needs to pay $250 in extra charges, not including the price of the car.
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
What is the simplest form of the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18
Please show all of your work.
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
we have
[tex]3\sqrt{24} -2\sqrt{54}+2\sqrt{18}[/tex]
we know that
[tex]\sqrt{24}=\sqrt{2^{3}3}=2\sqrt{6}[/tex]
[tex]\sqrt{54}=\sqrt{3^{3}2}=3\sqrt{6}[/tex]
[tex]\sqrt{18}=\sqrt{3^{2}2}=3\sqrt{2}[/tex]
Substitute
[tex]3(2\sqrt{6}) -2(3\sqrt{6})+2(3\sqrt{2})[/tex]
[tex](6\sqrt{6}) -(6\sqrt{6})+(6\sqrt{2})[/tex]
[tex]6\sqrt{2}[/tex]
When simplifying the square roots in the expression 3sqrt(24) - 2sqrt(54) + 2sqrt(18), we find that the simplified solution is 6sqrt(2).
Explanation:To simplify the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18, we first need to break down each square root into its simplest form. In order to do this, we look for perfect-square factors (numbers like 4, 9, 16, 25 that have an integer as a square root) within each number:
3sqrt(24) = 3sqrt(4*6) = 6sqrt(6)
2sqrt(54) = 2sqrt(9*6) = 6sqrt(6)
2sqrt(18) = 2sqrt(9*2) = 6sqrt(2)
Because the sqrt(6) terms are like terms we can combine those, and then include the sqrt(2) term:
6sqrt(6) - 6sqrt(6) + 6sqrt(2) = 6sqrt(2).
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What is the solution set?
❣ [̲̅R̲̅][̲̅e̲̅][̲̅f̲̅][̲̅e̲̅][̲̅r̲̅]
[̲̅T̲̅][̲̅h̲̅][̲̅e̲̅]
[̲̅A̲̅][̲̅t̲̅][̲̅t̲̅][̲̅a̲̅][̲̅c̲̅][̲̅h̲̅][̲̅m̲̅][̲̅e̲̅][̲̅n̲̅][̲̅t̲̅] ❣
❣❣... ℏ✺℘ḙ !т ℏḙℓ℘ṧ ʏ✺ṳ...❣❣
Answer:
The possible solution that is obtained from the system of equation are:
(1,3) and (6,13)
Step-by-step explanation:
We are asked to find the solution set of the given system of equation as:
[tex]y=x^2-5x+7-----------(1)[/tex]
and [tex]y=2x+1--------(2)[/tex]
We know that the solution of the system of equations is the possible set of x and y-values that satisfy both the equations.
Or we may say the point of intersection of the graph that is obtained from both the equations.
We solve the system by substitution method as:
We put the value of y from equation (1) in equation (2) to obtain:
[tex]x^2-5x+7=2x+1[/tex]
which is further written by combining the like terms as:
[tex]x^2-5x-2x+7-1=0\\\\x^2-7x+6=0\\\\x^2-6x-x+6=0\\\\x(x-6)-1(x-6)\\\\(x-1)(x-6)=0[/tex]
Hence, we get the possible values of x as:
x=1 and x=6
Also the value of y when x=1 is:y=2×1+1=2+1 ( Putting the value of x in equation (2))
y=3
when x=6 we have the value of y as:y=2×6+1
y=13
Hence, the possible solutions are:
(1,3) and (6,13)
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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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.
Equivalent expression
Answer:
The answer is C. 9^-2
Step-by-step explanation:
Don’t know but not the first one
In the space below, provide the larger of the two positive integers that add to 10 and have the largest possible product.
Answer:
5
Step-by-step explanation:
The integers 5 and 5 sum to 10 and have the largest possible product.
___
The two numbers will be x and (10-x). Their product is x(10-x), which describes a downward-opening parabola with zeros at x=0 and x=10. The maximum (vertex) of that parabola is halfway between the zeros, at x=5. Both integers have the same value: 5. Their product is 25.
If there is a requirement the integers be distinct, then 6 and 4 are the integers of choice. Their product is 24.
Determine the relationship between the quantities of the given graph.
D
The time worked is directly proportional to the wages. This means as the wages increase, the hours of work increases.