Solve the equation x + 5 = 12. Show and justify each step you take to solve the equation. x + 5 = 12 Write the equation. = 12 x + 5 Х X = Coning is not nermitted.
Answers
Answer:
7
Step-by-step explanation:
x+5=12
x=12-5
x=7
Related Questions
The student council at a large high school is wondering if Juniors or Seniors are more likely to attend Prom. They take a random sample of 40 Juniors and find that 18 are planning on attending Prom. They select a random sample of 38 Seniors and 19 are planning on attending. Do the data provide convincing evidence that a higher proportion of Seniors are going to prom than Juniors? Use a 5% significance level. What is the p-value? Round to two decimal places. O 0.33 0.21 O 0.56
Answers
The data provide convincing evidence that a higher proportion of Seniors are attending prom compared to Juniors. The p-value is 0.33.
To determine if a higher proportion of Seniors are attending prom compared to Juniors, we can conduct a hypothesis test using the given data. Let's set up the hypotheses:
Null hypothesis (H0): The proportion of Juniors attending prom is equal to or higher than the proportion of Seniors attending prom.
Alternative hypothesis (Ha): The proportion of Seniors attending prom is higher than the proportion of Juniors attending prom.
To test this, we can use a two-sample proportion z-test. First, let's calculate the proportions of Juniors and Seniors attending prom:
Proportion of Juniors attending prom: 18/40 = 0.45
Proportion of Seniors attending prom: 19/38 = 0.50
Next, we calculate the standard error of the difference in proportions:
SE = \(\sqrt{[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]}\)
SE = \(\sqrt{[(0.45 * 0.55 / 40) + (0.50 * 0.50 / 38)]}\)
SE ≈ 0.090
We can now calculate the test statistic (z-score):
z = (p1 - p2) / SE
z = (0.45 - 0.50) / 0.090
z ≈ -0.56
Looking up the z-score in the z-table, we find that the p-value associated with -0.56 is approximately 0.33. Since the p-value (0.33) is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have convincing evidence to conclude that a higher proportion of Seniors are attending prom compared to Juniors.
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If <1 = 140°, then
<2=
Answers
Answer:
∠ 2 = 140°
Step-by-step explanation:
∠ 1 and ∠ 2 are alternate exterior angles and are congruent , so
∠ 2 = ∠ 1 = 140°
Please help if you can.
Answers
Answer:
I’m not sure :/
Step-by-step explanation:
explain how you solved 72 ÷ 8 pls
Answers
If you multiply 8*9 you get 72
Help please !!!!!!!!!
Answers
Answer: (a): Good course, (b): Bad course
Step-by-step explanation:
Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.
Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.
Let A be a n x n matrix and let B = I - 2A + A²
a.) Show that if x is an eigenvector of A belonging to an eigenvalue α of A, then x is also an eigenvector of B belonging to an eigenvalue µ of B. How are ? and µ related?
b.) Show that if α = 1 is an eigenvalue of A, then the matrix B will be singular.
Answers
We assume that x is an eigenvector of A corresponding to an eigenvalue α of A. So, Ax = αx.Let's apply B to x:
Bx = (I - 2A + A²)x = Ix - 2Ax + A²x = x - 2αx + A(αx) = (1 - 2α + α²)x.
a.) We assume that x is an eigenvector of A corresponding to an eigenvalue α of A. So, Ax = αx.Let's apply B to x:
Bx = (I - 2A + A²)x = Ix - 2Ax + A²x = x - 2αx + A(αx) = (1 - 2α + α²)x.
So, we have: Bx = µx, where µ = (1 - 2α + α²). Therefore, x is an eigenvector of B belonging to an eigenvalue µ of B. The relations between α and µ are as follows: µ = (1 - 2α + α²) = (α - 1)².
b.) We need to show that if α = 1 is an eigenvalue of A, then the matrix B will be singular, or in other words, det(B) = 0.So, we have:B = I - 2A + A². Substituting α = 1, we have:
B = I - 2A + A² = I - 2I + I = 0. (since A is n x n and I is the n x n identity matrix).
Therefore, det(B) = 0 which means B is singular.
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(c) A non-uniform but spherically symmetric charge distribution has a charge density: rho(r)=rho 0
(1−r/R)
rho(r)=0
for r≤R
for r>R
where rho 0
=3Q/πR 3
is a positive constant. Show that the total charge contained in this charge distribution is Q. [4] Show that the electric field in the region r>R is identical to that created by a point charge Q at r=0 [2] Derive an expression for the electric field in the region r≤R. [5]
Answers
To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:
ρ(r) = ρ₀(1 - r/R) for r ≤ R,
ρ(r) = 0 for r > R,
where ρ₀ = 3Q/πR³.
To find the total charge, we integrate ρ(r) over the volume:
Q = ∫ρ(r) dV,
where dV represents the volume element.
Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.
The integral becomes:
Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.
Evaluating this integral gives:
Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.
Simplifying further, we get:
Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].
Simplifying the expression inside the parentheses:
Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].
Simplifying once more:
Q = ρ₀ * π * (R³ - R³/3),
Q = ρ₀ * π * (2R³/3),
Q = (3Q/πR³) * π * (2R³/3),
Q = 2Q.
Therefore, the total charge contained in the charge distribution is Q.
To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.
By Gauss's law, the electric field through a closed surface is given by:
∮E · dA = (1/ε₀) * Qenc,
where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.
Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.
For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q,
Simplifying:
E = Q / (4πε₀r²).
This is the same expression as the electric field created by a point charge Q at the origin (r = 0).
To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.
The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.
By Gauss's law, we have:
∮E · dA = (1/ε₀) * Qenc.
Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q.
Simplifying:
E = Q / (4πε₀r²).
This expression represents the electric field inside the charge distribution for r ≤ R.
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Misty correctly determined the equation of the linear function represented by the table of values below to be in slope-intercept form by using the ordered pairs (1, 7) and (2, 5). x y 1 7 2 5 3 3 4 1 What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
Answers
Answer:
y=-2x+9
Step-by-step explanation:
The diagram below is an oblique, or slanted, rectangular prism. Not all angles shown are 90 degrees. Complete the following sentence.
Answers
Answer:
Oblique rectangular prism
Could i get some help with these math questions?
Answers
69 ayyy lol
help me please and thank you
Answers
Answer: A, C, 57
Step-by-step explanation:
I multiply by 0.40 for the first one, and then multiply by 1.0625. 0.40 = 40% and multiplying by 1.0625 is the same as adding 6.25%. For the second, I multiply by 0.70 because that is 70%. For the last, I multiply by 0.95 for the same reason.
Rashad evaluated the power. (−2 10 )4 His value is 8 40. Is he correct? If not, what was his mistake? Yes, he is correct. No, his value should be negative. No, he multiplied the exponent by the base. No, he used the base as the exponent.
Answers
The evaluated result of the given number is 1/625 and not the 840 Thus the evaluated value of the Rashad is not correct, because he multiplied the exponent by the base.
What is the power rule of exponents?Power rule of exponents states that, when the two numbers with same base are multiplied then the exponents of both the numbers added.
Positive power of the negative number gives the positive result.
Given information-
The number which is evaluated by the Rashad is,
\((\dfrac{-2}{10})^4\)
Let the evaluated result of the number is n. Thus,
\(n=(\dfrac{-2}{10})^4\)
As the power is out of the bracket. This indicates that the power is for both numerator and denominator. Thus,
\(n=\dfrac{(-2)^4}{10^4}\)
Positive power of the negative number gives the positive result. Thus the above equation can be written as,
\(n=\dfrac{2\times2\times2\times2}{10\times10\times10\times10}\)
\(n=\dfrac{1}{625}\)
As the evaluated result of the given number is 1/625 and not the 840 Thus the evaluated value of the Rashad is not correct, because he multiplied the exponent by the base.
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Answer:
No, he multiplied the exponent by the base.
Step-by-step explanation:
Determine if the product CA is defined, state it’s dimensions not the product
Answers
Answer:
Dimensions of the product matrix = (3 × 3)
Step-by-step explanation:
If matrix P having dimensions (m × n) and matrix Q having dimensions (n × r) are multiplied,
Dimensions of the product matrix PQ will have the dimensions as (m × r).
That means product of the two matrices are defined when columns of first matrix P is equal to the rows of the second matrix Q.
Following this rule,
Dimensions of matrix A = (2 × 3)
[ Rows × Columns]
Dimensions of matrix B = (3 × 3) [Rows of B = 3, columns of B = 3]
Dimensions of matrix C = (3 × 2) [Rows of C = 3, columns of C = 2]
Since columns of C and rows of A are equal.
Therefore, product of C and A is defined.
Product of the matrices C & A will have the dimensions as (3 × 3).
Determine whether an observational or experimental study is appropriate to address the following statement. A car wash operator wants to identify if providing a discount for local residents will generate additional revenue. Answer 2 Points K Observational Experimental
Answers
This is an experimental research since the car wash owner will provide various discounts and then watch the extra money come in.
what is discount?The discrepancy between the purchase price and the face value is the amount of the discount. A rebate is a specific kind of cost reduction or deduction for a product. An amount or percentage off the regular retail cost of an item or service is known as a rebate. You could be given the option to get, as an illustration, a $10 or 10% discount off the product's advertised price. a decrease in the overall quantity or value of something (see gross entry 1 for further information). Regular or routine price reductions. Give your clients a 10% discount.
This is an experimental research since the car wash owner will provide various discounts and then watch the extra money come in.
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Solve for k.
6 + -4k = 18
k=
Answers
k=-3
6*(-4k)=18
subtract 6 from both sides
-4k=12
divide by -4 on both sides
k=-3
Answer:
\( \sf \: k = - 3\)
Step-by-step explanation:
Now we have to,
→ Find the required value of k.
The equation is,
→ 6 + (-4k) = 18
Then the value of k will be,
→ 6 + (-4k) = 18
→ 6 - 4k = 18
→ -4k = 18 - 6
→ -4k = 12
→ k = 12 ÷ (-4)
→ [ k = -3 ]
Hence, the value of k is -3.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n=56, x=30; 95% confidence
A. 0.426
Answers
The 95% confidence interval for the population proportion is approximately 0.3573 to 0.7141. None of the given options (A, B, C, D) match the calculated interval.
To construct a confidence interval for the population proportion, we can use the formula:
Confidence Interval = sample proportion ± critical value * standard error
Where the sample proportion (p-hat) is calculated by dividing the number of successes (x) by the total sample size (n). In this case, n = 56 and x = 30, so the sample proportion is 30/56 = 0.5357.
The critical value is determined based on the desired degree of confidence. For a 95% confidence level, which is given in this case, the critical value can be obtained from a standard normal distribution. For a two-tailed test, the critical value is approximately 1.96.
The standard error is calculated by taking the square root of (p-hat * (1 - p-hat) / n). Plugging in the values, we get sqrt(0.5357 * (1 - 0.5357) / 56) = 0.0907.Now, we can construct the confidence interval:Confidence Interval = 0.5357 ± 1.96 * 0.0907Calculating the upper and lower bounds of the interval:
Lower bound = 0.5357 - (1.96 * 0.0907) ≈ 0.3573
Upper bound = 0.5357 + (1.96 * 0.0907) ≈ 0.7141\
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In the relation (a+c)^2=t make C the subject
Answers
Answer:
See below
Step-by-step explanation:
(a+c)^2 = t
(a+c) = sqrt t
c = sqrt(t) - a
If f(x)=16x-30 and g(x)=14x-6, for which value of x does (f-g)(x)=0?
12
13
14
Answers
The value of x for which (f - g)(x) = 0 is x = 12.
To find the value of x for which (f - g)(x) = 0, we need to subtract g(x) from f(x) and set the resulting expression equal to zero. Let's perform the subtraction:
(f - g)(x) = f(x) - g(x)
= (16x - 30) - (14x - 6)
= 16x - 30 - 14x + 6
= 2x - 24
Now, we can set the expression equal to zero and solve for x:
2x - 24 = 0
Adding 24 to both sides:
2x = 24
Dividing both sides by 2:
x = 12
Therefore, the value of x for which (f - g)(x) = 0 is x = 12.
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Complete the sequence.
1/2,3/5,5/8,7/11, ___ , ____
(will mark brainliest)
Answers
Answer:
1/2,3/5,5/8,7/11,9/14,11/17
Explanation:
Each time, the numerator of the fraction goes up by 2 and the denominator goes up by 3.
Answer:
9/14, 11/17
Step-by-step explanation:
The pattern observed is :
Numerator increases by 2Denominator increases by 3Hence, the next 2 terms are :
9/14, 11/17Solve for y. I REALLY NEED HELP ON THIS!! 2(3y+6x)=2(5y-2x)
Answers
Answer:
y = 4x
Step-by-step explanation:
2(3y + 6x) = 2(5y - 2x)
Divide both sides by 2.
3y + 6x = 5y - 2x
Subtract 5y from both sides. Add 2x to both sides.
-2y = -8x
Divide both sides by -2.
y = 4x
Someone help me…….:///
Answers
Answer:
x's value is 12 while y's value is 6.
Step-by-step explanation:
now construct an equation that has solutions y=e−7x cos(5x) and y=e−7x sin(5x):
Answers
An equation with solutions y = e^(-7x) cos(5x) and y = e^(-7x) sin(5x) is y = e^(-7x) √(2) sin(5x + pi/4)
Let's start by noting that the sum of a sine and cosine function can be expressed as a single sine or cosine function with appropriate phase shift. Specifically, we have:
cos(x) + sin(x) = √(2) sin(x + pi/4)
Using this identity, we can write:
y = e^(-7x) cos(5x) + e^(-7x) sin(5x)
= e^(-7x) (cos(5x) + sin(5x))
= e^(-7x) √(2) sin(5x + pi/4)
Thus, an equation with solutions y = e^(-7x) cos(5x) and y = e^(-7x) sin(5x) is:
y = e^(-7x) √(2) sin(5x + pi/4)
We can verify that this equation indeed has the desired solutions by plugging them in:
y = e^(-7x) √(2) sin(5x + pi/4)
= e^(-7x) √(2) sin(5x + pi/4)
= e^(-7x) √(2) [sin(5x) cos(pi/4) + cos(5x) sin(pi/4)]
= e^(-7x) √(2) [cos(5x) + sin(5x)]
= e^(-7x) cos(5x) + e^(-7x) sin(5x)
Therefore, we have successfully constructed an equation with the given solutions.
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Use the models of f(x) and g(x) to compare the two functions. F(x)={3x+4, x≤1 1/3x+8, x>1
Answers
The functions f(x) and g(x) are defined differently based on the value of x. For x less than or equal to 1, f(x) is equal to 3x + 4, while for x greater than 1, f(x) is equal to (1/3)x + 8. This indicates that the two functions have different rules or formulas depending on the value of x.
The function f(x) is defined piecewise, meaning it has different expressions for different intervals of x. For x less than or equal to 1, f(x) is given by 3x + 4. This means that for values of x in this range, the function f(x) will produce outputs according to the equation 3x + 4. On the other hand, for x greater than 1, f(x) is given by (1/3)x + 8.
This means that for values of x in this range, the function f(x) will produce outputs according to the equation (1/3)x + 8. The difference in the rules or formulas for f(x) depending on the value of x distinguishes it from a typical linear function.
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Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. the table below shows the information about the two credit cards brandon currently uses. card a card b amount $1,463.82 $1,157.98 apr 13% 17% monthly payment $24.60 $22.14 after 8 years, how much will brandon have saved in interest by consolidating the two balances? a. $581.76 b. $194.40 c. $256.32 d. $325.44 please select the best answer from the choices provided. a b c d
Answers
The amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.
What is monthly payment?Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.
It can be calculated with the following formula.
\(M=P\left (\dfrac{r}{1-(1+r)^{-nt}}\right)\)
Here, (P) is the principal amount, (r) is the interest rate and (t) is time.
Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate.
The table below shows the information about the two credit cards Brandon currently uses.
Cards Amount APR Monthly PaymentCard a $1,463.82 13% $24.60Card b $1,157.98 17% $22.14
Interest rate for the card a is,
\(r=\dfrac{13}{12\times100}=0.01083\)
The time period is 8 years and there are 12 months in one year. Thus, the monthly payment of card A will be,
\(M=1157.98\left (\dfrac{0.01083}{1-(1+0.01083)^{-12(8)}}\right)\\M=19.47\)
In the 8 years, there is total 96 monthly payments. Thus, the total payment by card A is,
\(P_a=19.47\times96=1869.12\)
For the card B the monthly payment is $22.14. Thus the total payment by card B is,
\(P_b=22.14\times96=2125.44\)
The difference in the payment is,
\(d=2125.44-1869.12\\d=256.12\)
Hence, the amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.
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Answer:
C. 256.32
Step-by-step explanation:
Daniella has 3/4 cup of flour. She is making cookies that need 1/8 cup of flour for each batch. How many batches of cookies can she make?
(Just tell me the answer :)
Answers
Answer:
6
Step-by-step explanation:
3/4 = 6/8, if every batch needs 1/8, then she can make 6 batches
A fraction is a way to describe a part of a whole. The number of batches of cookies that Daniella can make is 6.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Given that Daniella has 3/4 cup of flour and She needs 1/8 cup of flour for each batch. Therefore, we can write,
Number of batches of cookies = Total flour Daniella / Flour needed for a batch
Number of batches of cookies = 3/4 cups of flour / 1/8 cup of flour
= (3/4) / (1/8)
= 6 batches
Hence, the number of batches of cookies that Daniella can make is 6.
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Simplify (6w) ^2 ?!!!!!! Help please
Answers
Answer:
\(36(w^{2})\)
What is 108 as a fraction of 648? Give your answer in its simplest form.
Answers
Answer:
The simplest form of 108/648 is 16
For the given condition 108 as a fraction of 648 will be 108/648.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have to write 108 as a fraction of 648, in simplified form.
p as the fraction of q in the simplified form can be written as,
=p/q
For the given condition we have to write the 108 as a fraction of 648 in the simplified form.
Write the fraction's numerator, hyphenate it, and then spell out the denominator to represent it verbally. The phrase p/q would be used to represent the fraction 108/648.
Thus, for the given condition 108 as a fraction of 648 will be 108/648.
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The sum is 16 and the difference is 12 what is the answer
Answers
Answer:
14 and 2 maybe?
Answer:
14, 2
Step-by-step explanation:
a + b = 16
a - b = 12
------------------
2a = 16 + 12
2a = 28
a = 14
14 + b = 16
b = 2
f(x) = square root 32x
g(x) = square root 2x
Answers
Given:
The two functions are:
\(f(x)=\sqrt{32x}\)
\(g(x)=\sqrt{2x}\)
To find:
The \((f\cdot g)(x)\). Assume \(x\geq 0\).
Solution:
We have,
\(f(x)=\sqrt{32x}\)
\(g(x)=\sqrt{2x}\)
Now,
\((f\cdot g)(x)=f(x)\cdot g(x)\)
\((f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}\)
\((f\cdot g)(x)=\sqrt{32x\times 2x}\)
\((f\cdot g)(x)=\sqrt{64x^2}\)
\((f\cdot g)(x)=8x\)
Therefore, the correct option is A.
i solved the problem i just don’t know what n cannot equal to
Answers
Recall that:
\(\begin{gathered} \text{If b}\ne0\text{ we get that:} \\ \frac{ab}{cb}=\frac{a}{c}\text{.} \end{gathered}\)Notice that:
\(\begin{gathered} 20n-16=4(5n-4), \\ 4n^2-4n^3=4n^2(1-n)=-4n^2(n-1), \\ 10n-10=10(n-1)\text{.} \end{gathered}\)Therefore:
\(\frac{20n-16}{5n-4}\cdot\frac{4n^2-4n^3}{10n-10}=\frac{4(5n-4)}{5n-4}\cdot\frac{-4n^2(n-1)}{10(n-1)}\text{.}\)Assuming that 5n-4≠0 and n-1≠0 we get:
\(\frac{4(5n-4)}{5n-4}\cdot\frac{-4n^2(n-1)}{10(n-1)}=4\cdot\frac{-4n^2}{10}\text{.}\)Simplifying the above result we get:
\(4\cdot\frac{-4n^2}{10}=-\frac{8n^2}{5}\text{.}\)Now, the restrictions are 5n-4≠0 and n-1≠0, therefore:
\(\begin{gathered} 5n-4\ne0\rightarrow5n\ne4\rightarrow n\ne\frac{4}{5}, \\ n-1\ne0\rightarrow n\ne1. \end{gathered}\)Answer:
\(\begin{gathered} -\frac{8n^2}{5}, \\ \text{For }n\ne1\text{ and }n\ne\frac{4}{5}. \end{gathered}\)