It is Given that f(x) = log₁₀(x) then the value of f(50) is 1.70.
What is logarithmic?Logarithmic functions are defined as the inverses of exponential functions.
Hence, exponential functions can be expressed in logarithmic form
Given that f(x) = log₁₀(x)
we need to find the value of f(50),
we have to substitute x to be 50 in the logarithm function,
f(50) = log₁₀(50)
f(50) = log₁₀(5 x 10)
f(50) = log₁₀(5) + log₁₀(10)
f(50) = 1 + log₁₀(5)
f(50) = 1 + 0.70
f(50) = 1.70
Hence, It is Given that f(x) = log₁₀(x) then the value of f(50) is 1.70.
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Cara is a high school student. On average, there are 26 students per class at her school, with a standard deviation of 3 students. What percentage of classes at Cara's high school will have between 20 students and 35 students?
A. 0.15%
B. 97%
C. 99%
D. 0.3%
Answer:
B. 97%
Step-by-step explanation:
20 students is -2 standard deviations away from the mean
35 is +3 standard deviations away from the mean
100 - 2.4 = 97.6
(2.4 is amount of data we are not using)
please refer to the standard deviation graph attached :)
A triangle with an area of 60 square inches has a height that is 16 less than 6 times its base.
Find the base and height, in inches, of the triangle
Step-by-step explanation:
the area of a triangle
baseline × height / 2
in our case
baseline × height / 2 = 60 in²
height = 6×baseline - 16
baseline × (6×baseline - 16) / 2 = 60
baseline × (3×baseline - 8) = 60
3×baseline² - 8×baseline = 60
baseline = x
3x² - 8x - 60 = 0
general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -8
c = -60
x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =
= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =
= (8 ± 28)/6
x1 = (8 + 28)/6 = 36/6 = 6
x2 = (8 - 28)/6 = -20/6 = -10/3
x2 as a negative number is not a valid solution for a length in a geometric shape.
so, x = 6 in is our solution for the baseline.
height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in
base = 6 in
what is 15/56 in simplest form
Answer:
15/56
Step-by-step explanation:
15 and 56 have a GCF of 1.
What is the lowest common denominator of the following set of fractions:1/6, 13/27, 4/5, 3/10, 2/5?
The lowest common denominator of the set of fractions 1/6, 13/27, 4/5, 3/10, 2/5 is 270.
What is lowest common denominator?The lowest common denominator of LCD is least common multiple of denominators of the fractions.
given fractions:
1/6, 13/27, 4/5, 3/10, 2/5
taking the Prime factorization of denominator of the fractions
6 = 2x3x1
27 = 3x3x3x1
5 = 5x1
10 = 2x5x1
5 = 5x1
Therefore, lcm is 2x3x3x3x5 = 270
so, LCD is 270
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A company provides snack-sized packages of nuts for its office employees.
employees can choose from among five kinds of nuts. which probabilities
correctly complete this probability distribution for 50 packages of nuts, in the
order listed?
nuts
almonds cashews mixed peanuts pecans
12
10
6
14
8
number of
packages
probability
a. probability 0.32 0.24 0.14 0.2 0.1
The probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
How to calculate the probability?From the information given, we have to find the probability for each fruit. This will be:
Almond = 12/50 = 0.24
Cashew = 10/50 = 0.2
Mixed = 6/50 = 0.12
Peanut = 14/50 = 0.28
Pecan = 8/50 = 0.16
Therefore, the probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
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Based on the data collected from 23 flights, what is the probability of at least one O-ring failing, regardless of temperature?
(Note: This probability is called an experimental probability because it’s based on only 23 flights, which is a fairly small number of events. To get a better approximation of the actual probability, we would need data from many more flights. Note also that even though there was O-ring failure on seven flights, all of those shuttles returned safely.)
Using it's concept, it is found that there is a 0.3043 = 30.43% probability of at least one O-ring failing.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, of the 23 flights, 7 had at least one failure, hence the probability is given by:
p = 7/23 = 0.3043.
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in a rectangle rent, or = 2x + 4 and ot = 3x + 1 , then the length rn is
Answer:
3
Step-by-step explanation:
Put both expressions equal to each other.
2x+4=3x+1
Solve:
2x+4=3x+1
4-1=3x-2x
3=1x
x=3
In a track field competition, A discus has a radius of 11 centimeters. What is the circumference, I centimeters, of the discus?
Given the radius of the discus used in the track field competition, the circumference of the discus is 69.08cm.
What is the circumference of the discus?Note that; a circumference is the perimeter of a circle or ellipse.
It is expressed as C = 2πr
Where r is the radius and π is the constant pi ( π = 3.14 )
Given that;
Radius of the discus r = 11cmCircumference C = ?C = 2πr
C = 2 × 3.14 × 11cm
C = 69.08cm
Therefore, given the radius of the discus used in the track field competition, the circumference of the discus is 69.08cm.
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Which of the following can be used to find the sum of the interior angles for
any regular polygon?
A. Multiply the number of sides by 180
B. Add 1 to the number of sides and multiply the sum by 180
OC. Divide the number of sides by 180
D. Subtract 2 from the number of sides and multiply the difference by
180
Write an explicit formula for ay, the nth term of the sequence 39, 33, 27, ....
Answer:
ay = 39 -6(n -1)
Step-by-step explanation:
The explicit formula for an arithmetic sequence can be written by using the first-term value and the common difference in the generic formula.
__
The generic formula for the n-th term of an arithmetic sequence is ...
[tex]a_n=a_1+d(n-1)[/tex]
where a₁ is the first term of the sequence (39), and d is the difference between sequential terms (33-39 = -6).
Using the values for this sequence in the generic formula, we have ...
ay = 39 -6(n -1)
find the surface area of the composite figure. Worth 25 points!!!!
please answer correctly!!!
Solve |5x + 15| = 10x. Identify the solution and an extraneous solution.
A. Solution: x= 3; extraneous solution: x=-3
B. Solution: x= 3; extraneous solution: X=-1
c. Solution: x= 1; extraneous solution: X=-3
D. Solution: ×= -1; extraneous solution: X=3
If 5x + 15 ≥ 0, then |5x + 15| = 5x + 15. The equation reduces to
5x + 15 = 10x
15 = 5x
x = 3
If instead 5x + 15 < 0, then |5x + 15| = -(5x + 15), and the equation becomes
-5x - 15 = 10x
-15 = 15x
x = -1
If x = 3, then |5x + 15| = 30 and 10x = 30, so x = 3 is a valid solution.
If x = -1, then |5x + 15| = 10 while 10x = -10, so x = -1 is the extraneous solution.
The cost to rent an rv is $150 per day plus $0.35 per mile. what is the maximum distance you can drive the rv in a day if your budget is $200?
Answer:
142.86 miles
Step-by-step explanation:
150 + .35m < 200
150 + .35m -150 < 200-150
.35m < 50
.35m/35 < 50/.35
m < 142.86
The maximum distance I can drive the rv in a day if my budget $200 is, approx. 142 miles
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
The cost to rent an rv is $150 per day + $0.35 per mile
The maximum distance in a day = ?
Budget is $200
So,
The maximum distance in a day ≤ 200
The maximum distance in a day = 150 + 0.35x
Now,
⇒ 150 + 0.35x ≤ 200
⇒ 0.35x ≤ 200 - 150
⇒ x ≤ 142.85
Hence, maximum distance in a day is approx. 142 miles
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On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 3, 3), (1, 4), (1, negative 4), (2, negative 4), (2, negative 2).
How many points need to be removed from this graph so that it will be a function?
1 point
2 points
3 points
0 points
Three points must be removed from this graph so that it will be a function
How to determine the number of points?The points are given as:
(-3, 2), (-3, 3), (1, 4), (1, -4), (2, -4), (2, -2).
For a set of point to represent a function;
Each x coordinate must point to only one y coordinate
From the given points, we have the following highlights:
The x value -3 has two y values (2 and 3)The x value 1 has two y values (4 and -4)The x value 2 has two y values (-4 and -2)In the above highlights, one point each must be removed.
This means we have a total of 3 points
Hence, three points must be removed from this graph so that it will be a function
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Answer:
C. 3 points
Step-by-step explanation:
One force of 700 pounds and one force of 490 pounds act on a body at the same point so that the resultant force is 1120 pounds. find the angle between the resultant and the smaller force, to the nearest degree.
Answer:
angle 700 < angle 1120 pounds
What does the phrase "in spite of" refer to?
The phrase "in spite of" refers to a scenario where regardless of what happened, there is always a yearning desire and ability to remain positive.
What is the meaning of the phrase "in spite of"?The meaning of the phrase "in spite of" mean notwithstanding or whatever the circumstances, there is no room for complaining and thinking negatively.
This phrase is used to rejuvenate the positive and optimism of a man's thoughts and desires during dark moments. Hence, "in spite of" what happened, there is always an ability to remain positive.
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It costs $363 to make 90 bags of cotton candy and $440 to make 200 bags of cotton candy.
a) find the cost equation.
Answer:
363=90bags
then you look into it and say
440=200bags
Which set represents the same relation as the graph below?
A coordinate plane has 7 points. The points are (negative 5, 4), (negative 3, negative 2), (negative 1, negative 2), (2, 0), (3, 3), (4, 5), (6, negative 4).
The set that represents the same relation as the graph given is: B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).
What is a Relation?
A relation is defined as a relationship between the input and output, which can be displayed on a graph on a coordinate plane.
From the graph as shown in the image attached below,
The set that has the same coordinate points as indicated on the graph is:
B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).
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PLS HELPPPPP !!!! Figure ABCD is transformed to figure A'B'C'D':
B
A
5-4-3-2-10 1 2
1
-2
C
Which angle in Figure A'B'C'D' is equal to ZBCD?
OZD'A'B'
OZA'B'C'
ZB'C'D'
OZC'D'A'
54
A volcanic eruption ejects about 43,600,000,000 cubic feet of volcanic rock. A smaller volcanic eruption ejects about 75% of this amount. What is the approximate amount of volcanic rock that the smaller volcanic eruption ejects? Write the result as a product of a single digit and a power of 10.
Answer:
3 × 10^10
Step-by-step explanation:
43,600,000,000 × 75% = 0.75 × 43,600,000,000 = 32,700,000,000 =
= 3.27 × 10^10
Answer: 3 × 10^10
What is 8 times the sum of x and 15 as an algebraic expression (written answer)
Answer:
8x+120 is the answer
Step-by-step explanation:
8(x+15)
=8x + 8×15
=8x+120
Caitlin has finished her schooling and training to be a dental hygienist. She has two job offers that she is considering.
Caitlin’s Job Offer Comparison
Job 1: Albuquerque, NM
Job 2: Ann-Arbor, MI
Salary
$54,000
$61,000
Benefits
$2,500 bonuses,
health insurance,
401K
Health insurance,
401K
Average Monthly Rent & Utilities
$925
$1,300
Which job would offer the best annual income considering the cost of living in each locale?
Job 2 is a better choice because the annual income after rent and utilities is $59,700 but that of job 1 is $55,575.
Job 2 is a better choice because the annual income after rent and utilities is $45,400 but the income for job 1 is $41,900.
Job 1 is a better choice because it costs $4,500 less per year to live there.
The jobs have equal annual incomes of $45,400 after rent and utilities so Caitlin should take the job in her favorite locale.
D) Caitlin should take the position in her preferred location because the annual salary is $45,400 after rent and utilities.
What is meant by annual income?To calculate your annual salary, multiply your gross income (before taxes) by the number of pay periods in a year. If an employee earns $1,500 each week, his or her annual income is $1,500 x 52 = $78,000.
Job 1 and Job 2 both generate the same or similar amount of income of $45,400 per year after additional expenses.
This means that Caitilin should choose her career based on the preferences of her neighboring neighborhood so that she can travel easily.
This is because moving to a more distant job location would result in no increase in her income, making it nonsensical to do so.
So, the correct answer is option D.
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Answer: D. edge 2023
The jobs have equal annual incomes of $45,400 after rent and utilities so Caitlin should take the job in her favorite locale.
honestly so confused
Answer:
The first part put 6
second, put 2
third put 1
Step-by-step explanation:
it was just asking for the number, not anything else, so you would just add like terms.
and could u pls put me as the brainliest
1. What is the difference between the altitude rule and the leg rule?
Answer:
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle
The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
need answer asap!!!!!
how would i solve this?
The height of the building to the nearest tenth of a meter is; 13 m
How to make use of Cosine Rule?The slant line from the top of Trevor's head to the base of the building is gotten from Pythagoras theorem;
15/x = sin 36°
x = 15/sin 36
x = 25.52 m
Angle between that slant line and base of building is;
90 - tan⁻¹(1.5/14) = θ
θ = 83.88°
Remaining angle of the bigger triangle is;
180 - (36 + 83.88) = 60.12°
Thus, if the height of the building is h, then;
h/sin 36 = 25.52/sin 60.12
h = 13 m
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*£ HELP PLS !! URGENT!! AFFECT MY GRADE!! *Problem 5.3
Here are three lines that intersect at
one point.
Laila wrote the equation
x + 18 = 90.
Describe the error that Laila might
have made.
Answer:
Laila assumed that the lines that formed the angles x and 18° added up to 90. This is in fact false because of the lack of the square marking to signify it as a right or 90 degree angle.
What are the first three terms of a geometric sequence in which (picture below) and the common ratio is 5?
Answer:
5, 10, 15
Step-by-step explanation:
the increase in the sequence is 5 so since it starts from 0 which you can find out because 25 is the 5th sequence and that means that +2*5 =25 . x=0
0+ 5 = sequence 1
0+ 5+5 = seq 2
0+5+5+5= seq 3
p and q are rational numbers which of the following expression cannot be used to find the distance between them on the number line
The expression that cannot be used to find the distance between them on the number line is |p + q|.
How to depict the infomation?p and q are rational numbers. Which of the following expressions cannot be used to find the distance between them on the number line.
A. |p - q|
B. |p + q|
C. |q + (-p)|
D. |q - p|
Rational number is a number that can be represented as the quotient p/q of two integers such that q ≠ 0.
Here, the expression that cannot be used to find the distance between them on the number line is |p + q|.
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In the diagram below, OO is circumscribed about quadrilateral ABCD. What is
the value of x?
B
A
93
O
x+30°
D
OA. 57
OB. 117
OC. 123
OD. 63
Answer:
Ans = A: 57
Step-by-step explanation:
Because
sum of the angke of opposite side of quardilateral triangle is 180°
x°+30°+93°=180°
x°+123°=180°
x°=180°-123°
x°=57°
Hence proved.
The value of x is option A. 57.
What is Cyclic Quadrilateral?A cyclic quadrilateral is a polygon with four sides where all of it's four vertices lie on a circle.
The circle thus formed is called circumcircle or circumscribed circle.
We have a property for the cyclic quadrilateral that the opposite angles formed on the quadrilateral is supplementary.
That is, sum of the opposite angles is 180°.
Here B and D are opposite angles.
So,
∠B + ∠D = 180
9x + x + 30 = 180
Solving,
x = 57
Hence the value of x is 57.
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Below are statements that can be used to prove that the triangles are similar.
1.
AB=BC
ZY
YX
Z
2. ZB and LY are right
angles.
3.7
345x
-5-3-2-1₁.
0
4.?
B
Which two statements are missing in steps 3 and 4?
OLX =
AABC-AZYX by the SAS similarity theorem.
O
5
4+
3+
2+
271
in bo & mp
-3-
U
3) [tex]\angle B \cong \angle Y[/tex]
4) [tex]\triangle ABC \sim \triangle ZYX[/tex] by the SAS similarity theorem
ΔABC is similar ΔZYX by the SAS similarity theorem. Therefore, option B is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
1. AB/ZY = BC/YX = 2
2. ∠B and ∠Y are right angles
3. ∠B=∠Y
4. ΔABC is similar ΔZYX by the SAS similarity theorem.
Therefore, option B is the correct answer.
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