Final answer:
To solve the equation log2 (x) + log2(x+7) = 3, you can combine the logarithmic terms using the property log(a) + log(b) = log(a*b). By applying this property and solving the resulting quadratic equation, we find that x = 1.
Explanation:
To solve the equation log2 (x) + log2(x+7) = 3, we need to combine the logarithmic terms using the property log(a) + log(b) = log(a*b). Applying this property, we get log2 (x*(x+7)) = 3. Next, we can rewrite this equation in exponential form as 2^3 = x * (x+7). Simplifying further, we have 8 = x^2 + 7x. Rearranging the equation, we get a quadratic equation x^2 + 7x - 8 = 0. Solving this quadratic equation, we find that x = -8 or x = 1. However, since the logarithm of a negative number is undefined, the solution is x = 1.
Ira bought a tennis racquet that cost $112. The sales tax rate is 9 percent. What is the total amount that she paid?
$121
$122.08
$122.80
Answer: The correct option is
(B) $122.08.
Step-by-step explanation: Given that Ira bought a tennis racquet that cost $112 and the sales tax rate is 9 percent.
We are to find the total amount that Ira paid.
The total amount Ira paid is the sum of the cost price and the sales tax.
The sales tax paid by Ira is given by
[tex]S_t=9\%\times 112=\dfrac{9}{100}\times112=\dfrac{1008}{100}=10.08.[/tex]
Therefore, the total amount paid by Ira will be
[tex]A_p=112+S_t=112+10.08=122.08.[/tex]
Thus, the total amount paid by Ira is $122.08.
Option (B) is CORRECT.
Answer:
The correct option is
(B) $122.08.
Step-by-step explanation:
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Ann picks a 4-digit number.
The first digit is not zero.
The 4-digit number is a multiple of 5
How many different 4-digit numbers could she pick?
Ann could pick from 1800 different 4-digit numbers that are multiples of 5, considering the range of possible digits for each position and the requirement that it must be a multiple of 5.
To determine how many different 4-digit numbers that are multiples of 5 Ann could pick, we need to consider three things:
The first digit can be anything from 1 to 9 (since the number cannot start with zero).
The second and third digits can be anything from 0 to 9.
The fourth digit must be either 0 or 5 (since the number is a multiple of 5).
For each of the first three digits, we have 9 possible choices (1-9 for the first digit, 0-9 for both the second and third digits), and for the last digit, we have 2 possible choices (0 or 5). Using the counting principle, we multiply the number of choices for each digit together to find the total number of possible 4-digit multiples of 5 Ann can pick:
9 (first digit) × 10 (second digit) × 10 (third digit) × 2 (fourth digit) = 1800 different 4-digit multiples of 5.
So, Ann could pick from 1800 different 4-digit numbers that are multiples of 5.
write the negation of the statement:
No vans have three wheels
A. Line a
B. Line b
C. Line c
D. Line d
A set of cards contains cards numbered 1 – 8. Mrs. Jacob’s class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. The class will conduct 1,000 trials. Based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?
Answer:
125
Step-by-step explanation:
Answer:
The best prediction for the number of times a 4 will be drawn from the pile is:
125
Step-by-step explanation:
It is given that:
A set of cards contains cards numbered 1 – 8.
So, the theoretical probability that 4 comes up is:
Ratio of Number of favorable outcome( outcome of 4) to the total umber outcome(i.e. 8 )
Hence, Theoretical Probability that 4 is drawn=1/8
Now, out of 1000 trials the best prediction of number of times 4 is drawn is:
(The probability of drawing 4)×(Number of experiments or trials)
=(1/8)×1000
=125
Find the discriminant of the following equation.
4x2 + 16x + 16 = 0 ...?
Answer:
The discriminant is 0.
Step-by-step explanation:
Since, the discriminant of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,
[tex]D=b^2-4ac[/tex]
Here, the given equation is,
[tex]4x^2+16x+16=0[/tex]
By comparing,
a = 4, b = 16 and c = 16,
Hence, the discriminant of the given equation is,
[tex]16^2-4\times 4\times 16[/tex]
[tex]=256 - 256[/tex]
[tex]=0[/tex]
Hilary wants to go on the latin club trip to italy , it will cost 2,730 for the trip the trip is 30 weeks away and she wants to make equal weekly payments , how much money altogether does hilary need to pay at the end of week 8
What is the result of adding the system of equations? 2x + y = 4
3x - y = 6
A.x=2
B.x=10
C.5x=10
What is the quotient: (3x2 + 4x – 15) ÷ (x + 3) ?
is it 3x – 1, r = 1?
i would just like for someone to confirm if it is or isnt ...?
Answer:
No, it is 3x-5 and r=0
Step-by-step explanation:
We can do it by long division method the required quotient is 3x-5 and r=0
not 3x-1 , r=1
multiply the divisor with 3x we will get [tex]3x^2+9x[/tex]to cancel out the first term of dividend
Now after solving we will get [tex]-5x-15[/tex]
Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.
if it rains tomorrow, the probability is 0.8 that john will practice the piano. if it does not rain tomorrow, there is only a .4 chance that john will practice. if there is a 60% that it will rain tomorrow, what is the probability that John will practice his piano lesson? i'm supposed to use a tree diagram to solve this ...?
Answer:64 %
Step-by-step explanation:
Given if it rains John Plays piano is 0.8
i.e. if it rains probability that john will not play is 0.2
If it not rain Then probability that john will play piano is 0.4
he will not play is 0.6
Given if there is 60 % chance that it will rain tomorrow
Thus Pobability that john will play is
[tex]=Probability\ that\ it\ will \times Probability\ john\ will\ play+Probability\ it\ will\ not\ rain\times Probability john will play[/tex]
[tex]=0.6\times 0.8+0.4\times 0.4=0.48+0.16=0.64[/tex]
Bill had 240 pieces of gum. he gave 1/6 of the piece of gum to his sister. how many pieces of gum did he give to his sister?
Factor completely 5x2 + 30x + 50
Answer: Complete factorization would be
[tex]5(x^2+6x+10)[/tex]
Step-by-step explanation:
Since we have given that
[tex]5x^2+30x+50[/tex]
We need to find the factors:
Since the terms of above expression is a factor of 5.
So, it becomes,
[tex]5x^2+30x+50\\\\=5(x^2+6x+10)[/tex]
Hence, complete factorization would be
[tex]5(x^2+6x+10)[/tex]
Solve the quadratic equation: 2x2 + 11x − 6 = 0 ...?
What is 8-8 to the power of -1 ?
Which choice is equivalent to the expression below?
Select the coordinates of two points on the line y = -2
a) (2, -2) and (-2, 2)
b) (-2, -2) and (-2, 0)
c) (2, -2) and (0, -2)
d) (-2, 2) and (-2, -2)
Answer:
C
Step-by-step explanation:
18 players and 3 coaches. this year, 162 players signed up to play soccer. how many coaches are needed?
Can you verify my answer?
I believe it's reflection.
linear differential equation question:
y"'-6y"+12y' -8y = 0
To solve this linear differential equation, we can use the method of characteristic equation. The general solution is y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.
Explanation:To solve this linear differential equation, we can use the method of characteristic equation. Let's assume that the solution is of the form y = e^(rx). Substituting this in the given equation, we get the characteristic equation as r^3 - 6r^2 + 12r - 8 = 0. This can be factored as (r - 2)^3 = 0. So, the characteristic roots are r = 2, 2, and 2.
Since we have repeated roots, the general solution is given by y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.
Therefore, the general solution to the linear differential equation y''' - 6y'' + 12y' - 8y = 0 is y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.
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You and three friends earn money by painting houses. You agree to split the profits equally. You buy brushes, tape, and paint for $750. If your total income is $2,600, how much is your share of the profit?
Quick Geometry Question:
1. A trapezoid has a 60-degree angle and a 45-degree angle. What are the other angles?
2. A trapezoid has a 60-degree angle and a 120-degree angle. What are the other angles?
Answer:
For trapezoids, we have some rules:
The angles always need to ad up to 360°
We also have that the base angles are suplementary, so they need to ad to 180°. (one smaller or equal than 90° and the other greater or equal than 90°)
Then, if the angles are one equal to 60° and the other 45°.
The other two angles are:
a1 = 180° - 60° = 120°
a2 = 180° - 45° = 135°
and now we have: 120° + 60° + 45° + 135° = 360°
for the other we have an angle of 60° and other of 120°.
This two angles can be one next to the other, so may be suplementary.
this mens that the other two angles may be any angles that add to 180° (again, one is less or equal than 90° and the other is greater or equal than 90°)
So we can have:
a1 = 110°
a2 = 70°
for example.
Your current schedule only lets you take two 1-credit courses every six months. You need 12 credits to get the degree you want. How long will it take you to get the degree?
When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?
Multiply each side by negative one over eight , add 35 to each side
Multiply each side by negative one over eight , subtract 35 from each side
Multiply each side by −8, subtract 35 from each side
Multiply each side by −8, add 35 to each side
Answer:
3
Step-by-step explanation:
i have done this test before
A math teacher is trying to analyze her test grades. She surveys the students to find out how many minutes they studied. She then makes a scatterplot of time studying and test grades. What is the domain?
Answer:
Step-by-step explanation:
The correct answer is the number of minutes the students studied. The student's grades is dependent on how long they studied. The domain is the independent variable or the amount of time.
Final answer:
The domain in a scatterplot of study time versus test grades represents all the reported study times of the students. It is visualized by plotting this data on a dot plot or analyzing the distribution to see the correlation between study time and grades.
Explanation:
The domain of a function in mathematics represents the set of all possible input values it can accept, typically the x-values on a graph. In the context of a scatterplot of time studying versus test grades created by a math teacher, the domain would consist of the various amounts of time that students reported studying. Analyzing the distribution of these values can showcase how study time correlates to test performance, assuming that this is a function with a one-to-one correspondence between study time and grade received, passing the vertical-line test.
To create a dot plot, as suggested in a collaborative classroom exercise, you would align a number line with the possible amounts of study time and place a dot above the corresponding value for each student's reported study time. Through this process, you could visualize the amount of study time on the x-axis and gain insights into the study habits of the class.
In a given scenario like the one described for Ms. Phan studying for an economics exam, the total benefit and the expected total gain in her score could be plotted to visualize the marginal benefits of additional study hours. This helps to understand the concept of diminishing returns in relation to study time and test score improvement.
What is the sum of the first 18 terms of the arithmetic series 11+15+19+23+...?
Line r is parallel to line t. Find the measurement of Angle 6. The diagram is not to scale.
A.32
B.138
C.42
D.142
What is a1 in the sequence?
−4, −2, −12, −14, ...
−4
−2
−12
−14
Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5.
What is the variance of the data? Round to the nearest tenth.
1.6
2.5
5.6
6.3
Since the variance is the square of the standard deviation, the variance here is 6.3.
What is variance?In statistics, the variance shows how much the values spread out around the mean. The standard deviation is obtained as the square root of the variance of a given value.
Now;
[tex]s = \sqrt{v}[/tex]
s = 2.5
[tex]v = s^2[/tex]
[tex]s = (2.5)^2 =[/tex]6.3
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How do I simplify 8x+10x-4+2x+20
3. What is another name for plane VTL?
Plane T
Plane Z
Plane ZXV
Plane LTX
Answer:
Plane Z
Step-by-step explanation: