Step-by-step explanation:
Some of the property of log are as follows :
1. [tex]\text{log a}-\text{log b}=\text{log} \dfrac{\text{a}}{\text{b}}[/tex]
2. [tex]\text{log a}+\text{log b}=\text{log}(a{\cdot} b)[/tex]
3. [tex]\text{log}a^n=n\ \text{log} a[/tex]
Now coming to question,
(a) [tex]\text{log 5}-\text{log 8}=\text{log} \dfrac{\text{5}}{\text{8}}[/tex] (using property 1)
(b) [tex]\text{log 1}+\text{log 3}=\text{log}(1{\cdot} 3)=\text{log} 3[/tex] (using property 2)
(c) [tex]\text{log} 4=\text{log} 2^2=2\ \text{log} 2[/tex] (using property 3)
Hence, this is the required solution.
List the coordinate of point Q' when the figure is reflected over the x-axis.
Answer:
The coordinate of point Q' is (3 , 4).
when x =7, x²-2x+6=
Answer:
41
Step-by-step explanation:
step 1. first, you should plug in all the x's. x² is 49, 2x is 14. The
equation would then be 49-14+6 which is 41
2x would be 2 x 7 because when 2 numbers are touching, they are to be multiplied.
x² would be 7 x 7 because, when you have a number to the power of 2, you multiply it by itself.
and finally you would get, 49-14+6 and according to PEMDAS, the eqaution hsould go left to right leaving us with the answer of 41.
i hope you understand this. :)
Answer:
41
Step-by-step explanation:
x²-2x+6
Let x = 7
7^2 -2*7 +6
49 -14 +6
41
lif a/b =⅔ find the value of 2a²+3b²/a²+b²
Answer:
95/4
Step-by-step explanation:
Given,
a/b =2/3
Therefore, 2a²+3b²/a²+b² = ?
We get,
a/b = 2/3
So, we can write
a = 2 and b = 3
Now,
2×(2)² + 3×(3)²/(2)² + (3)² [Putting the values of a and b]
= 2×4 + 3×9/4 + 9
= 8 +27/4 + 9
= (32+27+36)/4 [ Taking L.C.M, we get 4]
= 95/4
Aaliyah is drawing a ball from one bag and a tile from another bag. The first bag contains 4 green balls and 4 yellow balls. The second bag
contains tiles numbered 1 through 5.
What is the probability that she draws a green ball and a tile numbered with 4?
Step-by-step explanation:
P(green AND 4)
= P(green) × P(4)
= (4/8) × (1/5)
= 1/10
Using probabilities of independent events, it is found that there is a 0.1 = 10% probability that she draws a green ball and a tile numbered with 4.
-------------------
A probability is the number of desired outcomes divided by the number of total outcomes.If two events, A and B, are independent, the probability of both happening together is the multiplication of the probabilities of each happening.-------------------
Event A: Green ball, 4 out of the 8 balls are green, thus, [tex]P(A) = \frac{4}{8} = 0.5[/tex]Event B: Tile numbered with 4, which is one of the five, thus, [tex]P(B) = \frac{1}{5} = 0.2[/tex]The probability of both events is given by:
[tex]P(A \cap B) = P(A) \times P(B) = 0.5(0.2) = 0.1[/tex]
0.1 = 10% probability that she draws a green ball and a tile numbered with 4.
A similar problem is given at https://brainly.com/question/24174994
Check for Understanding: Karen found a job with an annual
salary of $67.3K. What is her monthly pay, rounded to the
nearest dollar
Answer:
5,608
Step-by-step explanation:
The total monthly pay of Karen is given by the equation A = $ 5,608
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total monthly pay of Karen be = A
Now , the equation will be
Let the annual pay of Karen be B = $ 67.3 K
1 K = 1000
The value of B = 67.3 x 1000
The value of B = $ 67300
So , annual pay of Karen B = $ 67300
Now , the monthly pay of Karen = annual pay of Karen / 12
Substituting the values in the equation , we get
The monthly pay of Karen A = $ 67300 / 12
The monthly pay of Karen A = $ 5,608.33
Rounding to the nearest dollar , we get
The monthly pay of Karen A = $ 5,608
Therefore , the value of A is $ 5,608
Hence ,
The total monthly pay of Karen is given by the equation A = $ 5,608
To learn more about equations click :
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write .9333 as a fraction
Answer:
9333/10000
Step-by-step explanation:
To write .9333 as a fraction you have to write .9333 as the numerator and put 1 as the denominator. Then you multiply the numerator and the denominator by 10.
Question is clipped on .
Answer:
Option (A)
Step-by-step explanation:
AE and RV are the two line segments intersecting at a point N.
Therefore, ∠ANR ≅ ∠ENV [Vertical angles are equal in measure]
(8x + 12)° = (5x + 57)°
8x - 5x = 57 - 12
3x = 45
x = 15
Since, m∠ENV = 5(15) + 57
= 75 + 57
= 132°
Therefore, Option (A) will be the answer.
solve z^2-2z-35=0 using zero product
Answer: z = 7 or z=-5
Step-by-step explanation:
First you need to factor the polynomial.
To factor [tex]z^{2}[/tex] - 2z -35 You will need to find two numbers that their product is -35 and their sum is -2 and the numbers -7 and 5 works out.
Rewrite the polynomial as,
[tex]z^{2}[/tex] - 7z + 5z - 35 = 0 factor the left by grouping
([tex]z^{2}[/tex] -7z) (5z -35) = 0
z(z -7) 5(z - 7) = 0 Factor out z-7
(z-7)(z+5) = 0 Now apply the zero product by setting each of them equal 0.
z-7= 0 or z+5=0
+7 +7 -5 -5
z = 7 or z= -5
(26÷13)⋅(−7)+14−4 ?
Answer:
the answer is -4 I think
Answer:
−4
Step-by-step explanation:
(26 ÷ 13) ⋅ (−7) + 14 − 4 =
= 2 ⋅ (−7) + 14 − 4
= −14 + 14 − 4
= 0 − 4
= −4
Which is the graph of the linear inequality y < 3x + 1?
3
1
3
4.
5
Answer:
Image below
Step-by-step explanation:
Hey there!
Well lets graph the given inequality,
y < 3x + 1
Look at the image below.
So the right graph should look like the image below.
Hope this helps :)
Find:
a. the mean
b. the deviation from the mean for each data item.
c. the sum of the deviations in part b.
147, 154, 156, 161, 162
Answer:
Step-by-step explanation:
Given the dataset 147, 154, 156, 161, 162,
Mean is the sum of the dataset divided by the total number of dataset.
a) Mean = [tex]\sum Xi/N[/tex]
[tex]\overline x = \dfrac{147+154+156+161+162}{5}\\ \\\overline x = \dfrac{780}{5}\\ \\\overline x= 156[/tex]
b) The formula for calculating the deviation from the mean for each value is expressed as [tex]Xi - \overline X[/tex] where;
Xi is value of each item
xbar is the mean = 156
Mean deviation of 147 = 147-156 = -9
Mean deviation of 154 = 154-156 = -2
Mean deviation of 156 = 156-156 = 0
Mean deviation of 161 = 161-156 = 5
Mean deviation of 162 = 162-156 = 6
c) Sum of the deviations [tex]\sum Xi - \overline X[/tex] = (-9-2+0+5+6)
[tex]\sum Xi - \overline X[/tex] = -11+11
[tex]\sum Xi - \overline X[/tex] = 0
Hence the sum of deviation from the mean is 0
if tan tetha =8/15,find the value of sin tetha+cos tetha all divided by cos tetha (1-cos tetha)
Answer: 195.5 or 12 7/32
Step-by-step explanation:
There is no letter tetha in the table so I use α instead. However it is not sence to final result.
The expression is:
(sinα+cosα)/(cosα*(1-cosα))
Lets divide the nominator and denominator by cosα
(sinα/cosα+cosα/cosα)/(cosα*(1-cosα)/cosα)= (tanα+1)/(1-cosα)=
=(8/15+1)/(1-cosα)= 23/(15*(1-cosα)) (1)
As known cos²α=1-sin²α (divide by cos²α both sides of equation)
cos²a/cos²α=1/cos²α-sin²α/cos²α
1=1/cos²α-tg²α
1/cos²α=1+tg²α
cos²α=1/(1+tg²α)
cosα=sqrt(1/(1+tg²α))= +-sqrt(1/(1+64/225))=+-sqrt(225/(225+64))=
=+-sqrt(225/289)=+-15/17 (2)
Substitute in (1) cosα by (2):
1st use cosα=15/17
1) 23/(15*(1-cosα)) =23/(15*(1-15/17))= 23*17/2=195.5
2-nd use cosα=-15/17
2)23/(15*(1-cosα)) =23/(15*(1+15/17))= 23*17/32=12 7/32
Find the slope of the line graphed below.
Answer:-3 over 7
Step-by-step explanation:
rise over run
Social Security is taxed at 6.2% up to $128,400. Medicare is taxed at 1.45%. How much
Social Security and Medicare tax should be collected from someone who earns $135,000?
$7,590.50
$9,450.35
$9,918.30
$10,817.25
Answer:
$9918.30
Step-by-step explanation:
The total tax is ...
6.2% × $128,400 + 1.45% × $135,000 = $7960.80 +1957.50
= $9,918.30
A rod was cut into 3 piece the length of the 3 piece are in the ratio of 5 : 3 :2 if the shortest is 25cm how long was the rod
Answer:
125 cm
Step-by-step explanation:
Ratio of pieces of the rod:
5:3:2In total, the rod is equal to:
5x+3x+2x= 10xSince the shortest peace:
2x = 25 cm,Length of the rod:
10x = 5* 2x = 5* 25 cm = 125 cmNoah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it. This is the graph Noah gets if he allows x to take on any value between -1 and 5.
Answer:
for more appropriate it would be 0-2.5, and the max is 15
Step-by-step explanation:
The domain of a graph is the possible x-values of the graph, while the range is the possible y-values.
The proper domain of Noah's graph is 0 to 2.5The maximum volume of the graph is 15From the attached graph (see attachment), we have the following observations.
The x values starts from -1 and ends at 5The domain of the graph is from 0 to 4 (i.e. x-values 0 to 4 have corresponding y-values on the graph)x-values 0 to 2.5 have corresponding non-negative y-valuesOther values of x have corresponding negative y-valuesThe maximum of the graph is at y = 15Because the volume of a box cannot be negative, the x-values to use must correspond to non-negative y-values.
Hence, the proper domain of Noah's graph should be 0 to 2.5
And the maximum of the graph is at y = 15
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15 POINTSSSSSSSSSSSSS!!!!!!!!!!!!!! The distance from Mercury to the sun is 35,904,200 miles. The distance from Earth to the sun is 9.3×107 miles. How far apart are Earth and Mercury?
Answer:
57,095,800 mi (= 5.71 x 10⁷ mi )
Step-by-step explanation:
given :
Distance from Mercury to Sun = 35,904,200 mi
Distance from Earth to Sun = 9.3x10⁷ = 93,000,000 mi
Distance between mercury and earth
= 93,000,000 - 35,904,200
= 57,095,800 mi
= 5.71 x 10⁷ mi (rounded to 3 sig. figures)
Explain how to use estimation to help find the product of two decimals
Answer:
1. Estimate the product.
2. Multiply to find the product. Multiply the decimals as if they were whole numbers. Ignore the decimal point.
3. Compare your estimate with your product to verify that your answer makes sense.
Why is a regression line referred to as the line of best fit?
When there is a linear relationship is observed between the variables, we use linear regression predict the relationship between them.
Also, we predict the values for dependent variable by modelling a linear model that best fits the data by drawing a line Y=a+bX, where X is the explanatory variable and Y is the dependent variable.
In other words: The line of best fit is a line through a scatter plot of data points that best describes the relationship between them.
That's why the regression line referred to as the line of best fit.
Describe in words the region of double-struck R3 represented by the equation: x2 + z2 ≤ 36.
Answer:
Step-by-step explanation:
Given that:
[tex]x^2 + z^2 \leq 36[/tex]
if we assume that x is zero, then [tex]z^2 = 36[/tex] , [tex]z = \pm \sqrt{36}[/tex] [tex]z = \pm 6[/tex] i.e the radius of the circle goes from -6 to +6, Similarly, if we assume that z is zero, then [tex]x^2 = \pm 36[/tex] , [tex]x = \pm \sqrt{36}[/tex] , [tex]x = \pm 6[/tex] . This implies that [tex]x^2 + z^2[/tex] describes the circle with radius 6
[tex]x^2 + z^2 \leq 36[/tex] is an equation at region which consist of those points whose distance from the centre is at least with radius -6 and at most 6.
Therefore, the region is the solid cylinder of radius 6, where the Y axis is also the axis of the cylinder.
Zamba has found a little black dress on sale for 50% off the original price of $239.99. She also has a coupon offering free shipping and an additional 10% off of her entire online purchase. If she buys the dress and a pair of shoes costing $34.70, how much will she pay for her ensemble?
108.00
$139.23
$94.23
$104.70
what is the sum of -5 + (-3)
Answer:
-8
Step-by-step explanation:
Both the numbers are negative so you add them together and keep the negative sign
Answer:
-8
Step-by-step explanation:
when negative and positive meet, the negative dominates the positive thereby making it negative.
-5 + (-3)
-5 - 3
-8
What is the answer to 27-45=
Answer:
-18 if youre asking about simple subtraction
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
its like saying (-45)+27.
you have to add the 27 to 45 to get to 0 and them see how much you have left
A water park charges $5 for entry into the park and an additional $2 for each of the big water slides. Steven spent $17 on his visit to the water park. Which equation can be used to find the number of big water slides, x, that Steven went on? (1 point)
Answer:
5+2x
Step-by-step explanation:
Answer:
Let X= Additional Amount
Equation= 5+2x=17
-5 -5
__________
2x=12
_______
2 2
X=6 is the answer, Hope that helped ya.
Step-by-step explanation:
The average score for all basketball players in a particular season has a mean of 75 and a standard deviation of 3.5. Suppose 49 played basketball today. Find the probability that the average score of the 49 players exceeded 76
Answer:
0.0228
Step-by-step explanation:
Given that:
mean (μ) = 75, Standard deviation (σ) = 3.5
The z score is a score used in statistics to measure by how many standard deviations the raw score is above or below the mean. If the z score is positive, it means that the raw sore is above the mean and if the z score is negative then the raw score is below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ \\For\ a\ sample \ n, the\ z\ score\ is:\\ \\z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
For x > 76 and a sample (n) = 49:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }\\\\z=\frac{76-75}{\frac{3.5}{\sqrt{49} } }=2[/tex]
From the normal distribution table, the probability that the average score of the 49 players exceeded 76 = P(x > 76) = P(z > 2) = 1 - P(z < 2) = 1 - 0.9772 = 0.0228
math help on this question!
Answer:
94
Step-by-step explanation:
sum of all angles in a triangle=180
total angle=3
sum of two angles=86
3rd angle=180-86=94
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of 0.8 years. If you randomly purchase one item, what is the probability it will last longer than 14 years
Answer:
probability of lasting longer = 1.7%
Step-by-step explanation:
We are given:
x' = 14 years
μ = 12.3 years
s = 0.8 years
Thus, let's use the formula for the Z-score value which is;
z = (x' - μ)/s
Thus;
z = (14 - 12.3)/0.8
z = 2.125
From the z-distribution table attached, the p-value is ;
P(x' > 2.125) = 1 - 0.983 = 0.017 = 1.7%
Thus,probability of lasting longer = 1.7%
A sample of size will be drawn from a population with mean and standard deviation . Use the TI-84 calculator. Part 1 of 2 Your Answer is incorrect Find the probability that will be more than . Round the answer to at least four decimal places. The probability that will be more than is . Part 2 of 2 Your Answer is incorrect Find the percentile of . Round the answer to two decimal places. The percentile is
This question is incomplete, the complete question is;
A sample of size 86 will be drawn from a population with mean 90 and standard deviation 24. Use the TI-84 calculator Part 1 of 2
Find the probability that x will be more than 89. Round the answer to at least four decimal places. The probability that will be more than 89 is Part 2 of 2 Find the 60 percentile of x. Round the answer to two decimal places. The 60 percentile is
.
Answer:
part 1) the probability that x will be more than 89 is 0.6517
part 2) the 60 percentile of x is 90.65
Step-by-step explanation:
Given that;
u = 90, α = 24, n = 86
Part 1 says Find the probability that x will be more than 89
p ( x > 89 ) = p (( x - u)/α√n > (89-90)/24/√86 ))
= p ( z > - 0.39 ) = 1 - p (z ≤ - 0.39 )
from z table, 0.39 → 0.3483
= 1 - 0.3483 = 0.6517
∴ the probability that x will be more than 89 is 0.6517
part 2 says Find the 60 percentile of x
p( Z < z ) = 0.60
now from the z-table, p(Z < 0.25 ) = 0.60
and we that x = u + z(α/√n)
x = 90 + 0.25( 24 / √ 86
x = 90.64699 ≈ 90.65
∴ the 60 percentile of x is 90.65
One Friday, Vace gave 11 more flu shots than Mike did. Together they gave 53 flu shots. How many flu shots did Vace give?
Answer:
32
Step-by-step explanation:
53 - 11 is 21, so they each gave 21, but vace gave 11 more so you add 11 to get 32
Can someone help me!!!
Answer:
Step-by-step explanation:
Hello, please consider the following.
First of all, we need to complete the squares, then move the constant to the right side, as below.
[tex]x^2+y^2+4x-10y-7=0\\\\(x+2)^2-4+(y-5)^2-25-7=0\\\\(x+2)^2+(y-5)^2=36=6^2[/tex]
And then, we can read the answers from the rearranged equation.
(a) The centre is then (-2,5)
(b) The radius is 6
Thank you.