Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
[tex]4 + 2x = 4x - 20[/tex]
[tex]4 + 20 = 4x - 2x[/tex]
[tex]24 = 2x[/tex]
[tex]x = \frac{24}{2} [/tex][tex]x = 12[/tex]
Hope it is helpful....(8-16) + (8 + 6)
If the parentheses are removed from the above
expression, how will the value of the expression
change?
A. no change
B. increase of 3
C. increase of 7
D. increase of 12
E. increase of 16
Step-by-step explanation:
Right now, we would solve everything within the parenthesis first.
(8 - 16) + (8 + 6)
(-8) + (14)
14 - 8
6
But if we remove the parenthesis, it doesn't matter what order we do things in.
8 - 16 + 8 + 6
8 + 8 - 16 + 6
16 - 16 + 6
6
The reason why both of these are the same, is because the only calculations we're doing are addition and subtraction, which don't care about parenthesis.
Answer:
A
plss i reallly need help
Answer:
7x^2 +7x
------------------
x^2 -9
Step-by-step explanation:
7x (x+1)
------- * ----------
(x+3) (x-3)
Multiply
7x^2 +7x
------------------
x^2 +3x-3x-9
7x^2 +7x
------------------
x^2 -9
Answer:
7x^2 +7x / x^2 -9
Step-by-step explanation:
the tub started with gallons of water
Answer:
huh?
Step-by-step explanation:
mr.brown can type 80 words in two minutes. how many words can he type in 40 minutes?
Answer:
Step-by-step explanation:
after how many years will Rs 21000 give Rs 5040 as interest at 6% pa simple interest
Answer:
within 4 years it will give the required interest
Element X is a radioactive isotope such that every 42 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 50 grams, how long
would it be until the mass of the sample reached 45 grams, to the nearest tenth of a
year?
Answer:
6.38548 years
Step-by-step explanation:
1 = 2 [tex]e^{42k}[/tex]
1/2 = [tex]e^{42k}[/tex]
ln(1/2) = 42k ln(e)
ln(1/2)/42 = k
k = -0.01650
~~~~~~~~~~~~~~
45 = 50 [tex]e^{-0.01650t}[/tex]
45/50 = [tex]e^{-0.01650t}[/tex]
ln(45/50) = -0.01650 t ln(e)
ln(45/50)/ -0.01650 = t
t = 6.38548 years
The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years
What is half-life of an element?The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the number of years be t
Let the initial mass of the element be a = 50 grams
The final mass of the element be ( a - x ) = 45 grams
Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half
And , half life t½ = 42 years
So , the decay constant k = 0.693/t½
k = 0.693 / ( 42 )
k = 0.0165
And , k= 2.303/t {log (a/a-x)}
So , t = 2.303 / ( 0.0165 ) log ( 50/45 )
On simplifying , we get
t = 6.384129 years
Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years
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The function fx) = 5 reflected over the y-axis. Which equations represent the reflected function? Select two
Answer:
y=5
Step-by-step explanation:
f(x) =5 is a line with the equation y=5
when reflected over the y-axis is still y= 5, because we reflected on to itself.
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate. A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is:
Answer:
The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).
Step-by-step explanation:
Before building the confidence interval, the central limit theorem and subtraction of normal variables is explained.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Northern half:
1062 out of 2000, so:
[tex]p_N = \frac{1062}{2000} = 0.531[/tex]
[tex]s_N = \sqrt{\frac{0.531*0.469}{2000}} = 0.0112[/tex]
Southern half:
900 out of 2000, so:
[tex]p_S = \frac{900}{2000} = 0.45[/tex]
[tex]s_S = \sqrt{\frac{0.45*0.55}{2000}} = 0.0111[/tex]
Distribution of the difference:
[tex]p = p_N - p_S = 0.531 - 0.45 = 0.081[/tex]
[tex]s = \sqrt{s_N^2 + s_S^2} = \sqrt{0.0112^2 + 0.0111^2} = 0.0158[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.081 - 1.96*0.0158 = 0.05[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.081 + 1.96*0.0158 = 0.112[/tex]
The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).
12
Use upper rectangles with areas equal to
Marks: 1
Area = f(x) · A3
to estimate the area under the curve of f(x) = x, on the interval from (1,3). Partition the interval into four subintervals. Hint:
Area = (F(1.5) + f(2) + f(2.5) + f(3))Ar = (1.53 +23 +2.53 +33)Az, where Ax =
Choose one answer.
ST
3-1
4
a. 35
b. 42
c. 27
d d. 19
Answer:
42
Step-by-step explanation:
Last month, Nate spent 12 % of his paycheck on
car repairs and 25 % of the remainder on food.
He gave $ 1,320 of the remaining money to his
parents and then bought a computer on sale. If
the usual price of the computer was $ 825 and
the discount was 20 %, how much money did
Nate have in the beginning?
Nate had $3000 at the beginning.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let the original amount of money is P
Nate spent 12 % of his paycheck on car repairs
⇒ 12% of P = 12P/100
And he spent 25 % of the remainder on food.
⇒ 0.25(88/100)P
He gave $ 1,320 of the remaining money to his parents
⇒ 1320
If the usual price of the computer was $ 825 and the discount was 20 %
⇒ 825 - 0.20(825) = 660
P = 12P/100 + 0.25(88/100)P + 1320 + 660
P - 34P/100 = 1980
100P - 66P = 198000
P = 3000
Hence, Nate had $3000 at the beginning.
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solve for x the triangles are the same
Answer: x=8
Step-by-step explanation:
So to begin with we need to find the connection being that they are the same triangle but with a dilation. We need to find the dilation by matching the new angles with each other H=E F=C and D=G. We need to find the relation ship between CD and FG. 65 divided by 24= 2.6 take ED and multiply 2.6 to find HG. HG= 91. Now we need to find x. 8 times x+ 3=91. Find the closest eight multiple to 91 which is 8 times 8= 88 and add 3 to see it makes 91.
8 is your answer.
you hold a sale for $5 sandwiches at your restaurant.you end up selling 359 sandwiches to 245 customers
A. how much money do you have in sandwich sales?
B. how many sandwiches per customer did you sell ?
Answer:
A. $1795
B. 7
Step-by-step explanation:
Given the following data;
Cost price, Cp = $5
Number of sandwiches sold, Ns = 359 sandwiches.
Number of customers, Nc = 245 customers.
a. To find how much money you have in sandwich sales;
Total amount of money = Cp * Ns
Total amount of money = 5 * 359
Total amount of money, T = $1795
B. To find how many sandwiches per customer did you sell;
Sandwiches per customer = T/Nc
Sandwiches per customer = (1795/245
= 7.33 ≈ 7
pls look at the image and solve all.
Answer:
Solution of question number 23
Step-by-step explanation:
Given,
5a - 12
= 5 × 12
= 15 - 12
= 3 answer
Find the value of each measure.
The two congruent base angles tell us that this is an isosceles triangle, meaning the triangle has two congruent sides. Therefore, we can set these two expressions equal to each other and solve from there.
15x + 7 = 23x - 17
7 = 8x - 17
8x = 24
x = 3
Side = 15(3) + 7 = 45 + 7 = 52
Hope this helps!
A rectangle with an area of 3990 cm2 is x centimeters wide and (x+4) centimeters long. To the nearest tenth of a centimeter, the width and length are
Answer: width:60.2 cm
Length: 64.2 cm
Step-by-step explanation:
Given
The area of the rectangle is [tex]3990\ cm^2[/tex]
Width of the rectangle is [tex]x\ cm[/tex]
Length of the rectangle is [tex]x+4\ cm[/tex]
Area of the rectangle is the product of length and width
[tex]\therefore 3990=(x+4)x\\\Rightarrow 3990=x^2+4x\\\Rightarrow x^2+4x-3990=0\\\Rightarrow x=60.198\ or\ -65.198\ cm\\\text{Neglecting negative term}\\\Rightarrow x=60.198\approx 60.2\ cm[/tex]
Width of the rectangle is [tex]60.2\ cm[/tex]
Length of the rectangle is [tex]60.2+4=64.2\ cm[/tex]
the product of 2x and 3 is 138. find the number x
Answer:
x = 23
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3(2x) = 138
Step 2: Solve for x
Simplify: 6x = 138[Division Property of Equality] Divide 6 on both sides: x = 23instruction Find m<LMN
Answer:
∠ LMN = 70°
Step-by-step explanation:
The tangent- secant angle LMN is half the difference of the measures of the intercepted arcs, that is
∠ LMN = [tex]\frac{1}{2}[/tex] (NK - NL) = [tex]\frac{1}{2}[/tex] (210 - 70)° = [tex]\frac{1}{2}[/tex] × 140° = 70°
how do i know when an equation has 1 solution
Answer:
you can plug it back into the original equation to see if it fits the solution. if not then you have another solution you need to solve for.
Answer:
if we're talking on linear equations, then the two equations would intersect at one point. or when you solve it, it'll be only 1 number that can fit that equation.
p.s.: sub to #gauthmath# sub reddit if ya can ^^
PLEASE FAST lenear equations
Answer:
y = 43
Step-by-step explanation:
(y-4)/3 = (y+9)/4
4(y-4) = 3(y+9)
4y-16 = 3y+27
4y-3y = 27+16
y = 43
The area of a segment of a circle is the area of the corresponding sector of the circle _____ the area of the corresponding triangle.
Answer:
The area of a segment of a circle is the area of the corresponding sector of the circle minus the area of the corresponding triangle.
Step-by-step explanation:
We know area of segment of a circle is the area of the corresponding sector of the circle minus the area of the corresponding triangle.
Find the value of n. A. 10 B. 6 C. 50 D. 25
find the measure of the indicated angle to the nearest degree
Answer:
28°
Step-by-step explanation:
sin ? = 19/41
? = arcsin (19/41)
? = 28° (rounded to the nearest degree)
Answered by GAUTHMATH
how do i convert y = 6x into y = mx + b form?
Answer:
it already is in that form
y = 6x
technically Y = 6x + 0 could be the answer...
but in math we tend to not rite "obvious" information
to reduce clutter and confusion
+1[tex]x^{1}[/tex] is technically correct but we drop the + sign for positive numbers
and also drop the exponent if it is a 1 ... similarly
+1[tex]x^{1}[/tex] + 0 + 0 + 0 would also be silly and we don't write the zeros
+1[tex]x^{1}[/tex] + 0 + 0 + 0 = x
Step-by-step explanation:
ILL GIVE POINTS!!
Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is pi/3 What is the length of the third side of the
triangle?
A. sqrt13
B. 4sqrt3
C. sqrt3
D. 3
Answer:
no A
Step-by-step explanation:
sqrt13 is the ans
hope it helps
What is the difference quotient for the function f(x) = 8/ 4x + 1
Answer:
Last option (counting from the top)
Step-by-step explanation:
For a given function f(x), the difference quotient is:
[tex]\frac{f(x + h) - f(x)}{h} = \frac{1}{h}*(f(x + h) - f(x))[/tex]
In this case, we have:
[tex]f(x) = \frac{8}{4x + 1}[/tex]
Then the difference quotient will be:
[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1})[/tex]
Now we should get a common denominator.
We can do that by multiplying and dividing each fraction by the denominator of the other fraction, so we will get:
[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1}) = \frac{1}{h}*(\frac{8*(4x + 1)}{(4(x + h) +1 )*(4x + 1)} - \frac{8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)})[/tex]
Now we can simplify that to get:
[tex]\frac{1}{h}*\frac{8*(4x + 1) - 8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)}} = \frac{1}{h}*\frac{-32h}{(4(x + h) +1 )*(4x + 1)}} = \frac{-32}{(4(x + h) +1 )*(4x + 1)}}[/tex]
Then the correct option is the last one (counting from the top)
Two standard dice are rolled together. What is the probability of rolling a sum less than 7 or a sum divisible by 5?
Answer:
Sum less than: 7 (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,5), (,4,1), (4,2), & (5,1)
Sum divisible by 5 (1,4), (2,3), (3,2), (4,1)
The equation of a line is y = 2x + 3. What is the equation of the line that is parallel to the first line and passes through (2, –1)?
A.
4x – 2y = –6
B.
y = 2x – 5
C.
y = 3x + 4
D.
2x + y = –1
Answer:
i think the answer is y = 3x + 4
Step-by-step explanation:
:)
Find the measure of each angle indicated.
A) 87°
C) 130°
B) 25°
D) 105°
Find the common ratio of the geometric sequence 17, -51, 153, ...
Answer:
an = 17 ( − 3 ) n − 1
Step-by-step explanation:
Use the formula an = a 1 r n − 1 to identify the geometric sequence.
Number 14 please and thank you so much
Answer:
0.13
Step-by-step explanation:
N(s)=310+276+155+445
=1186
P=155:1186
=0.13
