The solutions to the logarithm equations are;
1) Log₅3 = 0.6826
2) Log₅(27/50) = -0.383
How to solve logarithm Equations?
There are different rules of logarithm such as;
Product rule which is; Log a + Log b = Log (ab)
Quotient rule which is; Log a - Log b = Log(a/b)
Power rule which is; Log aˣ = x log a
We are given that;
Log₅2 = 0.4308
Log₅27 = 2.0478
We know that 27 = 3³. Thus;
Log₅27 = Log₅3³
Using power rule, we have;
Log₅3³ = 3Log₅3
Thus;
Log₅27 = 3Log₅3 = 2.0478
1) We want to solve Log₅3
We have;
3Log₅3 = 2.0478
Thus;
Log₅3 = 2.0478/3 = 0.6826
2) Log₅(27/50)
Using quotient rule, we have;
Log₅27 - Log₅50
This can also be expressed as;
Log₅3³ - Log₅ (25 * 2)
= 3Log₅3 - [2Log₅5 + Log₅2]
= 2.0478 - 2 - 0.4308
= -0.383
Read more about Logarithm Equations at; https://brainly.com/question/237323
#SPJ1
a sample of 49 parents found the mean time spent posting pictures of their children on social media per week was 19 minutes with a standard deviation of 3.9 minutes. find the p-value used to test a claim that the mean time parents spend posting pictures of their children per week is more than 18 minutes at the 5% significance level.
The p-value will be 0.9457
Sample size = 49
Meantime = 19 minutes
Standard deviation = 3.9 mins
Calculating the z-score for test statistic -
z = (x - μ) / (s / √n)
z = (19 - 18) / (3.9 / √49)
= 1 / 0.63
= 1.58
To find the p-value, we can use a standard normal table to find area under the normal curve of the z-score.
The p-value will be the area under the curve to the right of 1.58.
This value is 0.9457, which means that there is a 94.57% chance.
Now,
Since the p-value is greater than the significance level (0.9457 > 0.05), the null hypothesis can not be rejected. Therefore, the mean time parents spend posting pictures of their children per week is not significantly different from 18 minutes at the 5% significance level.
Read more about p-value on:
https://brainly.com/question/28027137
#SPJ4
Choose the correct answer below
Answer: B. Angle Bisector
Why: the line from D to be is intersecting or bisecting the 90 degree angle
A hypothesis test was used to test the hypothesis that people with a significant other are happier on average than people without. The P-value was 0.07 and the level of significance used was 0.1. Then there is sufficient evidence to conclude that, on average, people witha significant other are happier than single people. Hint Textbook Pages True False
True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.
The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.
The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.
Learn more about P-value here:
https://brainly.com/question/13786078
#SPJ4
Given the equation, y=3x, complete the table of values
x (input)
y (output)
-2
-1
0
1
2
Answer:
To find the answers you just need to multiply each value by 3. This is as we are given the information that y is equal to 3x. If we know this and we know the values of x we can easily work out the output (y)!!
-2 = 3 x -2 = -6-1 = 3 x -1 = -30 = 3 x 0 = 01 = 3 x 1 = 32 = 3 x 2 = 6We can also see a pattern of +3 going upwards!!
Hope this helps, have a great day!
rationalise the denominator and simplify
[tex]\frac{7}{\sqrt{} 7}[/tex]
Given surd [tex]\frac{7}{\sqrt{7} }[/tex] after rationalization we get it as [tex]\sqrt{7}[/tex]
What is Rationalization ?The process of rationalization can be thought of as the removal of a radical or an imaginary number from the denominator of an algebraic fraction. In other words, eliminate the radicals from a fraction so that the denominator is solely composed of rational numbers.
Here we use the Rationalization technique
Given surds,
[tex]\frac{7}{\sqrt{7} }[/tex]
Multiplying Numerator and Denominator [tex]\sqrt{7}[/tex]
Then,
[tex]\frac{7}{\sqrt{7} }[/tex] × [tex]\frac{\sqrt[]{7} }{\sqrt{7} }[/tex]
We get the result as [tex]\frac{7\sqrt{7} }{7}[/tex] which is equal to √7
To learn more about Rationalization, we get:
https://brainly.com/question/24291394
#SPJ1
Given δxyz ≅ δegf, find the measurements of the unknown sides and angles. zx = in. eg = in. m∠x = ° m∠g = °
The measure of the given sides and angles are,
1) ZX = 1.3 inch
2) EG = 3.0 inch
3) m ∠ X = 48°
4) m ∠G = 25°
What is congruent triangles?
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
Given: ΔXYZ ≅ ΔEGF
Because the triangles are assumed to be congruent, their corresponding angles and sides must have similar measurements and lengths.
a. ZX = _ in
ZX's length is the same as FE's length. Therefore, the length should be 1.3 inches.
b. EG = _ in
EG's length is the same as XY's length. The figure indicates that the answer should be 3.0 in.
c. m ∠X = _ °
Angle E and angle x should both have the same measure. This is stated to be 48 degrees.
d. m ∠G
Angle Z's measurement is the same as angle F's measurement.
In that case, 107° should be the value assigned to angle F.
Angle E in the triangle to the right measures 48°, while angle F measures 107°.
the sum of these angles is subtracted from 180°.
The angle G's measure, which is equal to 25°.
Hence,
1) ZX = 1.3 inch
2) EG = 3.0 inch
3) m ∠ X = 48°
4) m ∠G = 25°
To know more about congruent triangles, click on the link
https://brainly.com/question/2938476
#SPJ4
Complete question:
Complete question is attached below.
How many solutions does 2(3x+8)=2x+16+14 have
Answer: One solution
Step-by-step explanation:
6x+16=2x+30
4x=14
x=7/2
Two sets of elementary schoolchildren were taught to read by using different methods, 50 by each method. At the conclusion of the instructional period, a reading test yielded the results y1 =74,y2 =71,s1 =9,ands2 =10.
(a) and (b). (question (a) means: give the two hypothesis, and calculate the
p-value).
The null hypothesis and the alternate hypothesis for the set of elementary school children is given by H₀ : μ₁ = 2 and H₁ : μ₂ ≠ 0 and the p-value is 0.136 .
Given x₁ = 74 , x₂ = 72
s₁ = 9 , s₂ = 11 (standard deviation)
n₁ = 50 ,n₂ = 50
Let μ₁ be the true mean for x₁
Let μ₂ be the true mean for x₂
null and alternate hypothesis:
H₀ : μ₁ - μ₂ = 0
H₁ : μ₁ - μ₂ ≠ 0
Test statistic ,
Z = (x₁ - x₂ - D₀ ) / (√σˣ₁² /n₁ + √σˣ₂² /n₂ )
Now we will substitute the values to calculate the the test statistic.
D₀ = μ₁ - μ₂
hence Z₀ = (74 - 72) / √(81/80+121/50)
or, Z₀ = 1.49256..
or, Z₀ ≈ 1.49
Now we will calculate the p-value using the z-score.
p-value:
= 2P(Z > Z₀)
= 2P(Z>1.49)
= 2 {1-0.93189}
= 0.1362...
≈ 0.136
Hence the p-value is 0.136 .
A hypothesis is presented as a theory to explain a certain phenomenon. A hypothesis cannot be said to as a scientific hypothesis if it cannot be tested using the scientific process.
History-based observations that can't currently be fully explained by existing bodies of knowledge are typically where science starts. A hypothesis is a theory put out to explain an observed occurrence or a proven assertion regarding the relationship between two or more variables in a scientific field.
To learn more about hypothesis visit:
brainly.com/question/15980505
#SPJ4
How many times can 24 go into 528
Answer:
22
Step-by-step explanation:
7-radical 7 over10+radical 3
The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given statement is "7-radical 7 over10+radical 3".
Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]
Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].
Learn more about algebraic expressions here:
https://brainly.com/question/953809
#SPJ1
Use cylindrical coordinates.Evaluatex2 dV,iiintegral.gifEwhere E is the solid that lies within the cylinderx2 + y2 = 4,above the planez = 0,and below the conez2 = 16x2 + 16y2.
The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .
In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .
Cylindric coordinates will be used to calculate this integral [tex]\int\limits_e {x^2} \, dx[/tex].
The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.
x = r cos θ
y= r sin θ
With these coordinates, we shall characterize the solid E.
The boundary is then x² + y² = r²
The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )
Again z = 16r²
The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then
[tex]\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta[/tex]
[tex]=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta[/tex]
[tex]=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta[/tex]
= 512/3 π
Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .
To learn more about integral visit:
https://brainly.com/question/16553506
#SPJ4
true or false? when the direction of the bias is toward the null, it means that the error causes the true measure of association to be overestimated.
it is false that that when the direction of bias is towards love it means that the error causes the true measure of association to be overestimated
A Measurement process is biased if it systematically overstates or understates the true value of the measurement
Systematic error due to difference in accuracy or completeness of recall to memory of past or experience is the most associated with recall bias.
Positive association is biased toward the null null value it means that the error causes the true value of association to be underestimated
but in the given given question the statement states that when the direction of the bias is toward the null it means that the error causes the true measure of association to be overestimated which is false
To know more about systematic error here
https://brainly.com/question/14149934
#SPJ4
During a 20% off sale the sale price of a radio was 35.96 what was the regular price?
Answer:
43.152
Step-by-step explanation:
6/5*35.96=43.152
If Jasmine roller skates 280 miles in 7 weeks and skates the same distance each week, how many miles does she skate each week?
Answer:
40
Step-by-step explanation:
280 divided by 7
Factor this expression by dividing by the GCF first.
3n + 18
Answer:
3(n+6)
Step-by-step explanation:
3n+18= 3(n+6)
Find an equation in standard form for the ellipse graphed below.
The equation of the ellipse in the graph, with center at (0, 0), and semi major and minor axis of 3 and 2 can be presented as follows;
[tex]\dfrac{x^2}{2^2} +\dfrac{y^2}{3^2 } = 1[/tex]
What is the locus of an ellipse?An ellipse is the locus of a point that moves such that the sum of the distance from two points is constant.
The standard form of the equation of an ellipse can be presented as follows;
[tex]\dfrac{(x - h)^2}{b^2} + \dfrac{(y - k)^2}{a^2} = 1[/tex]
Where;
(h, k) = The coordinates of the center of the ellipse
a = The semi major axis
b = The semi minor axis
From the attached graph the coordinates of the center of the ellipse is; (0, 0)
The semi major axis, a = 3
The semi minor axis, b = 2
Therefore;
[tex]\dfrac{(x - 0)^2}{2^2} + \dfrac{(y - 0)^2}{3^2} = 1[/tex]
The equation of the ellipse in standard form is therefore;
[tex]\dfrac{x^2}{2^2} + \dfrac{y ^2}{3^2} = 1[/tex]
Lsearn more about the equation of an ellipse here:
https://brainly.com/question/27745454
#SPJ1
PLEASE HELPPPPP
Also that’s a 14 and 17
17. Differentiate
X^2/(2x+1)
with respect to x
Answer:
cheese is cheese
Determine whether the pair of lines appear to be parallel or perpendicular.
1. The lines are perpendicular because they are always the same distance apart and never intersect.
2. The lines are parallel because they intersect at a right angle.
3. The lines are parallel because they are always the same distance apart and never intersect.
4. The lines are perpendicular because they intersect at a right angle.
someone pleasee help
The table of values and the linear equations indicates
4. Andy is correct, the equation of the table of values is; y = 2·x + 4
5. The Three equations are the same
What is a linear equation in algebra?A linear equation is an equation that produces a straight line graph, when plotted on the coordinate plane and can be expressed in the form; y = m·x + c
Where;
m = The slope of the straight line graph of the equation
c = The y-intercept
4. The values in the table indicate that the difference between consecutive terms in the x-values and the first difference in the y-value is constant, therefore, the values represent a linear relationship.
The slope, m, of the linear relationship is constant and it can be found using any two pair of points as follows;
m = (4 - 2)/(0 - (-1)) = 2
The equation is therefore;
y - 2 = 2·(x - (-1)) = 2·(x + 1) = 2·x + 2
y = 2·x + 2 + 2 = 2·x + 4
The equation, y = 2·x + 4 is in the form y = m·x + c, therefore;
Andy is correct
5. The slope-intercept form of the equation of a straight line is; y = m·x + c
Therefore;
y + 1 = 2·x -3
y + 1 - 1 = 2·x - 3 - 1 (subtraction property)
y = 2·x - 4
The equation, y = 2·x - 4, is in the form, y = m·x + c
2·x - 3 = y + 1
2·x - 3 - 1 = y + 1 - 1 (subtraction property)
2·x - 4 = y
y = 2·x - 4 (symmetric property)
The equation, y = 2·x - 4 is in the form, y = m·x + c, which is the same as the first equation
2·y + 2 = 4·x - 6
2·y + 2 - 2 = 4·x - 6 - 2 (subtraction property of equality)
2·y = 4·x - 8
2·y ÷ 2 = (4·x - 8) ÷ 2 (division property)
y = 2·x - 4
The above equation is the same as the first two equations, therefore, the equations are the same
Learn more about linear functions and equations here:
https://brainly.com/question/15602982
#SPJ1
a university charges students $2,300 less for tuition each year to encourage them to stay in school. the tuition for freshman year is $34,000. write a regression equation for this formula, with y
The regression equation of the formula regarding tuition will be given as y = 34000 - 2300x.
Regression method of writing an equation is used to show relation between two variables. The two variables include an independent variable and a dependent variable. The dependent variable is related to the independent variable and their relation and changes can be shown with the help of regression model. According to the question
the charge for tuition = $32000
Charge deduced from tuition per year = $2300
So we assume the tuition cost as y and the number of years as x.
The regression equation will be
y = 34000 - 2300x
where y is the tuition cost and x is the number of years in school and y is dependent variable and x is independent variable.
Learn more about regression at:
brainly.com/question/28178214
#SPJ4
shelby was asked to determine the number of packages that can be wrapped with 12 feet of ribbon if it takes a half of a foot to wrap one package.
The number of packages that can be wrapped with 12 feet of ribbon is 24.
Explain the term unitary method?The unitary approach is a strategy for problem-solving that involves first obtaining the value of a specific unit, then multiplying that value to determine the required value.The unitary approach includes determining the value of a single unit, from which we can calculate the values of the appropriate number of units.For the stated question.
Total length of the ribbon = 12 feet.
Ribbon required to wrap a one box = 1/2 foot.
Number of boxes = Total length / required ribbon for one box
Number of boxes = 12/ (1/2)
Number of boxes = 12 x 2
Number of boxes = 24
Thus, the number of packages that can be wrapped with 12 feet of ribbon is 24.
To know more about the unitary method, here
https://brainly.com/question/24587372
#SPJ4
a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700. if the firm produced 800 units per day, its total cost would be $450, and if it produced 500 units per day, its total cost would be $425.
a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61
The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:
1. 1,000 units per day at a total cost of $700.
ATC = Total cost/output
ATC = $700/1000
ATC = $0.58
2. If the firm produced 500 units per day, its total cost would be $450.
ATC = Total cost/output
ATC = $450/500
ATC = $0.45
3. If it produced 700 units per day, its total cost would be $425.
ATC = Total cost/output
ATC = $425/700
ATC = $0.61
learn more about of amount here
https://brainly.com/question/17099986
#SPJ4
Which correctly describes the points of discontinuity of the function? Select all that apply.
The statements that correctly describes the points of discontinuity of the function include the following;
A. There is an infinite discontinuity at x = -2.
C. There is a removable discontinuity at x = -1.
E. There is a jump discontinuity at x = 1.
What are the types of discontinuity?In Mathematics, there are three (3) main types of discontinuity in a function and these include the following:
Jump discontinuity Infinite discontinuityRemovable discontinuityWhat is a jump discontinuity?A jump discontinuity can be defined as a point on the graph of a function at which the left-hand limit [tex]\lim_{x \to x^-_0} f(x) = A_2[/tex] and right-hand limits [tex]\lim_{x \to x^+_0} f(x) = A_2[/tex] are not equal (A₁ ≠ A₂).
By critically observing the graph representing this function, we can logically deduce that there is a jump discontinuity at x is equal to 1 (x = 1).
What is a removable discontinuity?A removable discontinuity can be defined as a point on the graph of a function at which it is not connected. This ultimately implies that, a removable discontinuity refers to a point on the graph of a function that is considered to be undefined or doesn't accurately fit the other part of a graph.
By critically observing the graph representing this function, we can logically deduce that there is a removable discontinuity at x is equal to negative 1 (x = -1) while there is an infinite discontinuity on the vertical asymptote at negative 2 (x = -2).
Read more on jump discontinuity here: https://brainly.com/question/28760518
#SPJ1
Complete Question:
Which correctly describes the points of discontinuity of the function? Select all that apply.
A. There is an infinite discontinuity at x = -2.
B. There is a jump discontinuity at x = -2.
C. There is a removable discontinuity at x = -1.
D. There is an infinite discontinuity at x = 1.
E. There is a jump discontinuity at x = 1
from a population with a standard deviation of 35, a sample of 150 items is selected. at 95% confidence, what is the margin of error for the population mean? round your answer to three decimal places.
The margin of error for the population mean is 5.601
What does the term "margin of error" mean?
Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.
Given c = 0.95
The significance level is obtained as follows:
alpha = 1 - c
alpha = 1 - 0.95
alpha = 0.05
Also, it is given that n = 150 and sigma = 35 .
The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:
Thus, [tex]Z_{0.005/2}=1.96[/tex]
Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error
[tex]Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601[/tex]
Thus, the margin of error for the population mean is 5.601
Learn more about margin of error
https://brainly.com/question/10218601
#SPJ4
question content area top part 1 a sheet of paper is cut into 6 same-size parts. each of the parts is then cut into 6 same-size parts and so on. a. after the 4th cut, how many of the smallest pieces of paper are there? b. after the nth cut, how many of the smallest pieces of paper are there?
After the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.
Here, we are given that a sheet of paper is cut into 6 same-size parts. Each of the parts is then cut into 6 same-size parts and so on.
Thus, after one cut we will have 6 pieces
After second cut, we will have 6*6 = 36 pieces
After the third cut, we will have 36*6 = 216 pieces
After the fourth cut, we will have 216*6 = 1,296 pieces
Now, we can clearly see a pattern here. The number of pieces follow a geometric progression with a common ratio of 6.
Thus, after the nth cut, the number of pieces will be-
a[tex]r^{n-1}[/tex]
where a = first term which is 6
and r = common ratio which is also 6
⇒ 6*[tex]6^{n-1}[/tex]
= [tex]6^{n}[/tex]
Thus, after the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.
Learn more about geometric progression here-
https://brainly.com/question/24643676
#SPJ4
PLSSS HURRYYYY!!! 30 POINTS!
The slopes of the sides of quadrilateral JKLM are: 3,-3,, and -3.
Why you lie you say 30 but give a 15
wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. based on this information, what is a possible amount of time, in hours, that it could take wyatt to husk 72 dozen ears of cor
The possible amount of time that it could take Wyatt to husk 72 dozen ears of corn is 4 to 6 hours.
What are time and work?
Time is the span of any action or work that occurs or is ongoing. Work is a task or series of activities carried out to accomplish a specific goal.
Given, Wyatt can husk anywhere from 12 to 18 dozen ears of corn per hour.
Thus, to find the time taken to husk 72 dozen ears of corn,
the maximum time = 72/12 =6 hours
And, the minimum time = 72/18 =4 hours
Thus, depending on his speed, Wyatt takes anywhere from 4 to 6 hours to husk 72 dozen ears of corn.
To learn more about time and work
https://brainly.com/question/1979919
#SPJ4
An important measure of location for categorical data is the mean b. median c.mode d. margin
An important measure of location for categorical data is the mode.
While the mean and median can only be determined for numeric data, the mode can be used to describe categorical variables. The mode's principal benefit as a gauge of central tendency is this. When continuous or discrete variables are expressed as intervals, it is also helpful.
The mode represents the value that occurs most often in a dataset.
A dataset can have no mode (if no value repeats), one mode, or multiple modes.
A set of data values' mode is the value that appears the most frequently. The value x (i.e., X = x) at which the probability mass function takes its maximum value is known as the mode if X is a discrete random variable. In other words, it is the value that will be sampled most frequently.
Know more about Mode at:
https://brainly.com/question/63398
#SPJ4
Express the triple integral f(x, y, z)dV as an iterated integral in cylindrical coordinates for the given function f and solid region E
Evaluate the iterated integral.
f(x, y, z) = xy ZA 256-x-y? -y E == x + y ? 0
The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.
In two-dimensional space R2, a point with rectangular coordinates (x, y) can be identified with (r, θ) in polar coordinates and vice versa, where x=rcosθ, y=rsinθ, r2=x2+y2 and tanθ=(y.x) are the relationships between the variables.
In three-dimensional space R3, a point with rectangular coordinates (x, y, z) can be identified with cylindrical coordinates (r,θ,z) and vice versa. We can use these same conversion relationships, adding z as the vertical distance to the point from the x y-plane
According to the question:
The integrated integral in cylindrical coordinates is given by:
∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz
Evaluating the integral yields:
∫∫∫f(ρ, θ, z)dV = 256π∫zdz
= 256πz²
= 256π(256 - x - y)²
Learn more about Triple Integral:
https://brainly.com/question/2289273
#SPJ4