Answer:
2/4
Step-by-step explanation:
1/4 = 0.25
3/4 = 0.75
0.75 - 25 = 0.50
0.50 is your answer
Evaluate the log without a calculator ( Show your work )
[tex]log_{81} 27[/tex]
Answer:
[tex]\log_{81}(27)=\frac{3}{4}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]\log_{81}(27)[/tex]
Let us change to base 3.
[tex]\log_{81}(27)=\frac{\log_3(27)}{\log_3(81)}[/tex]
[tex]\log_{81}(27)=\frac{\log_3(3^3)}{\log_3(3^4)}[/tex]
[tex]\log_{81}(27)=\frac{3\log_3(3)}{4\log_3(3)}[/tex]
[tex]\log_{81}(27)=\frac{3(1)}{4(1)}[/tex]
[tex]\log_{81}(27)=\frac{3}{4}[/tex]
Answer:
3/4 ( or 0.75).
Step-by-step explanation:
let y = log81 27, then:
27 = 81^y ( by the definition of a logarithm).
27 = 3^3 and 81 = 3^4
So 27 = 81 ^3/4
so y = log81 27 = = 3/4.
Your basketball team scored 4 fewer than twice as many points, x, as the other team. a. Write an expression for the number of points your team scored. expression: b. The other team scored 24 points. How many points did your team score? Your team scored points.
Answer:
A) p = 2x - 4 for the expression. B) Your team scored 44 points.
Step-by-step explanation:
Let P represent the points your team made.
Since the question says "Your basketball team scored 4 fewer than twice as many points as the other team." this is how I came up with the expression.
p = 2x - 4 ( our points = 2 times more then the other teams points minus 4.
Using this expression and the given information that the other team made 24 points, I solved B.
44 = 2(24) - 4.
The expression for given statement can be found by system equation. We can create the system equation as per the statement.
(a) The expression for the number points your team scored is [tex]P=2x-4[/tex].
(b) Your team score 44 points.
Given:
Other team score [tex]x[/tex].
Let the [tex]P[/tex] is points scored by your team.
As per the statement, your basketball team scored 4 fewer than twice as many points, [tex]x[/tex] as the other team.
Convert the above statement in form of expression.
[tex]P=2x-4[/tex]
Thus, the expression for the number points your team scored is [tex]P=2x-4[/tex].
Substitute 24 for [tex]x[/tex] in above expression.
[tex]P=2\times 24-4\\P=44[/tex]
Thus, your team score 44 points.
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PLEASE HELP! Points A and B split the circle into two arcs. Measure of minor arc is 150°. Point M splits major arc with the ratio 2:5 (point M is closer to point B). Find m∠BAM.
Answer:
30 degrees
Step-by-step explanation:
Answer: Measure of ∠BAM is 30°.
Step-by-step explanation:
As given in the question, points A and B split the circle with center O into two arcs in the attached figure below. Major of the minor arc is 150°. And, the point M splits the major arc in the ratio 2 : 5.
We are to find the measure of ∠BAM.
Since the measure of minor arc AB is 150°, so the measure of major arc AB will be
360° - 150° = 210°.
Also, point M divides the major arc AB in the ratio 2 : 5, so we have
[tex]arc~BM:arc~MA=2:5.[/tex]
Therefore, the measure of ∠BOM is given by
[tex]m\angle BOM=\dfrac{2}{2+5}\times210^\circ=\dfrac{2}{7}\times 210^\circ=60^\circ.[/tex]
We know that
the measure of the angle subtended at the center by an arc is equal to twice the measure of the angle subtended at the circumference by the same arc.
That is, on arc BC, we get
[tex]m\angle BOM=2\times m\angleBAM\\\\\Rightarrow m\angle BAM=\dfrac{m\angle BOM}{2}\\\\\\\Rightarrow m\angle BAM=\dfrac{60^\circ}{2}\\\\\Rightarrow m\angle BAM=30^\circ.[/tex]
Thus, the measure of ∠BAM is 30°.
FIND X. ASSUME SG IS TANGENT TO CIRCLE O AT POINT S.
We have a right triangle 9,12,15 which is 3,4,5 scaled.
So OG=15 and OH=9 (the radius) so x = 15-9 = 6
Answer: 6
3 out of five picks are orange . If 12 picks are orange , how many picks are there in all?
20 picks in total .
A croissant shop has plain croissants, cherry croissants, chocolate croissants,almond croissants,apple croissants, and broccoli croissants. How many ways are there to choose a) a dozen croissants? b) three dozen croissants? c) two dozen croissants with at least two of each kind? d) two dozen croissants with no more than two broccoli croissants? e) two dozen croissants with at least five chocolate croissants and at least three almond croissants? f) two dozen croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants,and no more than three broccoli croissants?
Answer:
a) 110,880
b) 8.61x10^37
c) 7.18x10^19
Step-by-step explanation:
To find the amount of options, use the following combination equation.
n!/[r! * (n - r)]
In this equation, n represents the amount of possible options and r represents the amount being chosen at a time. We can now calculate out the answer for each possibility.
a) In this case, n would equal 12 and r would equal 6.
n!/[r! * (n - r)]
12!/[6! * (12 - 6)]
479001600/[720*6]
479001600/4320
110,880
b) In this case, n would equal 36 and r would equal 6
n!/[r! * (n - r)]
36!/[6! * (12 - 6)]
3.72x10^41/[720*6]
3.72x10^41/4320
8.61x10^37
c) For this one, n would equal 24 and r would equal 6. We would also then have to divide the answer at the end by 2.
n!/[r! * (n - r)]
12!/[6! * (12 - 6)]
6.20x10^23/[720*6]
6.20x10^23/4320
1.44x10^20 ÷ 2 = 7.18x10^19
This question deals with calculating combinations of croissants chosen under various conditions, which exemplifies the use of combinations with repetition in mathematics. Solutions depend heavily on the specifics of each part, many of which require customized approaches to account for constraints like minimum selections or caps on certain items.
Explanation:This question involves calculating different combinations of items from a set, which in this context are types of croissants being chosen in various quantities and conditions. Solving these problems requires understanding permutations and combinations, specifically combinations with repetition, as the order in which the croissants are selected does not matter but repeats are allowed.
We utilize the formula for combinations with repetition: C(n+r-1, r), where n is the number of types of items (in this case, croissants) and r is the number of items to choose.
For example, in part a) choosing a dozen croissants from 6 types would involve finding the combination with repetition of these 6 types over 12 selections.
However, specific formulas need to be applied to cater to the unique conditions stated in parts c) through f). Each of these parts imposes different constraints (e.g., minimum numbers of specific items, caps on how many of certain items can be chosen) that complicate the calculation and often require a piecewise approach or the inclusion/exclusion principle to accurately count the number of valid combinations.
Due to the complex and varied nature of each part of this question, and without specific formulas for parts c) through f), a general overview is provided instead of detailed solutions.
Each condition requires a tailored approach that involves breaking down the problem into smaller, manageable parts, and sometimes subtracting the cases that do not meet the given criteria from the total possible combinations.
Mr.Martin drove away from his house without his wallet.He did a 180.Where is he heading now?
Hey there!
He turned 180° degrees so he is going back to his house (to probably get his wallet)
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
if you had to read for 20 hours in total and you read 20 minutes a day how many days would it take you to finish?
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the larger circle (blue).
Answer:
380.13
Step-by-step explanation:
11^2 x pi = 380.13
The perimeter of a rectangle is 24 centimeters.Its length is 9 centimeters.Find the width
length of rectangle =9cm
width of rectangle = b
perimeter of rectangle =24cm
perimeter of rectangle =2(l+b)
24=2(9+b)
9+b=12
b=3cm
Using the perimeter formula for a rectangle, the width of the rectangle is calculated to be 3 centimeters.
To find the width of the rectangle when the perimeter is 24 centimeters and the length is 9 centimeters, we can use the formula for the perimeter of a rectangle: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. From the given information:
P = 24 cm
l = 9 cm
We can set up the equation as follows:
24 = 2(9) + 2w
24 = 18 + 2w
2w = 24 - 18
2w = 6
We then divide both sides by 2 to solve for w:
w = 6 / 2
w = 3 cm
Thus, the width of the rectangle is 3 centimeters.
PLEASE HELP!
1. Given the following graph, would the point (1, 2) be a solution of the inequality? Explain
Answer:
No
Step-by-step explanation:
No because (1,2) falls on the line, and the line is a dotted line, which means that any point on the line is not a solution to the inequality.
A stack of 9 different cards are shuffled and spread out face down. If 4 cards are tired face up, how many different 4-card combinations are possible?
Answer:
126.
Step-by-step explanation:
This is the number of combinations of 4 cards from 9 cards:
= 9C4
= 9! / 4! 5!.
A quick way of calculating this is
9*8*7*6
----------- = 9*2*7 = 126 combinations.
4*3*2*1
There are 126 different 4-card combinations possible when selecting 4 cards from a shuffled stack of 9 different cards.
To find out how many different 4-card combinations are possible from a stack of 9 different cards when 4 cards are turned face up, we need to use combinatorial mathematics. The formula needed here is the combination formula, which for selecting r items from a set of n items is given by C(n, r) = n! / (r!(n-r)!), where '!' denotes factorial.
Substituting the given values, we get C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9×8×7×6) / (4×3×2×1) = 3024 / 24 = 126. So, there are 126 different combinations of 4 cards that can be turned face up from a shuffled stack of 9 different cards.
Please Help!! A septic tank has the shape shown in the figure. How many gallons does it hold? (1 cu ft = 7.48 gallons.) (Round to the nearest gallon)
The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).
Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3
Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3
Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3
The tank holds 641 gallons since the volume of the tank is 85.66 cubic feet. The tank has a cylindrical part and two hemispheres.
What is the volume of the cylinder?The volume of the cylinder is V=Bh or V=2πrh.
Where B is the base area, h is the height of the cylinder and r is the radius.
What is the volume of the hemisphere?The formula for the volume of a hemisphere: V = (2/3)πr³
Where r is the radius of the hemisphere.
Calculating the Volume of the septic tank:The tank has a cylindrical part and two hemispheres.
So, the volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)
Finding the volume of the cylinder:
The height of the cylinder is h=5'9'' and the diameter is 3'6''.
(1 feet = 12 inches)
So, the diameter = 3 feet 6 inches = 3+(6/12) feet = 3.5 feet
Then, the radius r = 3.5/2 = 1.75 feet and
The height h=5 feet 9 inches = 5 + (9/12) feet = 5.75 feet
The volume of the cylinder = 2πrh
= 2π×1.75×5.75
= 63.22 cubic feet
Finding the volume of the hemisphere:
The diameter of the sphere is 3'6'' i.e., 3.5 feet
So, radius r = 1.75 feet
Then the volume of a hemisphere:
V = (2/3)πr³
= (2/3)π×(1.75)³
= 11.22 cubic feet
So,
The volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)
⇒ Volume of the tank = 63.22 + 2×11.22 =85.66 cubic feet.
Since it is given that for 1 cubic ft it holds 7.48 gallons then for 85.66 cubic ft it holds 85.66 × 7.48 = 640.73 gallons
Rounding to the nearest gallon. So, it holds 641 gallons.
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Consider the enlargement of the rectangle. Use the proportion to find the missing dimension bod the original rectangle. (Sorry the pic is horrible)
Here's the right way:
[tex]\dfrac{x}{\frac 3 5} = \dfrac{20}{12}[/tex]
[tex]x = \dfrac{20}{12} \cdot \dfrac{3}{5} = 1[/tex]
Here's the way they want you to do it:
[tex]\dfrac{x}{\frac 3 5} = \dfrac{20}{12}[/tex]
[tex]12 x = 20 \times \dfrac{3}{5} = 12 \textrm{ FIRST BOX}[/tex]
[tex]x = 12/12 = 1 \textrm{ SECOND BOX}[/tex]
Answer: 12×=12
×=1, this the correct answer :3
What is the distance between -1 and 7 on the number line? A) -8 B) -6 C) 6 D) 8
Answer:
D
Step-by-step explanation:
-1 0 1 2 3 4 5 6 7
9 units. distance is always positive.
ans. D
f your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? Why? A. The z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. B. The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score. C. The z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score. D. The z score of 0 is most preferable because it corresponds to a test score equal to the mean. E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
Answer:
E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
Step-by-step explanation:
A z score tells us how many standard deviations away from the mean a given value is.
The higher the z-score, the farther above the mean the value is. Since we are referring to the score on a test, we want the value to be as far above the mean as possible; this means that our best choice out of those given is 2.00, since it is 2 standard deviations above the mean.
I need help! C is highlighted but I don’t know if it’s correct. I give out brainliest
Answer:
Congrats! you are correct, the answer is C.) This is because if you look at the line, it intercects with the points you recieved.
C is correct because the y intercept is 1 and the slope is going down 4 for every next x value
Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -3 x intercepts at x = -4 and x = 4 y intercept at 6
Answer:
[ -9(x^2 - 16)] / [4(x^2 + 5x + 6)] = 0
Step-by-step explanation:
Ok this will be a rational function with denominator (x + 2)(x + 3) - to give the vertical asymptotes.
The numerator will be a(x + 4)(x - 4) to give the x-intercepts . The a is some constant.
As the y intercept is (0,6) we have:
6 = a(0-4)(0+4) / (0+2)(0+3)
6 = -16a / 6
-16a = 36
a = - 36/16 = -9/4.
So our equation is -9(x^2 - 16)/ 4(x^2 + 5x + 6) = 0.
The fishbowl has a diameter of 16 inches which measurement is closest to the volume of water in the fishbowl in cubic inches
Answer:
Volume of sphere = 4/3×22/7×radius×radius
4/3×22/7×8×8=268.19
Therefore the answer is approximately 268 cubic inches.
Hope this answer helps you.
(please help i have 30 min left )
coefficient: A number that multiplies a variable.
Find a coefficient of x in –7x, and a coefficient of y in 9/4 y.
What is the distance between the points (3, 7) and (15, 16) on a coordinate plane?
The answer is 15 units
- Ap3x
Determine all numbers at which the function is continuous
Answer
Please see attached image for full understanding of the solution
If we plot the function we can see that it has a discontinuity at x = 1.
Also,
If we evaluate at x = -9, we see that the values of the piecewise function in both cases are completely different.
Therefore, x = -9 is also a discontinuity.
The right answer is option a
(discontinuity at x = 1 and x = -9)
Answer:
C
Step-by-step explanation: EDGE 2020
Fred went to catch a minimun of 2 pounds of fish.He caught 5/16 pounds.He caught another fish that was 7/8 pounds.How many pounds of fish did he catch so far? What shoud be the minimun weight of the third fish so that he can catch at least 2 pounds of fish in total?
Answer:
1 3/16
Step-by-step explanation:
5/16 + (7/8= 14/16)
14/16 + 5/16= 19/16
16/16 = 1
3 LEFT OVER
1 3/16
Answer:
He caught 1 3/16 pounds of fish.
Minimum weight = 13/16 pounds.
Step-by-step explanation:
So far he caught 5/16 + 7/8
= 5/16 + 14/16 = 19/16
= 1 3/16 pounds.
Minimum wight of the third fish = 2 - 1 3/16
= 32/16 - 19/16
= 13/16 pounds.
A pair of shoes at Nordstrom’s costs $120. The shoes are on sale for 15% off. You have a coupon that allows you take an additional 10% off. How much will the shoes cost?
okay so you multiply .15 by 120 which is 18. then you multiply .10 by 120 which is 12. so you do 120 subtracted by 12 and 18 which the answer is 90
Final answer:
The shoes will cost $91.80 after both discounts have been applied.
Explanation:
To find the cost of the shoes, we need to apply two discounts.
First, we calculate the discount amount of 15% off $120 by multiplying $120 by 0.15, which gives us $18.
Then, we subtract this discount from the original price:
$120 - $18 = $102.
Next, we calculate the additional discount of 10% off $102 by multiplying $102 by 0.10, which gives us $10.20.
We subtract this discount from the discounted price:
$102 - $10.20 = $91.80.
So, the shoes will cost $91.80 after both discounts have been applied.
Which pair of terms can also be used to describe the shape of the sanbox, a square
where are the options??
A group of neighbors is holding an end of summer block party. They buy p packs of hot dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party. Write an equation to describe this situation
Answer:
56 divided by 8 would equal p.
Step-by-step explanation:
If you want to find how many packs there are, it would be 56 divided by 8 would equal p.
Brainiest Please :D
Answer:
The equation is [tex]p*8=56[/tex]
Step-by-step explanation:
The neighbors buy a number of packs (p) of hot dogs and each one has 8 hot dogs. To calculate the number of hot dogs resulting we have to multiply the packs (p) by the number of hot dogs in each pack (8), this is:
[tex]p*8=56[/tex]
Then to calculate p we have to clear it:
[tex]p=\frac{56}{8} =7[/tex]
The number of packs bought were 7.
Which is the distance between parallel lines with the equations 3x-5y=1 and 3x-5y=-3
The distance between the parallel lines 3x - 5y = 1 and 3x - 5y = -3 is 4/√34 units.
Explanation:To find the distance between two parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3, we need to use the formula for distance between two parallel lines in a coordinate plane. This formula is:
Distance = |C2 - C1| / sqrt(A^2 + B^2)
In this case, your A coefficient is 3, the B coefficient is -5, and the constants (C1 and C2) are -1 and 3 respectively (from the given equations). Substituting these values into the formula gives:
Distance = |3 - (-1)| / sqrt(3^2 + (-5)^2)
Distance = 4 / sqrt(9 + 25)
Distance = 4 / sqrt(34)
So, the distance between parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3 is 4/sqrt(34) units.
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Final answer:
The distance between the parallel lines described by the equations 3x-5y=1 and 3x-5y=-3 is calculated using a standard formula for the distance between parallel lines, resulting in a distance of 4 / √34.
Explanation:
The distance between two parallel lines can be calculated using a formula once the equations of the lines are in standard form. The equations 3x-5y=1 and 3x-5y=-3 are indeed in standard form and clearly show that the lines are parallel because they have the same coefficients for x and y. To find the distance between these parallel lines, one can use the formula involving the absolute difference of the constants in the equations and the square root of the sum of squares of the coefficients of x and y.
The formula for the distance d between two parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by:
d = |C2 - C1| / √(A² + B²)
Applying this to our equations, we have:
A = 3, B = -5, C1 = 1, and C2 = -3.
Thus,
d = |-3 - 1| / √(3² + (-5)²) = 4 / √(9 + 25) = 4 / √34
Distance between parallel lines, standard form, and formula are essential in solving this problem.
Six students are working on math 2/3 of them are working on fractions. How many students are working on fractions
Answer:
4 students are working on fractions
Step-by-step explanation:
There are 100 books in the library. There are non-fiction and fiction books.Write the fraction of the books that are fiction
is there anything else that you didn't include in this problem?
Which of the following represents (Picture provided)
Answer:
B.
Step-by-step explanation:
You are given the double inequality
[tex]1<x\le 6.[/tex]
This means that x is greater than 1 and less than or equal to 6.
Thus, point 1 must be excluded (with bracket "(") and 6 must be included (with bracket "]").
Hence, the correct answer is [tex](1,6].[/tex]
Answer:
b. [tex](1,6][/tex]
Step-by-step explanation:
The given inequality is [tex]1\:<\:x\le6[/tex].
We use the parenthesis [tex]()[/tex] to represent an open interval < or >.
We use the square brackets [tex][][/tex] to represent a closed interval [tex]\le[/tex] or [tex]\ge[/tex].
[tex]1\:<\:x\le6[/tex] represents [tex](1,6][/tex].
The correct choice is B.