Answers
Step-by-step explanation:
To solve for x, we set up our equation like this:
7x - 7 = 4x + 14
Next, we subtract 4x from the right side to cancel it out and then subtract 4x from the left side.
7x (-4x) - 7 = 4x (-4x) + 14
3x - 7 = 14
Then, we add 7 on both sides (to cancel the -7 out and place it on the right)
3x - 7 (+7) = 14 + 7
3x = 21
Finally, we divide both sides by 3 to isolate our variable, x.
3x ÷ 3 = x
21 ÷ 3 = 7
Our final answer: x = 7
Related Questions
How many 4 digit palidromes are there?
Answers
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answers
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
the bold answer is incorrect. what is the right answer?
Answers
Explanation:
A complementary angle are two angles add up to 90 degree
Which expression is equivalent to 8 square root 6 ?
Answers
Answer:
(2.13982638787^3) x 2
Scott start his banking account with 150 and is spending $7 per day on lunch . How would one describe the graph of this model?
Answers
Answer:
So this is giving us the slope the slope is y=-7x+150
Step-by-step explanation:
It is giving us the Y intercept which is $150 because thats how much he starts out with
It is giving us the slope -7 dollars because he is spending that everyday
I WILL RATE YOUR BRAINLIEST Marius opened a savings account. The sequence {200, 208, 216.30, 225, …} describes the amount of interest he earns each year his account is active. If this pattern continues, how much total interest will Marius have earned by the 30th year the account is active?
Answers
Answer:
11,215Step-by-step explanation:
Given the sequence of interest earned by Marius on his savings account as
200, 208, 216.30, 225, …, the sequence of interest forms a geometric sequence since they have a common ratio.
[tex]r =\frac{T_2}{T_1}= \frac{T_3}{T_2}= \frac{T_4}{T_3}\\ r =\frac{208}{200}= \frac{216.30}{208}= \frac{225}{216.30} \approx 1.04[/tex]
To get how much total interest will Marius have earned by the 30th year the account is active, we will find the sum of the first 30 terms of the geometric sequence as shown.
[tex]S_n =\frac{ a(r^n-1)}{r-1} \ for \ r> 1\\ \\\\ n = 30, a = 200, r = 1.04\\S_{30} = \dfrac{ 200(1.04^{30}-1)}{1.04-1}\\\\S_{30} = \dfrac{ 200(3.243-1)}{0.04}\\\\S_{30} = \dfrac{ 200(2.243)}{0.04}\\\\S_{30} = \dfrac{ 448.6}{0.04}]\\\\S_{30} = 11,215[/tex]
Hence total interest that Marius will earn by the 30th year the account is active is 11,215.
the correct answer is
S30= 200(1-1.04^n)/1-1.04
i took the test
Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is
Answers
Answer:
The true true level of significance of this test is more than 0.01.
Step-by-step explanation:
No standard deviation and we are told that the investigator still used z rather than the more appropriate t - distribution.
This method of using the z-distribution when standard deviation is unknown will definitely result in a smaller critical value and this in turn simply means that the p-value will be smaller than what it should really be.
Thus, it means the critical value is getting closer to the mean value than the way it should be.
Therefore, means that for a given significance of 0.01 and using the z-distribution under this no standard deviation situation, the true true level of significance of this test is more than 0.01.
Marking as brainyest PLEASE HELP
How does f(x) = 9x change over the interval from x = 3 to x = 4? A) f(x) increases by 100% B) f(x) increases by 800% C) f(x) increases by 900% D) f(x) increases by 1000%
Answers
Answer:
C) f(x) increases by 900%
Step-by-step explanation:
The rate of change is
f(4) - f(3)
---------------
4-3
f(4) = 9*4 = 36
f(3) = 9*3 = 27
36 -27
---------------
4-3
9
-----
1
The rate of change is 9
To change to a percent, multiply by 100%
9*100% = 900%
Answer:
Increases by 900%
Step-by-step explanation:
● f(x) = 9x
The rate of change is:
● r = (36-27)/(4-3) = 9
So the function increses nine times wich is equivalent to 900%
What is 2-(-8)????? And how do you solve it????
Answers
Subtracting a negative is the same as adding a positive. So 2-(-8) is really 2+8 = 10.
With something like 2-8, we start at 2 and move to the left 8 units to arrive at -6 on the number line. When we do 2-(-8), we start at 2 and move 8 units in the opposite direction since -8 is the opposite of 8.
In terms of money, you can think of a negative number as an IOU or it represents the amount of debt. Writing -8 means you are 8 dollars in debt. If we subtract away debt, then we have less of it and effectively its the same as adding dollars to your pocket. Subtracting away 8 dollars of debt is the same as adding 8 dollars to your pocket, which is one interpretation of how 2-(-8) is the same as 2+8.
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answers
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years? Round your answer to the nearest whole number.
Answers
Answer:
Final population after 10 years
= 288911718
Step-by-step explanation:
Present population p = 258,316,051
Rate of growth R%= 1.12%
Number of years t= 10 years
Number of times calculated n = 10
Final population A
= P(1+r/n)^(nt)
A= 258,316,051(1+0.0112/10)^(10*10)
A= 258,316,051(1+0.00112)^(100)
A= 258,316,051(1.00112)^100
A= 258,316,051(1.118442762)
A= 288911717.6
Approximately A= 288911718
Final population after 10 years
= 288911718
The function g is defined as follows for the domain given.
g(x) = 2x+1,
domain = (-5, -1, 2, 3)
Write the range of g using set notation. Then graph g
Answers
Answer:
g(x): 2(-5)+1= -10+1=-9
2(-1)+1= -2+1=-1
2(2)+1= 4+1=5
2(3)+1=6+1= 7
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given that,
The function g is defined as follows for the domain given.
[tex]g(x) = 2x+1,[/tex] and domain [tex]= (-5, -1, 2, 3)[/tex]
So,
[tex]x=-5\\2(-5)+1\\= -10+1\\=-9\\\\x=-1\\2(-1)+1\\= -2+1\\=-1\\\\x=2\\2(2)+1\\= 4+1\\=5\\\\x=3\\2(3)+1\\=6+1\\= 7[/tex]
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
To know more about the function
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Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answers
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
What percent of the area underneath
this normal curve is shaded?
Answers
Answer:
The area shaded is 95%
Step-by-step explanation:
The total area under the curve is 100 percent
1 standard deviation away from the mean is 68 percent
2 standard deviations away is 95 percent
The area shaded is 95%
The percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.
What is the 68-95-99.7 rule?The 68-95-99.7 rule is also referred to as the empirical rule or the three-sigma rule and it can be defined as a shorthand which is used in statistics to determine the percentage of a population parameter that lie within an interval estimate in a normal distribution curve.
Basically, the 68-95-99.7 rule states that 68%, 95%, and 99.7% of the population parameter lie within one (1), two (2), and three (3) standard deviations of the mean respectively.
This ultimately implies that, the percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.
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The higher the bowling score the better. The lower the golf score the better. Assume both are normally distributed. a. Suppose we have a sample of the Santa Ana Strikers' bowling scores. Q1 = 125 and Q3 = 156. Would it be usual or unusual to have a score of 200?b. Suppose the mean bowling score is 155 with a standard deviation of 16 points. What is the probability that in a sample of 40 bowling scores, the mean will be smaller than 150?c. Suppose the mean golf score is 77 with a standard deviation of 3 strokes We will give a trophy for the best 5% of scores. What score must you get to receive a trophy? d. Suppose the mean golf score is 77 with a standard deviation of 3 strokes. Would a golf score of 70 be ordinary, a mild outlier, or an extreme outlier?
Answers
Answer:
Explained below.
Step-by-step explanation:
(a)
The first and third quartiles of bowling scores are as follows:
Q₁ = 125 and Q₃ = 156
Then the inter quartile range will be:
IQR = Q₁ - Q₃
= 156 - 125
= 31
Any value lying outside the range (Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) are considered as unusual.
The range is:
(Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) = (125 - 1.5×31, 156 + 1.5×31)
= (78.5, 202.5)
The bowling score of 200 lies in this range.
Thus, the bowling score of 200 is usual.
(b)
Compute the probability that the mean bowling score will be smaller than 150 as follows:
[tex]P(\bar X<150)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{150-155}{16/\sqrt{40}})[/tex]
[tex]=P(Z<-1.98)\\=1-P(Z<1.98)\\=1-0.97615\\=0.02385\\\approx 0.024[/tex]
Thus, the probability that in a sample of 40 bowling scores, the mean will be smaller than 150 is 0.024.
(c)
It is provided that, the lower the golf score the better.
So, the best 5% of scores would be the bottom 5%.
That is, P (X > x) = 0.05.
⇒ P (Z > z) = 0.05
⇒ P (Z < z) = 0.95
⇒ z = 1.645
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.645=\frac{x-77}{3}\\\\x=77+(3\times 1.645)\\\\x=81.935\\\\x\approx 82[/tex]
Thus, the score is 82.
(d)
A z-scores outside the range (-2, +2) are considered as mild outlier and the z-scores outside the range (-3, +3) are considered as extreme outlier.
Compute the z-score for the golf score of 70 as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\farc{70-77}{3}\\\\=\frac{-7}{3}\\\\=-2.33[/tex]
As the z-score for the golf score of 70 is less than -2, it is considered as a mild outlier.
Using the FOIL method, find the product of x - 2 and x - 3 .
Answers
(x - 2)(x - 3)
x^2 -3x - 2x + 6
x^2 - 5x + 6
Answer:
[tex] \boxed{ {x}^{2} - 5x + 6}[/tex]Step-by-step explanation:
[tex] \mathsf{(x - 2)(x - 3)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex] \mathsf{x×x - 3x - 2x - 2 × ( - 3 )}[/tex]
Calculate the product
[tex] \mathsf{ {x}^{2} - 3x - 2x - 2 \times (- 3)}[/tex]
Multiply the numbers
[tex] \mathsf{ {x}^{2} - 3x - 2x + 6 }[/tex]
Collect like terms
[tex] \mathsf{ {x}^{2} - 5x + 6}[/tex]
Hope I helped!
Best regards!
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answers
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
Subtract these polynomials.
(3x2 – 2x + 5) – (x2 + 3) =
Answers
Answer:
D. 2x^2 - 2x + 2
Step-by-step explanation:
(3x2 – 2x + 5) – (x2 + 3) add or subtract like terms
3x^2 - x^2 - 2x - 3 + 5 = 2x^2 - 2x + 2
Answer:
2x^2 - 2x + 2
Step-by-step explanation:
Ape-x
Question 15 please and i will mark the brainliest!!! And thank you to whoever answers
Answers
Explanation:
We have 4 options for the first choice and 3 options for the next. So there are 4*3 = 12 different combos possible. The tree diagram below shows 12 different paths to pick from. For instance, the right-most path has us pick the number 4 and the color yellow.
-10 + 7x + 24 - 2x
Your answer
Answers
Hope this helps
3a-27=0
How to solve
Answers
Answer:
a = 9
Step-by-step explanation:
3a - 27 = 0
3a = 27
a = 27/3
a = 9
3*9 - 27 = 0
27 - 27 = 0
Answer:
a = 9
Step-by-step explanation:
3a-27=0
Add 27 to each side
3a = 27
Divide by 3
3a/3 = 27/3
a = 9
explain why the APR does not compare loans for different lengths of time
Answers
Answer:
APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.
Step-by-step explanation:
Solve for x. 2x+3≤x−5 x≤−8 x≤2 x≤8 x≤−2
Answers
Answer:
x≤−8
Step-by-step explanation:
2x+3≤x−5
Subtract x from each side
2x-x+3≤x-x−5
x+3≤−5
Subtract 3 from each side
x+3-3≤−5-3
x≤−8
Answer:
[tex]\huge \boxed{x \leq -8}[/tex]
Step-by-step explanation:
[tex]2x+3 \leq x-5[/tex]
[tex]\sf Subtract \ x \ from \ both \ parts.[/tex]
[tex]2x+3 -x\leq x-5-x[/tex]
[tex]\sf Simplify \ the \ inequality.[/tex]
[tex]x+3 \leq -5[/tex]
[tex]\sf Subtract \ 3 \ from \ both \ parts.[/tex]
[tex]x+3-3 \leq -5-3[/tex]
[tex]\sf Simplify \ the \ inequality.[/tex]
[tex]x \leq -8[/tex]
Charlie needs a $275,000 mortgage and he'd like to pay it off in 30 years. He is considering two banks. Bank A: 3.5% with monthly payments of $1234.87 Bank B: 4% with monthly payments of $1312.89 Charlie doesn't think a 0.5% difference is that much. What is the difference between these two bank loans with total interest paid over the life of the loan?
Answers
Answer:
Difference in interest= $41,250
Step-by-step explanation:
To calculate the interest paid on each bank loan we use the following formula
Interest = Principal * Rate * Time
For Bank A
Interest = 275,000 * 0.035 * 30
Interest = $288,750
For Bank B
Interest = 275,000 * 0.04 * 30
Interest = $330,000
Therefore
Difference in interest= 330,000 - 288,750
Difference in interest= $41,250
Therefore if the mortgage is taken from Bank B he will pay an extra $41,250 on the loan.
The 0.5% difference in rates has a large impact over the 30 year term loan
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answers
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answers
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Answer the questions attached about the given sequence: -33, -27, -21, -15, ...
Answers
Answer:
see below
Step-by-step explanation:
-33, -27, -21, -15,....
-33 +6 = -27
-27+6 = -21
-21+6 = -15
This is an arithmetic sequence
The common difference is +6
explicit formula
an=a1+(n-1)d where n is the term number and d is the common difference
an = -33 + ( n-1) 6
an = -33 +6n -6
an = -39+6n
recursive formula
an+1 = an +6
10th term
n =10
a10 = -39+6*10
= -39+60
=21
sum formula
see image
The sum will diverge since we are adding infinite numbers
If Q(x)=x2−6x−2, find Q(−4).
Answers
Answer:
Q(-4) = 38Step-by-step explanation:
Q(x)=x² − 6x − 2
To find Q(−4) substitute the value of x which is - 4 into Q(x)
That's
Q(-4) = (-4)² - 6(-4) - 2
Q(-4) = 16 + 24 - 2
We have the final answer as
Q(-4) = 38Hope this helps you
Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.
Answers
Correction:
P(AΔB) = P(A) + P(B) - 2P(AnB)
is what could be proven using the axioms of probability, and considering the case of symmetric difference given.
Answer:
P(AΔB) = P(A) + P(B) - 2P(AnB)
Has been shown.
Step-by-step explanation:
We are required to show that
P(AUB) = P(A) + P(B) - 2P(AnB)
directly using the axioms of probability.
Note the following:
AUB = (AΔB) U (AnB)
Because (AΔB) U (AnB) is disjoint, we have:
P(AUB) = P(AΔB) + P(AnB)..................(1)
But again,
P(AUB) = P(A) + P(B) - P(AnB)...............(2)
Comparing (1) with (2), we have
P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)
P(AΔB) = P(A) + P(B) - 2P(AnB)
Where AΔB is the symmetric difference of A and B.
State the correct polar coordinate for the graph shown:
Answers
Answer:
Solution : ( - 8, - 5π/3 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° ) . - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° ) . - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).
