[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(12)\implies \log_5(4\cdot 3)\implies \log_5(2^2\cdot 3) \\\\\\ \log_5(2^2)~~ + ~~\log_5(3)\implies 2\log_5(2)~~ + ~~\log_5(3)[/tex]
The sum of two consecutive odd numbers is 28. Find their product
We will see that the first odd number is 13 and the second odd number is 15, the product is:
P = 13*15 = 195
How to find the two consecutive odd numbers?
Let's say that the first number is x, the next odd number will be x + 2.
The sum of these two odd numbers must be 2, then we need to solve the linear equation:
x + (x + 2) = 28
We can solve that for x:
2x + 2 = 28
2x = 28 - 2 = 26
x = 26/2 = 13
Then the first number is x = 13 and the second number is x + 2 = 13 + 2 = 15.
The product of these two numbers is:
13*15 = 195
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35 Points Mark Brainliest Help
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's write the equation of line in slope point form ~
[tex]\qquad \sf \dashrightarrow \:y - y1 = m(x - x1)[/tex]
[tex]\qquad \sf \dashrightarrow \:y -2 = 3(x -1)[/tex]
[tex]\qquad \sf \dashrightarrow \:y -2 = 3x - 3[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 3x -1[/tex]
Now, let's use this equation of line to plot two points ~
when x = 0, y = (3 × 0) - 1 = - 1 when x = -1, y = (3 × -1) -1 = -4Now, plot these points on graph ~
(0 , -1) and (-1, -4)What is the slope of the line that passes through (9,3) and (2,1)
Answer:
2/7
Step-by-step explanation:
[tex]slope = \frac{1 - 3}{2 - 9} \\ = \frac{ - 2}{ - 7} \\ = \frac{2}{7} [/tex]
I can buy a box of cereal for $3.50 that comes with 35 half-cup servings.
order 130 inches, 4 yards, 10 feet from greatest to least
Answer:
Step-by-step explanation:
Before comparison can take place, these three measurements must be expressed in the same unit of measurement:
130 inches becomes 130/12 feet, or 10.83 ft;
4 yards becomes 4*3 feet, or 12 feet; qne
10 feet stays as is.
It becomes obvious that the greatest measurement is 12 feet, followed by 10.83 feet, followed by 10 feet.
The ordered list from greatest to least is 4 yards, 130 inches, 10 feet.
What is Unit of Measurement ?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
First, we need to convert all the units to a common unit before we can compare them.
Let's convert them all to inches:
4 yards = 12 feet × 4 = 48 feet = 48× 12 inches = 576 inches
10 feet = 10 × 12 inches = 120 inches
Now we have: 130 inches, 576 inches, 120 inches
Ordering from greatest to least, we get:
576 inches, 130 inches, 120 inches
4 yards, 130 inches, 10 feet
Therefore, the ordered list from greatest to least is 4 yards, 130 inches, 10 feet.
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Please help guys love you
Answer:
1. SSS
2. SAS
3. ASA
4. ASA
Step-by-step explanation:
1. All three sides are equal.
2. Two sides are equal and the angle between the two sides is equal.
3. Two angles are the same and a corresponding angle is the same.
4. Two angles are the same and a corresponding angle is the same.
The nth term of a different arithmetic sequence is 3n + 5
(b) Is 108 a term of this sequence? Show how you get your answer.
Answer:
No 108 is not a term of this sequence.
Step-by-step explanation:
3n+5 = 108
3n = 108 - 5
3n = 103
Divide both side with 3.
n = 103/3
n = 34.33
since n is not equal to 108 there it is not
Answer:
see below
Step-by-step explanation:
We can determine if 108 is a solution by setting 3n+5 =108
3n+5= 108
Subtract 5 from each side
3n+5-5=108-5
3n = 103
Divide by 3
3n/3 = 103/3
n = 103/3
This is not an integer so 108 is not a solutions
sabir makes a chart to track the total calories he burns on the treadmill Flow
the chart below to show how many calories Sabir will have burned after following
his morning treadmill workout for seven days.
25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625
Calories Burned This Week
To know how many calories has Sabir burned in his workout, first identify the calories he burnt every day, and then add them.
How to know the total of calories Sabir has burned?The total of calories burnt is equal to adding the calories burnt everyday:
Total = day one calories + day two calories + day three calories, etc.Due to this, the steps recommended are:
Identify the number of calories he burned everyday.Add these results to obtain the total.Here is a hypothetical example:
Day 1: 250 calorieDay 2: 420 caloriesDay 3: 560 caloriesDay 4: 210 caloriesDay 5: 340 caloriesDay 6: 510 caloriesDay 7: 120 calories250+420+560+210+340+510+120 = 2410 calories.
Note: This question is incomplete because the chart is not given; due to this, the answer is based on general knowledge.
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Find the lateral area and surface area of a cone with an altitude of 5 feet and a slant height of 9 and 1/2 feet. Round to the nearest tenth, if necessary.
Check the picture below.
we know the LA is 9 and 1/2 or namely 19/2 and the height is 5, so
[tex]\stackrel{slant~height}{\cfrac{19}{2}}~~ = ~~\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies \left( \cfrac{19}{2} \right)^2~~ = ~~r^2+5^2\implies \cfrac{361}{4}~~ = ~~r^2+25 \\\\\\ \cfrac{361}{4} - 25~~ = ~~r^2\implies \cfrac{261}{4}=r^2\implies \sqrt{\cfrac{261}{4}}=r\implies \boxed{\cfrac{3\sqrt{29}}{2}=r} \\\\[-0.35em] ~\dotfill\\\\ LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies LA=\pi \left( \cfrac{3\sqrt{29}}{2} \right)\cfrac{19}{2}\implies \boxed{LA=\cfrac{57\pi \sqrt{29}}{4}}[/tex]
[tex]~\dotfill\\\\ SA=\pi r\sqrt{r^2+h^2}~~ + ~~\pi r^2\implies SA=LA~~ + ~~\pi r^2 \\\\\\ SA=\cfrac{57\pi \sqrt{29}}{4}~~ + ~~\cfrac{3\pi \sqrt{29}}{2}\implies \boxed{SA=\cfrac{63\pi \sqrt{29}}{4}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill LA\approx 241.1\qquad SA\approx 266.5~\hfill[/tex]
A gas tank holds exactly 14 gallons of gas. if the tank is 2/3 empty, how many gallons remain in the tank? (help!)
Answer:
4 and 2/3 is the answer
Step-by-step explanation:
14/3= 4 and 2/3
Solve the following inequality for s. Write your answer in simplest form.
-10 + 5(78 + 8) < - 4s +3 - 8
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - 10 + 5(78 + 8) < - 4s + 3 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10 + 5(86) < - 4s - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10 +430 < - 4s - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: 420 + 5 < - 4s [/tex]
[tex]\qquad \sf \dashrightarrow \: 42 5 < - 4s [/tex]
[tex]\qquad \sf \dashrightarrow \: 42 5 \div 4 < - s [/tex]
[tex]\qquad \sf \dashrightarrow \: 106.25 < - s [/tex]
Inequalities change when it is multiplied by -ve number
[tex]\qquad \sf \dashrightarrow \: - 106.25 > s [/tex]
3
(08.01)
Line M is represented by the following equation: x - y = 8
Which equation completes the system that is satisfied by the solution (18, 10)? (4
points)
1) 2x - y = 26
2) x + y = 18
3) 2x - 2y = 36
04) x - y = -28
Answer:
1) 2x - y = 26.
Step-by-step explanation:
Solution = (18, 10)
2x - y = 26 fits the bill
as 2(18) - 10
= 36 - 10
= 26.
HELPPP WHATS THE AREA
Answer:
Area of the trapezoid is 120
1. If ∠KAT and ∠GIF are supplementary angles then_________. *
A. they are both acute
B. one is acute and the other is obtuse
C. they must both measure 90º
D. no determination can be made
2.If ∠DEF and ∠IPN are congruent, they are_________. *
A. complementary angles
B. right angles
C. supplementary angles
D. no determination can be made
3.If the sides of a triangle measure 3, 4 and 5, then the triangle is__________. *
A. acute
B. right
C. obtuse
D. scalene
4. If two sides of a triangle measure 4 and 14, and an angle measures 34º, then the triangle is_________. *
1 point
A. acute
B. right
C. obtuse
D. it cannot be determined
Answer:
1. B. one is acute and the other is obtuse
2. D. no determination can be made
3. B. right
4. D. it cannot be determined
Step-by-step explanation:
1. If ∠KAT and ∠GIF are supplementary angles then one is acute and the other is obtuse
example : m∠KAT = 70° and m∠GIF = 110°
2.If ∠DEF and ∠IPN are congruent, they are no determination can be made
counter-example:
m∠DEF = 50° and m∠IPN = 50°
3.If the sides of a triangle measure 3, 4 and 5, then the triangle is right
because : 5² = 3² + 4²
4. If two sides of a triangle measure 4 and 14, and an angle measures 34º, then the triangle is it cannot be determined
The heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and have a standard deviation of 0.55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9.5 cm?
0.0612
0.6351
0.9388
approximately 1
Using the normal distribution and the central limit theorem, it is found that the probability that the mean plant height is less than 9.5 cm is of 0.9388.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 9.31, \sigma = 0.55[/tex].
For samples of n = 20, the standard error is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.55}{\sqrt{20}}[/tex]
s = 0.123.
The probability that the mean plant height is less than 9.5 cm is the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9.5 - 9.31}{0.123}[/tex]
Z = 1.54.
Z = 1.54 has a p-value of 0.9388.
Hence the probability that the mean plant height is less than 9.5 cm is of 0.9388.
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The perimeter of a rhombus is 84 inches. one
diagonal is 12 inches. find the area of the
rhombus. round your answer to the nearest
hundredth if necessary.
Answer: 241.5 square inches
Step-by-step explanation:
I am 1,000 times as big as a gram what am i
Answer:
One Kilogram
Step-by-step explanation:
1kg = 1000g
Answer:
Kilogram
Step-by-step explanation:
Past experience shows that Mr.Reisman will have 3 left-handed students in ever class of 25 math students. If Mr.Reisman teaches 125 students in one day, what is the most likely total number of left-handed students in his classes?
Answer:
15 students
Step-by-step explanation:
125/25=5
5x3=15
3x^2+18x-27=0
Answer in Quadratic formula
Use the defined sets to answer the questions. assuming 0 is an even integer, which set is the complement to set b? which set is an empty set? which set would contain the subset e = {1, 3, 5, 7}?
The universal set contains all possible elements in the set
The complement of set B is the set D.The empty set is the set CThe set D contains the subset E = {1, 3, 5, 7}The complement of set BThe sets are given as:
A = {x | x ∈ U and x > 3} B = {x | x ∈ U and x is an even integer} C = {x | x ∈ U and 2x is an odd integer} D = {x | x ∈ U and x is an odd integer}Where the universal set is:
U = {all integers}
The set B is the set of all even integers.
So, its complement would be the set of all odd integers i.e. set D
Hence, the complement of set B is the set D.
The empty setFrom the set definition, we have:
C = {x | x ∈ U and 2x is an odd integer}
This means that the set C contains elements 2x, where 2x is an odd number.
The element x is an integer, and twice an integer (i.e. 2x) is an even number.
This means that 2x cannot be an odd number;
Hence, the empty set is the set C;
The set that contains the subset E = {1, 3, 5, 7}The subset E = {1, 3, 5, 7} contains odd integers.
From the set definition, set D represents the set of odd integers
Hence, the set D contains the subset E = {1, 3, 5, 7}
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Answer:
D,C,D
Step-by-step explanation:
On edge 2023
+
Sasha earns $10,50 per hour at
her job. She deposits everything she earns into
her savings account. She currently has $150 in
his savings account. Jack earns $9.00 per hour
at his job. He deposits everything he earns into
his savings account. He currently has
$300 in his savings account.
What month will both Sasha and Jack have the
same amount of money in their account?
Plssssss helpp me
does anybody know the answer to this question?
Answer: 56 yd
Step-by-step explanation: if you continue the 8 yd line across, it would show that the missing side is 4yd less than the 13 yd side, meaning the missing side is 9 yd long. So after adding 7 + 13+ 15+ 4 + 8 + 9= 56 yd
A rectangular prism has a base area of 14 in², and a height of 7 inches. What is the volume of the prism?
Enter your answer in the box.
Given Information :-
⠀
A rectangular prism, with dimensions,
Base area ( l x b ) = 14 in²Height = 7 in.⠀
To Find :-
⠀
The volume of the prism⠀
Formula Used :-
⠀
[tex] \qquad \star \: \underline{ \boxed{ \green{ \sf Volume = l \times b \times h }}} \: \star[/tex]
⠀
Here, we have already been provided with the base area that is the value of the product of length and breadth. Now, we just have to multiply the base area by height.
⠀
Solution :-
⠀
[tex] \sf : \implies Volume =14 \: {in}^{2} \times 7 \: {in}^{} \\ \\ \\ \sf : \implies Volume = \underline{ \boxed{ \frak{ \orange{ {98 \: in}^{3} }}}} \: \star \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the volume of the rectangular prism is 98 m³.
⠀
[tex] \underline { \rule{227pt}{2pt}} \\ \\ [/tex]
Answer:
98
Step-by-step explanation:
14 x 7=98
The first equation in the system models the height in feet, h, of a falling baseball as a function of time, t. the second equation models the height in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t. which statement describes the situation modeled by this system? startlayout enlarged left-brace 1st row h = 35 minus 16 t squared 2nd row h = 6 18 t 16 t squared endlayout the height of the baseball is 18 feet at the moment the player begins to leap. the height of the baseball is 16 feet at the moment the player begins to leap. the height of the baseball is 35 feet at the moment the player begins to leap. the height of the baseball is 6 feet at the moment the player begins to leap.
The height of the baseball is 6 feet at the moment the player begins to leap. Then the correct option is D.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The first equation in the system models the height in feet, h, of a falling baseball as a function of time, t. the second equation models the height in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t.
h(t) = 35 - 16t²
h(t) = 6 + 18t + 16t²
At t = 0, Then we have
h(0) = 35 - 16(0)²
h(0) = 35
And
h(0) = 6 + 18(0) + 16(0)²
h(0) = 6
The height of the baseball is 6 feet at the moment the player begins to leap.
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Answer:
option 2 or B
Step-by-step explanation:
Write an expression equivalent to the expressions 12x+16y using the gcf
pls help
Answer:4(3x+4y)
Step-by-step explanation: the gcf of 12x+16y is 4. we factor out 4 by dividing both terms by 4.
Answer:
[tex]4(3x+4y)[/tex]
Step-by-step explanation:
Hey there!
This would be the correct answer because the GCF of 12 and 16 is 4.
Now that we know that it is 4 we can divide the eqiasion by 4 and then you get
[tex]4(3x+4y)[/tex]
If you need to ckeck if this answer is corret then you will need to use the distributive property to distribute 4 to 3y and 4y.
The equasion would then look like this
[tex](4(3x)) (4(4y))[/tex]
Next you would need to solve the equasion to get the origional equasion
[tex]12x+16y[/tex]
Toilet prices changed drastically during the pandemic! In February, customers were paying 90% of the full price. By April, customers were paying 106%!
Step-by-step explanation:
ok but wheres the question? these are just statements.
What is the measure of angle 1?
90
Step-by-step explanation:
It's a right-angle triangle
Hope this helps!
Suppose 140 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of theâ balance, not all the readings are equal. The results are found to closely approximate a normalâ curve, with mean 82 g and standard deviation 3 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 79 g and 85 g
Using the Empirical Rule, it is found that 95 students reported readings between 79 g and 85 g.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering that the mean is of 82g and the standard deviation is of 3g, readings between 79g and 85g are within one standard deviation of the mean, hence it will compreend 68% of the 140 readings, so the number of students is given by:
0.68 x 140 = 95.
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I need help with this
Answer:
Class 1.
Step-by-step explanation:
Class 1 has the greater interquartile range.
Answer:
Class #2
Step-by-step explanation:
IQR of Class #1:
85 - 72 = 13
IQR of Class #2:
90 - 70 = 20
Class #2 has a greater IQR!
Hope this helps!
helpppppppppppppp this is hardddddddddd
Answer:
#1: 4) D
#2: 1) 34.89 = 3 × C
#3: 4) 6y + 18
Step-by-step explanation:
#1
Using the distributive property:
3 × 5z = 15z
3 × -3 = -9
The correct expression is 15z - 9. Hence, D is the right option.
#2
You need to find the cost of each box.
3 × C = 34.89
34.89 ÷ 3 = 11.63
3 × 11.63 = 34.89
Hence, 1) is the right option.
#3
Using the distributive property:
6 × y = 6y
6 × 3 = 18
The expression is 6y + 18. Hence, 4) is the right option.
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