Answers
Explanation:
The rule is that if log(A) = log(B), then A = B
Using this idea, we can then say,
log(t - 3) = log(17 - 4t)
t - 3 = 17 - 4t
t+4t = 17+3
5t = 20
t = 20/5
t = 4
The solution to the logarithmic equation is t = 5
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
log ( t - 3 ) = log (17 - 3t ) be equation (1)
On simplifying , we get
The bases of the logarithm are equal
So , the values are equal and therefore
t - 3 = 17 - 3t
Adding 3t on both sides , we get
4t - 3 = 17
Adding 3 on both sides , we get
4t = 20
Divide by 4 on both sides , we get
t = 20 / 4
t = 5
Therefore , the value of t is 5
Hence , the logarithmic equation is solved
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Related Questions
I need help please IVE BEEN AT THIS FOREVER
Answers
Answer:
.3
Step-by-step explanation:
Take path A = .5
Then Path D = .6
P(a and D) = .5 *.6 = .3
Which of the following best describes a three-dimensional solid made from
two parallel and congruent discs not in the same plane and all the points
between them?
A. Cylinder
B. Cone
C. Cube
D. Prism
Answers
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
The solid is described as a three-dimensional solid made from
two parallel and congruent discs, not in the same plane, and all the points
between them is a Cylinder.
Hence, the correct option is A.
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an expression equivalent to 12+ 21 is
Answers
Answer:
33
Step-by-step explanation:
The answer is 1628. Because 16 x 21 = 28 x 12 = 336
Hope this helps
Find the area of the shaded regions.
Answers
Answer: About 21.98 cm²
Step-by-step explanation:
First, find the area of the large shaded circle:
[tex]r^{2} \pi =3^{2} \pi =9\pi[/tex]
Find the area of the two small unshaded circles:
[tex]1) r^{2} \pi =1^{2} \pi =1\pi \\2) r^{2} \pi =1^{2} \pi=1\pi[/tex]
Subtract the area of the small circle from the large circle:
[tex]9\pi -1\pi -1\pi =9\pi -2\pi =7\pi[/tex]
Therefore, the area of the shaded region is:
[tex]7\pi =7*3.14=21.98[/tex]
A simple random sample of 41 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts(a) through (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ (Round to three decimal places as needed.)
c. Find the P-value; P-value = ____ (Round to four decimal places as needed.)
d. State the conclusion. (choose one from each ( x, y) set)
(Do not reject, Reject) Upper H0, because the P-value is (greater than, less than, or equal to) the level of significance. There is
(sufficient, insufficient) evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to
10 beats per minute.
Answers
Answer:
H0 : σ²=10²
H1 : σ²>10²
χ² = 45.796
Pvalue = 0.2442
Do not reject H0 because Pvalue is greater Than significance level
There is insufficient evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
Step-by-step explanation:
Given that :
Sample size, n = 41
Sample standard deviation, s = 10.7
Population standard deviation, σ = 10
Significance level, α = 0.10
The Hypothesis :
H0 : σ²=10²
H1 : σ²>10²
Using the χ² test for population variance :
The test statistic, χ² = (n-1)*s²/σ²
χ² = (41 - 1) * 10.7²/ 10²
χ² = (40 * 114.49) / 100
χ² = 4579.6 / 100
χ² = 45.796
The Pvalue ;
df = n - 1 ; 41 - 1 = 40
Pvalue(45.796, 40) = 0.2442
Since Pvalue > α ; WE fail to reject H0
Do not reject H0 because Pvalue is greater Than significance level
There is insufficient evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
PLEASEEEE HELPPPP ASAPPPPPP
Answers
Find a vector v that is perpendicular to the plane through the points
A=(5,−4,4), B=(−5,0,−3), and C=(−4,2,−5).
v =
Answers
The value of vector v that is perpendicular to the plane through the points is,
⇒ v = (6, - 27, - 24)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Points are,
A = (5,−4,4), B = (−5,0,−3), and C = (−4,2,−5).
Hence, We get;
AB = [- 10, 4, - 7]
AC = [-9, 6, -9]
So, The value of vector v that is perpendicular to the plane through the points is,
⇒ v = AB x AC
⇒ v = (- 10, 4, - 7) x (- 9, 6, - 9)
⇒ v = (6, - 27, - 24)
Thus, The value of vector v that is perpendicular to the plane through the points is,
⇒ v = (6, - 27, - 24)
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!!!!PLEASE HELP!!!!
What is the following quotient?
2
√13+ /11
O 13-2./11
13+ 11
6
13+ V11
12
√13 - 1
Answers
(D)
Step-by-step explanation:
Multiply and divide the fraction by the conjugate:
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}×\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]
[tex]= \dfrac{2(\sqrt{13} - \sqrt{11})}{(\sqrt{13})^2 - (\sqrt{11})^2}[/tex]
[tex]=\dfrac{2(\sqrt{13} - \sqrt{11})}{2}[/tex]
[tex]=\sqrt{13} - \sqrt{11}[/tex]
Four- sevenths of the children in class earned A's on the last math test. 18 children did not earn an A. How many earned A's? SHOW ALL WORK!!!
Answers
Answer: 24 people earnt As
Step-by-step explanation:
1. We know that 18 people are the other 3/7 of the class
2. We first find out 1/7, which is calculated by dividing 3/7 by 3, which is 18 / 3 so 6
3. We can then find 4/7 by multiplying the amount of 1/7 by 4, so 6 x 4 = 24
What is the midpoint of the line segment AB?
Answers
Answer:
(5.5,0)
Step-by-step explanation:
Mid point is ((3+8)/2,(4-4)/0)=(5.5,0)
Which behavior would best describe someone who has good communication skills with customers ? a) Following up with some customers b) Talking to customers more than listening to them c) Repeating back what the customer says d) Interrupting customers frequently
Answers
Answer:
C. repeating back what the customer says
Last Thursday, each of the students in M. Fermat's class brought one piece of fruit to school. Each brought an apple, a banana, or an orange. In total, 20% of the students brought an apple and 35% brought a banana. If 9 students brought oranges, how many students were in the class
Answers
Answer:
20 students
Step-by-step explanation:
Step 1:
Calculate the percentage of students who brought oranges by taking away the percentage of students who brought bananas and apples from the total percentage of students.
100-(20+35)
=45
Step 2:
Equate the percentage of students who brought oranges to the number of students who brought oranges
45%=9
100%
(100×9)/45
=20 students
75,000 live bacteria are present in a culture in a flask. When an antibiotic is
added to the culture, the number of live bacteria is reduced as shown by the
equation. Approximately how many hours have passed when there are 4500
bacteria left alive?
4500 = 75,000 e-0.1733t
Answers
Answer:
16.23 hours
Step-by-step explanation:
To obtain the number of hours that have passed ; we have to solve for t on the equation ;
4500 = 75,000 e^-0.1733t
Divide both sides by 75000
4500/75000 = e^-0.1733t
0.06 = e^-0.1733t
Take the In of both sides ;
In(0.06) = - 0.1733t
-2.813410 = - 0.1733t
Divide both sides by - 0.1733
t = 16.23 hours
A wedge of cheese is shaped like a triangular prism. The wedge of cheese is 7 inches tall. The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches. If you ate this whole block of cheese, about how many cubic inches would you have eaten (ignoring the holes)?
420 in
193 in
385 in
210 in
Answers
Answer:
193 in
Step-by-step explanation:
Volume of a triangular prism:
The volume of a triangular prism is the base area multiplied by the wedge, that is:
[tex]V = A_bw[/tex]
The base area is one half times the triangle base times it's height, so:
[tex]V = 0.5*b*h*w[/tex]
The wedge of cheese is 7 inches tall.
This means that [tex]w = 7[/tex]
The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.
This means that [tex]b = 11, h = 5[/tex]
Volume:
[tex]V = 0.5*b*h*w = 0.5*11*5*7 = 192.5[/tex]
Rounding, approximately 193 in.
The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $440 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1
Answers
Answer:
$465.6 should be budgeted.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean $440 and standard deviation $20.
This means that [tex]\mu = 440, \sigma = 20[/tex]
How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.1?
The 100 - 10 = 90th percentile should be budgeted, which is X when Z has a p-value of 0.9, so X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 440}{20}[/tex]
[tex]X - 440 = 1.28*20[/tex]
[tex]X = 465.6[/tex]
$465.6 should be budgeted.
Hello my ''brainiest intelligent minds'' once again I'm counting on you, lol, I'm trying to figure this out.
f(x)=2x+3
g(x)=3x+2
What does (f+g)(x) equal?
Answers
Answer:
(f + g)(x) = 5x + 5
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 2x + 3
g(x) = 3x + 2
Step 2: Find
Substitute in function values: (f + g)(x) = 2x + 3 + 3x + 2Combine like terms: (f + g)(x) = 5x + 5Q: EXPRESS IT IN THE FORM OF LINEAR EQUATION IN ONE VARIABLE:
•The ordinate of a point is thrice its abscissa.
Answers
Answer:
y = 3x
Step-by-step explanation:
abscissa is the x coordinate
ordinate is the y coordinate
y = 3x
A person earns $23,600 one year and gets a 5% raise in salary. What is the new salary?
Answers
Answer:
24780
Step-by-step explanation:
might not be right but 24780 because 23600*5% is 1180 and add that to the original 23600 to get 24780
5% more is 105% in total, including the the 100% we start with, so:
23,600 * 1.05 = 24780
Helppp!!!!!
Please!!!
{ is question #1 is right?? }
{ i need help with question #2 please }
Please!!
Helppp!!!!!
Answers
Answer:
fyi b's answer has imaginary numbers in it...
Imaginary: 1 +[tex]\frac{\sqrt{2i} }{2 }[/tex]
Imaginary: 1 - [tex]\frac{\sqrt{2i} }{2 }[/tex]
Step-by-step explanation:
[tex]2x^{2} - 4x -3 = 0[/tex]
[tex]\sqrt{-4^{2} -4(2)(3)}[/tex] = [tex]\sqrt{-8}[/tex] ... the negative root will produce imaginary solutions
9514 1404 393
Answer:
1a. -4, 3/4
1b. 1-0.71i, 1+0.71i
Step-by-step explanation:
The directions tell you to use the quadratic formula. Factoring may get you the solution somewhat more easily, but does not comply with the directions.
The quadratic formula tells you ...
[tex]\text{The solution to }ax^2+bx+c=0\text{ is given by }\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
__
1a. a=4, b=13, c=-12
[tex]x=\dfrac{-13\pm\sqrt{13^2-4(4)(-12)}}{2(4)}=\dfrac{-13\pm\sqrt{361}}{8}=\dfrac{-13\pm19}{8}\\\\x=\left\{-4,\dfrac{3}{4}\right\}[/tex]
__
1b. After adding 3 to both sides, a=2, b=-4, c=3
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(3)}}{2(2)}=\dfrac{4\pm\sqrt{-8}}{4}=1\pm\dfrac{\sqrt{2}}{2}i\\\\x=\left\{1-\dfrac{\sqrt{2}}{2}i,1+\dfrac{\sqrt{2}}{2}i\right\}\approx\{1-0.71i,1+0.71i\}[/tex]
An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.
y = 40x - 25
y = 25x + 40
y = 25x - 40
y = 40x + 25
Answers
Answer:
y = 25x + 40
Step-by-step explanation:
The electrician charges $25 per hour.
The number of hours is x.
Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)
Therefore fee(y) charged by the electrician = $40 + $25x
Hence y = 25x + 40
Find the length represented by x for each pair of similar triangles.
18cm, 9cm, and x
30cm, 15cm, and 25cm
Answers
Answer:
15 cm
Step-by-step explanation:
Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.
We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.
Hope this helped,
~cloud
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answers
Answer:
y= -6x-6, I think, hope it helped
Step-by-step explanation:
FX) is defined by the equation f(x) = 4x2 - 2x +17. What effect will multiplying
f(x) by 0.5 have on the graph?
A. The graph will be stretched horizontally.
B. The graph will be compressed horizontally.
C. The graph will be stretched vertically.
D. The graph will be compressed vertically.
Answers
Step-by-step explanation:
the graph will be compressed vertically
Enter the equation of the line in slope-intercept form. Slope is 4, and (6,4) is on the line. The equation of the line is y=
Answers
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
WILL GIVE BRAINLISTAnother copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
Answers
f(1)=8(b)^1
4/8=b
1/2=b
f(1)=4
a is initial value/ y intercept which is 8.
f(x)=8(1/2)^x
Answer:
f(x)=8 (0.5)^x
Step-by-step explanation:
Answer from plato
Carlos owns a small business. There was a profit of $9 on Saturday and a loss of $6 on Sunday. Find the total profit or loss for the weekend. $15 profit $3 loss $3 profit $15 loss
Answers
Answer:
$3 profit
Step-by-step explanation:
Since you got a profit of $9 on Saturday and a loss of $6 on Sunday, you have to subtract 9 and 6, which is 3.
n eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a blue on your next toss of the die
Answers
Answer:
The answer is "21%".
Step-by-step explanation:
[tex]\to 26 + 20 + 29 + 49 = 124\\\\=\frac{26\ \text{brown times}}{124 \ \text{total times}} \\\\= \frac{26}{ 124} \\\\ = 0.209677 \\\\[/tex]
Calculating the percentage:
[tex]= 20.9677 \times 100\\\\=20.9677\% \approx 21\%[/tex]
What is the x-intercept of the graph of the function f(x) = x2 − 16x + 64?
(−8, 0)
(0, 8)
(8, 0)
(0, −8)
Answers
Answer:
(8,0)
Step-by-step explanation:
f(x) = x^2 − 16x + 64
The x intercepts ( or zeros) are found by setting y=0
0 = x^2 − 16x + 64
Factor
0 = (x-8)(x-8)
Using the zero product property
x-8 =0 x-8 =0
x=8 x=8
(8,0)
Answer:
8,0
edge 20201
the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student
Answers
The ratio/proportion is young / old = young / old.
We know that one ratio is 3 / 5, so we need to complete the other.
3 / 5 = young / 40
5 goes into 40, 8 times, therefore we need to multiply the numerator by 8 also.
3 x 8 = 24
The younger student is 24 years old.
Hope this helps!
Answer:
24
Step-by-step explanation:
younger : older
3 :5
The older is 40
40/5 = 8
Multiply each by 8
younger : older
3 *8 :5 *8
24 : 40
The younger is 24
Find the measure of the missing angles.
Answers
We know that vertically opposite angles are equal.
So, k = 131° [Vertically opposite angles]
and g = 43° [Vertically opposite angles]
We know that linear pair of angles are supplementary (180°).
So, h + 43° = 180° [Linear pair of angles]
=> h = 180° - 43°
=> h = 137°
and m + 131° = 180° [Linear pair of angles]
=> m = 180° - 131°
=> m = 49°
