Given:
[tex]x=\log_{10}31,500[/tex]
To find:
Select the true statements from the given options about the given value.
Solution:
We have,
[tex]x=\log_{10}31,500[/tex]
It can be written as
[tex]x=\log_{10}(2^23^25^37)[/tex]
[tex]x=\log_{10}(2^2)+\log_{10}(3^2)+\log_{10}(5^3)+\log_{10}(7)[/tex] [tex][\because \log(ab)=\log a+\log b][/tex]
[tex]x=2\log_{10}2+2\log_{10}3+3\log_{10}5+\log_{10}(7)[/tex]
[tex]x=2\left(0.30105\right)+2\left(0.47712\right)+3\left(0.69897\right)+0.8451[/tex]
[tex]x=4.49835[/tex]
Clearly, the value of x lies between 4 and 5. So, [tex]x>4[/tex] and [tex]x<5[/tex].
Therefore, the correct options are C and D.
The true statements are: (c) x > 4 and (d). x < 5
The logarithmic expression is given as:
[tex]x = \log_{10}(31500)[/tex]
Express 31500 as a product of 100
[tex]x = \log_{10}(315 * 100)[/tex]
Apply the law of logarithm
[tex]x = \log_{10}(315) + \log_{10}(100)[/tex]
Evaluate log 100 base 10
[tex]x = \log_{10}(315) + 2[/tex]
Evaluate log 315 base 10
[tex]x = 2.50 + 2[/tex]
Add the expressions
[tex]x \approx 4.50[/tex]
4.5 is greater than 4 and less than 5
Hence, the true statements are: (c) x > 4 and (d). x < 5
Read more about logarithms at:
https://brainly.com/question/25710806
Help Broo i'm lost il give brainiest
Answer: here is your answer
Step-by-step explanation:
A= 16
B= -8
C= 6
D= -16
E= -4
Can someone help me ASAP!!!
9514 1404 393
Answer:
f(x) = {-x for x < 2; 2x-3 for x ≥ 2}
Step-by-step explanation:
The blue line extending to the left has a slope of -1 and a y-intercept of 0. Its equation is y = -x. That part of the definition of f(x) is applicable for values of x less than 2. (The open dot at (2, -2) tells you that point is not included.)
The red line extending to the right has a slope = rise/run = 2/1 = 2. The y-intercept can be found by extending the line to the y-axis, or from the computation ...
b = y -mx
b = 1 -2(2) = -3 . . . . . for the point (x, y) = (2, 1)
Then the slope-intercept equation for the red line is ...
y = 2x -3
That part of the definition of f(x) is applicable for values of x ≥ 2. The solid dot tells you the point (2, 1) is included.
Putting these parts together, we get ...
[tex]f(x)=\left\{\begin{array}{cc}-x&\text{if $x<2$}\\2x-3&\text{if $x\ge2$}\end{array}\right.[/tex]
PLEASE ANSWER THE QUESTION IN THE PICTURE BELOW
Answer:
35 cm^3
Step-by-step explanation:
the area is 35 hoped that helped
Help plz find x and y
Answer:
y = 18
x = 15.588
Answer:
The value of X should be 0
The value of Y should be 30
However your teacher gave next to no context, so these might be wrong
Step-by-step explanation: protractor
I need assistance if anyone would be so kind.
NO LINKS!! URGENT HELP PLEASE!!!
Solve each continuous exponential growth problem.
24. A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1727.00, what will the balance be 6 years from now?
Answer:
$2,067.59
Step-by-step explanation:
To calculate the balance of the savings account, we can use the continuous compounding interest formula:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given values:
P = $1,727.00r = 3% = 0.03t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]
Therefore, the balance of the savings account 6 years from now is $2,067.59.
Please help! Find the area of the regular hexagon. Round your answer to the nearest tenth.
Answer and explanation please!
Answer:
Here is the formula of what u want . so the answer would be A≈841.78 .
plz check the final answer yourself again ^^
hope it helps u . ⚘
bathroom that is 6 feet long. If the mirror sells for $4.00 per square foot, what will the total cost of the mirror be?
You are conducting a study of three types of feed supplements for cattle to test their effectiveness in producing weight gain among calves whose feed includes one of the supplements. You have four groups of 30 calves (one is a control group receiving the usual feed, but no supplement). You will conduct a one-way ANOVA after one year to see if there are difference in the mean weight for the four groups. What is k for this experiment?
a. 3
b. 30
c. 4
d. 120
Answer:
since we have four groups, the number of population k = 4
Option C. 4 is the correct answer
Step-by-step explanation:
Given the data in the question;
Number of group k = 4
the number of cases in each group = 30
so
n = 4 × 30
n = 120
SS_total = df = n - 1
= 120 - 1
= 199
SS_between = k - 1
= 4 - 1
= 3
since we have four groups, the number of population k = 4
Option C. 4 is the correct answer
Can someone give me the answer to question 4
Answer:
105+54=Z [being sum if interior angle of triangle equal to opposite exterior angle]159=Ztherefore,Z=159Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.
sin(2sec^-1 u/10)
Answer:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
Step-by-step explanation:
We want to write the trignometric expression:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]
As an algebraic equation.
First, we can focus on the inner expression. Let θ equal the expression:
[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]
Take the secant of both sides:
[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]
Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:
[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]
By substitutition:
[tex]\displaystyle= \sin(2\theta)[/tex]
Using an double-angle identity:
[tex]=2\sin(\theta)\cos(\theta)[/tex]
We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:
[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]
Simplify. Therefore:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
Select all possible cross sections of a sphere.
А
circle
B
square
C
triangle
D
point
The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process. The standard deviation of active concentration is known to be 3 grams per liter regardless of the catalyst type. Ten observations on concentration are taken with each catalyst, and the data follow:
Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0
Catalyst 2: 66.4, 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8.
a. Find a 95% confidence interval on the difference in mean active concentrations for the two catalysts. Find the P-value.
b. Is there any evidence to indicate that the mean active concentrations depend on the choice of catalyst? Base your answer on the results of part (a).
c. Suppose that the true mean difference in active concentration is 5 grams per liter. What is the power of the test to detect this difference if α = 0.05?
d. If this difference of 5 grams per liter is really important, do you consider the sample sizes used by the experimenter to be adequate? Does the assumption of normality seem reasonable for both samples?
Answer:
a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57
b. Yes
c. The power of the test is 0.03836
d. The sample size can be considered adequate
Step-by-step explanation:
a. The given data in the study
Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0
Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8
Using the Average, Standard Deviation function from Microsoft Excel, we have;
The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22
The standard deviation for catalyst 1, σ₁ = 3.444416
The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42
The standard deviation for catalyst 2, σ₂ = 2.22401
The 95% confidence interval on the difference in mean is given as follows;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]
The critical-z for a 95% confidence interval = 1.96
Therefore, we have;
[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]
Therefore, we have;
The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57
The test statistics is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Therefore we have;
[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]
The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684
b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst
c. The power of the test
The sample mean difference is given as follows;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]
Therefore, we have;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]
The z-value is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
μ₁ - μ₂ = 5
When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]
[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]
When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]
[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]
The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836
The power of the test = 0.03836
d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean
The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;
(-5.74, -0.66) which also contains -5 which is the difference in the population mean
Can anyone help me out with this answer?
9514 1404 393
Answer:
7×10⁻¹ +6×10⁻² +5×10⁻³
Step-by-step explanation:
Place value in any place-value number system increases by a factor of the base for each place to the left of the "decimal" point. It is reduced by a factor of the base for each place to the right of the "decimal" point.
For base-10 numbers, the powers of 10 are -1, -2, -3, ... as you go to the right of the decimal point. Hence the number 0.765 decomposes as ...
7×10⁻¹ +6×10⁻² +5×10⁻³
The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? Use the value 3.14 for pi, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer. Please helpp.
Answer:
Step-by-step explanation:
radius of the cylindrical construction pipe = 2.5 ft
height of cylinder = 25 ft
volume of cylinder = [tex]\pi r^{2} h[/tex]
= 3.14 x 2.5 x 2.5 x 25
= 490.625
= 490 [tex]ft^{3}[/tex]
Hope this helps
please mark as brainliest!!!
Answer:
490 ft³
Step-by-step explanation:
The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? 490 ft³
What is the volume of the figure?
Answer:
12.57
Step-by-step explanation:
same as last time you know
Only two more questions
Answer:
60
Step-by-step explanation:
if it has a square in the center of the angle it means it is 90 degrees
so a straight line adds up to 180b
90 +30+x=180
x=60
1) Determine if the side lengths given form a triangle
Using the triangle inequality theorem, we can figure this out.
2- Yes
3- No
4- No
5- Yes
6- Yes
What is the value of the expression 8 divided by 12?
Answer:
2/3 or .66666666
Step-by-step explanation:
what is 3times9 3/5 as a mixed number
Find the zeros of ƒ(x) = (x + 2)(x – 1)(x – 3)(x + 1).
Answer:
X=-2 x=1 x=3 and x=-1
Step-by-step explanation:
When the problem asks you to find the zeros all they are asking for is the solution so to solve all you need to do is set each individual piece equal to zero.
Determine the missing factor in × 4.3 = 12.9
Answer: 3
Step-by-step explanation:
12.9/4.3 will give you the number it was multiplied by.
PLEASE ANSWER EXTRA POINTS AND NAMED BRAINLIEST

Answer:
5,8 8,3
Step-by-step explanation:
hoped this helped <33
Does the equation below represent a relation, a function, both a relation and a function or neither
y = x2 – 9x
a2 + b ÷ 3= helpppppppp mmmmmeeeeeeeee! pls
Answer: 2a/3 + b/3
Since it has two different variables, there is no final answer. To find the answer, you must first expand the equation and then apply the fraction rule.
http://www.gilbertmath.com/uploads/1/4/2/7/14279231/3c_u4_assignment1.pdf
i need DESPERATE HELP!!!
my teacher didn't even teach us this and expects us to do it
heres the link for it if needed theres the other work sheet thing to fill out the answers and i have no idea how to do it please im begging you!!
Answer:
1=94 max 2=96 max
Step-by-step explanation:
Review the simple interest rate based on FICO scores to answer the question:
FICO Score Simple Interest Rate
800–850 5.295%
740–799 6.597%
670–739 9.132%
580–669 10.358%
300–579 14.313%
Kamryn plans to borrow $13,250.00 with a simple interest rate loan. Determine the amount of interest Kamryn will save if she is able to raise her credit score from 665 to 680.
Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.
According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.
Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.
Interest = Principal * Rate
= $13,250.00 * 0.10358
≈ $1,370.56
Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.
Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.
Calculating the interest with a credit score of 680:
Interest = Principal * Rate
= $13,250.00 * 0.09132
≈ $1,210.57
Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.
Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
For more question on interest visit:
https://brainly.com/question/25720319
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In an examination, 40% students passed in Maths only, 30% passed in Science only and 10%
students failed in both the subjects. If 400 students passed in Science, find the total number of
students by drawing a Venn diagram.
help me
Answer:
The total number of students is 800.
Step-by-step explanation:
Given that in an examination, 40% students passed in Maths only, 30% passed in Science only and 10% students failed in both the subjects, to determine the total number of students if 400 students passed in Science the following calculation must be performed:
100 - 40 - 30 - 10 = 20
20 + 30 = 50
50 = 400
100 = X
100 x 400/50 = X
800 = X
Thus, the total number of students is 800.
What number is equal to its opposite? Please enter your answer as a number.
Answer:
there is no opposite number but no means opposite
Step-by-step explanation:
Pump B alone fills a tank in 9 hours. Pump C takes 15 hours to fill the same tank alone. If pumps A, B and C are used, the tank fills in 5 hours. How long does it take pump A to fill the the tank alone?
Answer:
19
Step-by-step explanation:
9+15=24
24-5=
19 is the answer