see the picture attached log3 a/3
Answer: -1.631
Step-by-step explanation:
[tex]\log_{3} \frac{a}{3}=\log_{3} a-\log_{3} 3=-0.631-1=-1.631[/tex]
Write 531.246 in expanded form.
Answer:
Step-by-step explanation:
Answer: 500 + 30 + 1 + 0.2 + 0.04 + 0.006
1. You begin working at Tasty Tacos with the payment schedule listed in the table below:
Write an equation that describes the relationship between the years (x) and the earnings per hour (y).
2. If this pattern continues, what would the earnings per hour be after working for 15 years?
3. If this pattern continues, after how many years of service would you earn $9.65 per hour?
The earnings per hour be after working for 15 years is $11.4.
From the given table (2, 6.85), (4, 7.55), (6, 8.25).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)
1) Now, put (x1, y1)=(2, 6.85) and (x2, y2)=(4, 7.55) in slope formula, we get
m=(7.55-6.85)/(4-2)
= 0.7/2
= 0.35
Substitute m=0.35 and (x, y)=(2, 6.85) in y=mx+c, we get
6.85=0.35(2)+c
⇒ 6.85=0.7+c
⇒ c=6.85-0.7
⇒ c=6.15
Now, equation is y=0.35x+6.15
2). Put x=15 in the obtained equation, we get
y=0.35×15+6.15
⇒y=$11.4
3). Put y=9.65 in the obtained equation, we get
9.65=0.35x+6.15
⇒0.35x=9.65-6.15
⇒0.35x=3.5
⇒x=3.5/0.35
⇒x=10 years
Therefore, the earnings per hour be after working for 15 years is $11.4.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The sides and angles of the right triangle are as follows:
a = 8.0 unitsb = 0.7 unitsB = 5 degreesHow to find the sides and angles of right triangle?A right tangle triangle is a triangle that has on e of its angles as 90 degrees. The sides of a right triangle can be named based on the position of the angles.
The sides includes opposite side, adjacent side and hypotenuse side. The longest side of a right angle triangle is the hypotenuse side.
The sides of the right angle triangle can be found using trigonometric ratios as follows:
sin 85 = opposite / hypotenuse
sin 85 = a / 8
a = 8 sin 85
a = 7.96955758473
a = 8.0
cos 85 = adjacent / hypotenuse
cos 85 = b / 8
b = 8 cos 85
b = 0.69724594198
b = 0.7 units
Angle B = 180 - 90 - 85 = 5 degrees.
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y=3x-1 passes through (3,2)
The equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.
According to the question,
We have the following information:
y = 3x-1 and the point through which line is passing is (3,2)
We know that the slope of the given line (denoted by m) is 3.
Now, the following formula is used to find the equation of the line passing through a point:
y-y' = m(x-x')
In this case, we have x' = 3 and y' = 2.
y-2 = 3(x-3)
y-2 = 3x-9
Moving 2 from the left hand side to the right hand side will result in the change of the sign from minus to plus:
y = 3x-9+2
y = 3x-7
Hence, the equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.
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A small van can hold 50 crates and boxes. For every 7 crates the van can hold, there is
room for 3 boxes. How many crates and boxes are in the van when it is completely full?
There are 15 crates and 35 boxes in the van when it is completely full.
Given,
Total number of crates and boxes=50
For every 7 crates the van can hold, there is room of 3 boxes.
let,
Number of crates =x
Number of boxes =y
As given,
Equation for total number of crates and boxes can be written as
[tex]x+y=50....i[/tex]
Space for 7 crates is equal to space for 3 boxes in van, it's equation can be written as
[tex]7x=3y\\\\x=\frac{3y}{7}[/tex].
Substituting 'x' in eq.[tex]i[/tex]
[tex]\frac{3y}{7}+y=50\\\\ \frac{3y+7y}{7}=50 \\\\10y=7*50\\\\10y=350\\\\y=\frac{350}{10}\\ \\y=35[/tex]
Substituting 'y' in eq.[tex]i[/tex]
[tex]x+35=50\\\\x=50-35\\\\x=15[/tex]
Thus, there are 15 crates and 35 boxes in the van when it is completely full.
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Karen, Pete, Rose, and David are comparing their solutions to a hornework problem below. Select the student who correctly subtracted the rational expressions.
Answer:
Step-by-step explanation:
we cant see the problem or there answers
To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio . To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used?
Answer:
Red paint = 12.5 gallons
Blue paint = 7.5 gallons
Step-by-step explanation:
The given ratio of red paint to blue paint is:
red : blue = 5 : 3Let x be the number of gallons of purple paint.
Therefore, the expression for each color of paint needed per x gallons of purple paint is:
[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8}x$}[/tex]
[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}x$}[/tex]
To calculate the number of gallons of red and blue paint needed to make 20 gallons of purple paint, substitute x = 20 into the found expressions:
[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8} \times 20=\dfrac{100}{8}=12.5$}[/tex]
[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}\times 20=\dfrac{60}{8}=7.5$}[/tex]
Therefore, the number of gallons of paint that should be used are:
Red paint = 12.5 gallonsBlue paint = 7.5 gallonsIf m/ABD = 78°, what are m/ABC and m/DBC?
I need help with this please
The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43°
In the given figure the angle ∠ABD is intersected by the straight line BC such that two new angles are formed ,∠ABC and ∠ADC .
Now from the properties of angles on a 2-dimensional plane we can see that :
m ∠ABC + m ∠ADC = m ∠ABD
The values of the angles given are:
m ∠ABC = 5x - 5
m ∠ADC = 5x + 3
m ∠ABD = 78°
now we put these above values in the equation:
(5x - 5) + (5x + 3) = 78
or, 10 x - 2 = 78
or, 10 x = 80
or , x = 8
m ∠ABC = 5×8 - 5 = 35°
m ∠ADC = 5×8 + 3 = 43°
The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43° .
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Write an equation for line L in point-slope form and slope-intercept form.
L is parallel to y = 5x.
A plant grow 1.67cm in it 1st week. Each week it grow by 4% more than it did the previous week by how much does it grow 9 week including the 1st week
If each week it grow by 4% more than it did the previous week by it grow in 9 week is 17.67cm.
How to find the growth in 9 week?Now let find the growth in 9 week
Growth in 9 week = 1.67cm × [( 1+ 0.04)^9 -1] ÷ [(1+0.04)-1]
Growth in 9 week = 1.67cm × [( 1.04)^9 -1] ÷ (1.04)-1]
Growth in 9 week = 1.67cm × [( 1.4233 -1) ÷ 0.04
Growth in 9 week = 1.67cm × [0.4233 ÷ 0.04
Growth in 9 week = 1.67cm × 10.5825
Growth in 9 week = 17.67cm
Therefore 17.67cm is the 9 week growth.
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GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58.
Find the z-score for a GPA of 2.98
The Z-score for a GPA of 2.98 is 1.60345
Calculating Z - score:A Z-score is a numerical value or measurement that explains the relationship between a value of data and the mean of a group of values. It will be calculated in terms of standard deviations from the mean.
The formula to calculate the Z -score is given by
Z - score = [tex]\frac{( \bar{x} -\mu) }{\sigma}[/tex]
Where [tex]\bar {x}[/tex] = test value
μ = mean and σ = standard deviation
Here we have
GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58
⇒ mean μ = 2.05
⇒ Standard deviation σ = 0.58
And we need to find the z-score for a GPA of 2.98
⇒ [tex]\bar {x}[/tex] = 2.98
From above observations
Z - score = [tex]\frac{( 2.98 -2.05) }{0.58}[/tex]
= [tex]\frac{( 0.93) }{0.58}[/tex]
= 1.60345
Therefore,
The Z-score for a GPA of 2.98 is 1.60345
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4(x-b) = x solve for x
[tex]4(x)+4(-b)=x\\4x-4b=x\\4x-x=4b\\3x=4b\\\frac{3x}{3} =\frac{4b}{3} \\x=\frac{4b}{3}[/tex]
⇒They simply wanted you to simplify and make x the subject of the equation.
The path of a baseball is modeled by the equation [tex]y= -0.25x^{2} +4x+3\\[/tex] where x represents the time (in seconds) and y represents the height of the baseball.
- Find and interpret the y-intercept. Find the maximum height of the baseball. Then sketch a graph of the path.
(please provide steps on how to solve if you can)
The y-intercept is y = 3, and this is the initial height of the ball, and the maximum height is y = 19
What is the y-intercept?The y-intercept is what we get when we evaluate in x = 0, then:
y = -0.25*x² + 4x + 3
replacing x by zero we get:
y = -0.25*0² + 4*0 + 3 = 3
The y-intercept is y = 3.
The maximum height is at the vertex, we know this because the leading coefficient is negative, which means that the parabola opens down.
The vertex is at:
x = -4/(2*-0.25) = 8
Evaluating there:
y = -0.25*8² + 4*8 + 3 = 19
that is the maximum height.
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Find m<1 then classify the angle.
Answer:
81 degrees
This is an acute angle since it’s less then 90 degrees
Step-by-step explanation:
All three angles of a triangle always equal 180 degrees
180-(78+31)
180-109
81 degrees
Hopes this helps please mark brainliest
A radio station claims that the amount of advertising per hour of broadcast time has an average of 13 minutes and a standard deviation
equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of
advertising time is equal to 8 minutes. Calculate the z-score for this amount of advertising time.
A. z = -0.52
B. z = -4.17
C. O z = 4.17
D. z = 0.52
The z-score for this amount of advertising time is z = -4.17 so option B is correct.
Given:
Average = 13 minutes
Standard deviation = 1.2 minutes.
Advertising time x = 8 minutes.
z = x - mean / standard deviation.
= 8 - 13/1.2
= -5/1.2
= -5/12/10
= -50/12
= -4.17.
Therefore the z-score for this amount of advertising time is z = -4.17 so option B is correct.
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Find the slope of the line that passes through (4, 8) and (7, 4).
Answer:
[tex] \huge{ \bold{ \orange{ - \frac{4}{3} }}}[/tex]
Step-by-step explanation:
The slope of a line passing through two points can be found by using the formula
[tex]m = \frac{y2 - y1}{x2 - x1} \\ [/tex]
where
(x1, y1) and (x2, y2) are the points
From the question
The points are (4, 8) and (7, 4)
We have
[tex]m = \frac{4 - 8}{7 - 4} = - \frac{4}{3} \\ [/tex]
We have the final answer as
[tex] \bold{ - \frac{4}{3} }[/tex]
Hope this helps you
Measures of center (mean, median) are affected by addition, multiplication, or both?
Answer:
Measures of center generally tell us about the middle , or center of a distribution. They are the mean , the Mexican , and the mode. Each plays a useful role in statistics. The mean or arithmetic average , is calculated by adding all the data values and dividing by the number of values.
Elsa the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday
there were 6 clients who did Plan A and 5 who did Plan B. On Thursday there were 2 clients who did Plan A and 3 who did Plan B. Elsa trained her Wednesday
clients for a total of 7 hours and her Thursday clients for a total of 3 hours. How long does each of the workout plans last?
The perimiter of a square is 60 cm how long is one side of the square
Answer: 15 cm
Step-by-step explanation:
just divide 60 by 4 and because a squar has 4 sides and that is it
The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases about 11.5%. What is the pressure at an altitude of 5000 m?
The pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is 58.08 kPa.
What is percentage?A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Given:
The atmospheric pressure, P = 101 kPa,
For every 1000 meters, the pressure decreases by 11.5%,
So at the height of 5000 meter, the % decrease will be 5 × 11.5 = 57.5%,
Now let the 57.5% of 101 kPa be x then,
x = 57.5/100 × 101 kPa,
x = 58.08 kPa,
Therefore, the pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is 58.08 kPa.
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Someone j need help with this pls
Answer:
27/256
Step-by-step explanation:
=(27)(1/4)(1)/(64)
=27/256
Tommy left his house and rode his bike 15 miles north. He then rode 8 miles east.
How far is Tommy from his house in miles?
Answer: Tommys dispacement 17 miles
Step-by-step explanation:
pyhagorean theorem
he went 15 up (leg 1)
and then right 8 (leg 2)
and Tommy's displacement is the hypotenuse
15^2+8^2=c^2
c^2 = 289
c = 17
complete the table below with the needed data
help please help me because this is due tomorrow
The factors are mentioned in the table given below.
Number Number of factors prime or composite
12 6 composite
20 6 composite
21 4 composite
31 2 prime
43 2 prime
Factors are those numbers which when divide the given number leaves zero as a remainder.
Factor of 12 = 1, 2 ,3, 4, 6 , 12
Factor of 20 = 1, 2 , 4,5,10 , 20
Factor of 21 = 1 ,3, 7, 21
Factor of 31 = 1, 31
Factor of 43 = 1, 43.
Prime number is a number which has only 2 factors that is number one(1) and the number itself.
Composite numbers which has more than 2 factors.
Therefore, the number of factors are mentioned in the table.
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PLEASE HELP ASAP PLEASE HELP ASAP
The materials travel faster on Belt One, considering the constants of the proportional relationships.
What is a proportional relationship?A proportional relationship is a linear function with intercept zero in which the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, according to the equation presented as follows:
y = kx
For each belt in this problem, the constant gives the velocity that the materials travel.
For Belt One, the relation is:
y = 157.1x.
Hence the velocity is of 157.1 inches per minute.
For Belt Two, the velocity is obtained as follows:
k = 125.6/2 = 62.8 inches per minute.
157.1 > 62.8, hence it travels faster on Belt One.
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the table represents a function.
x
-6
-2
0
3
f(x)
3
1
4
-2
The value of the function f(x) at x = -2 is , f(-2) = 1 , the correct option is (c) .
Function is defined as an expression that defines a relationship between one variable and another variable .
In the question ,
it is given that ,
the value of the function f(x) at different values of x is given ,
we have to find the value of the f(-2) , that is the value of the function f(x) at x = -2 .
from the table , we see that when x [tex]=[/tex] -2 , the value of f(x) is [tex]=[/tex] 1 ,
that means f(-2) [tex]=[/tex] 1 .
Therefore , The value of the function f(x) at x = -2 is , f(-2) = 1 , the correct option is (c) .
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11x-4>-15 how do i do this?????????
Answer: x>-1
Step-by-step explanation:i just did that question
Answer:
Step-by-step explanation:
add 4 to -15 then divide that by 11x the answer should be x=-1.
If MLDEF = 119, then what are m/FEG and m ZHEG? The diagram is
not to scale.
The measure of <FEG= 61 and <HEG = 119.
What is Vertical Opposite Angle?The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.
when two lines in a plane intersect, one of the angles that are directly across from one another.
Given:
m< DEF= 119
Now, <DEF + <FEG= 180 (Linear Pair)
119+ <FEG = 180
<FEG = 180- 119
<FEG = 61
and, <DEF= <HEG = 119 (Vertical opposite angle)
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Find an equation of the line containing the given pair of points (3,4) and (9,9
what is 12 x 6 because area = L x w a = 12 x 6 a= ?
Answer: _______________________________
72