The value of the exponential function when x = 2 is 64
Exponential functionsThe standard form of exponential equation is expressed as y = ab^x
Given the exponential function expressed as:
f(x) = 2^x
For the value f(6)
f(6) = 2^x
f(6) = 2^6
f(6) = 64
Hence the value of the exponential function when x = 2 is 64
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8. A school cafeteria
purchased 256
hotdogs, 332 apples,
and 154 cookies. How
many items did they
purchase in all?
the school purchased 742 items in total.
Just add 256+332+154
which equals...742. :)
Answer:
742 items
Step-by-step explanation:
Add up all the items that the cafeteria purchased. 256+332+154=742!
Which is the equation in slope-intercept form for the line that passes through (−1, 5) and is parallel to 3x + 2y = 4?
y=−23x+72
y=−32x+72
y=32x−72
y=23x+72
Answer:
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).
Original Equation:
3x + 2y = 4
Subtract 3x from both sides
2y = -3x + 4
Divide both sides by 2
y = -3/2x + 2
Generally any parallel line will be in the form:
[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.
So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b
[tex]5=-\frac{3}{2}(-1) + b[/tex]
Multiply and
[tex]5=\frac{3}{2}+ b[/tex]
Convert 5 into a fraction with a denominator of 2
[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]
Write equation using this form of 5:
[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]
Subtract 3/2 from both sides
[tex]\frac{7}{2}=b[/tex]
Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
Find the range of the parent function below. y = |x| A. all real numbers B. all positive numbers C. all positive numbers and 0 D. all negative numbers
Answer:
c
Step-by-step explanation:
absolute values are positive and abs value of 0 = 0
Solve
f(x)= 2x -13
g(x) = x^2 - 6x + 3
Answer:
just hey effect me II rieirjttjhg shewtha
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
49^2m-m : Not equivalent
7^2m-2m : Not equivalent
7^2m-m : Not equivalent
This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.
For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.
Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.
Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.
But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!
Hope this helped!
please help me im d-mb
Answer:
5621 years
Step-by-step explanation:
Plug everything in first.
[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]
Round to closest amount of years = 5621 years
Determine the equation of the linear function that generates the following table of values.
Answer:
y = -19x + 14
Step-by-step explanation:
For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14
If m∠B = 14°, and m∠D = 49°, what is m∠BEA?
Answer:
117 degrees
Step-by-step explanation:
There are red and blue files in a box. The ratio of red to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box? There are red and blue files in a box . The ratio of red to blue tiles is 3 : 5 . There are 12 more blue tiles than red tiles in the box . How many red tiles are in the box ?
The number of red tiles in the box given the chance ratio of red to blue tiles is 18
RatioNumber of red tiles = xNumber of blue tiles = 12 + xTotal tiles = x + 12 + x= 12 + 2x
Ratio of red = 3Ratio of blue = 5Total ratio = 3 + 5 = 8Number of red tiles = 3 / 8 × 12+2x
x = 3(12 + 2x) / 8
x = (36 + 6x) / 8
8x = 36 + 6x
8x - 6x = 36
2x = 36
x = 36/2
x = 18 tiles
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Answer: 28
Step-by-step explanation:
The following are the temperatures in
°C for the first 12 days of January:
-5.5, 6, -1.5, 3, 4, -2.5,
0, 6.5, -3, 2.5, -1, 5.5
What is the median temperature for
those 12 days?
Give your answer as a decimal.
ABC Check
↑
XI
Answer:
1.25 is the median for the first 12 days in January
Consider a banking system where the Federal Reserve uses required reserves to control the money supply. (This was the case in the U.S. prior to 2008.) Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is demand deposits. To simplify the analysis, suppose the banking system has total reserves of $400. Determine the money multiplier and the money supply for each reserve requirement listed in the following table.
The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 $8,000
10 10 $4,000
What is the money multiplier?The money multiplier is the ratio of the reserve to the money supply.
The formula for determining the money multiplier is 1/r where r is the reserve ratio.
What is the money supply?The money supply is the total amount of money circulating in the commercial banking system.
The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.
Data and Calculations:Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 (1/0.05) $8,000 ($400 x 20)
10 10 (1/0.1) $4,000 ($400 x 10)
Question Completion:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5
10
Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.
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A video game randomly chooses your car color and type. The
probability of getting a red car is 0.20, and the probability of
a getting a convertible is 0.30.
Event A = You get a red car.
Event B = You get a convertible.
A and B are independent events if
• A. The probability of getting a red car or a convertible is 0.06.
O
B. The probability of getting a red convertible is 0.06.
• C. The probability of getting a red car or a convertible is 0.50.
O D. The probability of getting a red convertible is 0.
The correct statement regarding when the events will be independent is given as follows:
B. The probability of getting a red convertible is 0.06.
What are independent events?Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, the probabilities are given as follows:
P(A) = 0.2.P(B) = 0.3.The events will be independent if:
[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]
The intersection of events A and B is a red convertible car, hence the correct option is:
B. The probability of getting a red convertible is 0.06.
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sin A - sin B - sin C=-4cos A 2 .sin B 2 .sin C 2
sinA+sinB+sinC
=2sin(A+B)/2cos(A-B)/2+sin C
=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2
=2cosC/2(cos(A-B)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2
= RHS
z varies directly as x^3 and inversely as y^3. if z=59 when x=8 and y=8, find Z if x=3 and y=4
[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]
Determine the slope of the line that contains the given points
J(-5, -2), K(5, −4)
Answer:
[tex]-\frac15[/tex]
Step-by-step explanation:
Hello!
We can utilize the slope formula to find the slope.
Slope Formula: [tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex]
Remember that a coordinate is written in the form (x,y)
Find the Slope[tex]S = \frac{y_2-y_1}{x_2-x_1}[/tex][tex]S = \frac{-4-(-2)}{5-(-5)}[/tex][tex]S = \frac{-2}{10}[/tex][tex]S = -\frac15[/tex]The slope of the line is [tex]-\frac15[/tex].
Answer:
-1/5
Step-by-step explanation:
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-4 - (-2)) / (5 - (-5))
Simplify the parentheses.
= (-4 + 2) / (5 + 5)
= -2 / 10
Simplify the fraction.
-2/10
= -1/5
This is your slope.
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Prove: m∠TSE + m∠RSO = m∠TSK
Answer:
down there
Step-by-step explanation:
we can see that angel rso and esk are congruent because they are verticle angels.
we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra
Question 6 of 10
If and
A.D
BD B.C
are rational expressions, then:
OA. True
OB. False
The expression a/b ÷ c/d = ad/bc is A. true.
Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.
The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.
Here we have a ,b ,c and d in the form of p/q form.
We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.
so, L.H.S = a/b ÷ c/d
= a/b × 1/(c/d)
= a/b × d/c
= ad/bc
= R.H.S
since L.H.S = R.H.S
a/b ÷c/d = ad/bc
Hence the expression a/b ÷ c/d = ad/bc is A.true.
Your question was incomplete. Please find the missing content here.
If A/B and C/D are rational expressions, then: A/B ÷C/D
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Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:
x + y = 28500 (1)
Also:
(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310
0.1x - 0.04y = 1310 (2)
From equation 1 and 2:
x = 17500, y = 11000
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
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-2+12-2^3 divided by 2^0 times 3
Answer:
The correct answer is -14
Step-by-step explanation:
PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
The Csc θ = [tex]\frac{8}{5}[/tex] is equivalent to which of the following expressions?
A. sin θ = [tex]\frac{5}{8}[/tex]
B. cos θ = [tex]\frac{5}{8}[/tex]
C. tan θ = [tex]\frac{5}{8}[/tex]
D. sin θ = [tex]\frac{8}{5}[/tex]
E. cos θ = [tex]\frac{8}{5}[/tex]
F. tan θ = [tex]\frac{8}{5}[/tex]
Answer:
A. sin θ = 5/8
Step-by-step explanation:
csc θ = 1/sin θ
csc θ = 8/5
1/sin θ = 8/5
sin θ = 5/8
What is the domain of the following relation?
{(-3, -8), (-2, 9), (1, -1), (5,3)}
O {-8, -1, 3, 9}
O {-3, -2, 1, 5}
O (-3, -8)
O {-8, -3, -2, -1, 1, 3, 5, 9}
Answer: {-3, -2, 1, 5}
Step-by-step explanation:
The domain is the set of x-values.
If there are 3 liquids in a Density column, which liquid would be the least dense?
The liquid on the bottom of the column.
The liquid floating on the top.
The liquid in between the liquid on the top of the column and the liquid on the bottom layer of the column.
The liquid that will be the least dense liquid in the density column is; The liquid floating on the top.
How to identify least dense liquid?
The formula for density is;
Density = Mass/Volume
Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.
Thus, this means that the liquid that is most dense will be at the bottom of the liquid.
The liquid that is least dense will be at the top of the liquid.
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Does anyone how to solve this sum? It’s urgent
The required value for the sum is 9580.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
Simplification in mathematics to solve the given condition on its operators.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]
= 9580
The required solution is given as 9580.
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n August 31 of the current year, the assets and liabilities of Gladstone, Inc. are as follows: Cash $27,900; Supplies, $900; Equipment, $8,500; Accounts Payable, $7,300. What is the amount of stockholders’ equity as of August 31 of the current year?
The amount of stockholders’ equity as of August 31 of the current year is $26400.
How to calculate the equity?The owner's equity will be:
= Cash + Supplies + Equipment - Account payable
= 27900 + 900 + 8500 - 7300
= 26400
Therefore, the amount of stockholders’ equity as of August 31 of the current year is
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What is the value of the following radical expression?
Answer:
b.) 2
Explanation:
Given:
[tex]\sf - \sqrt[\sf 5]{\sf -32}[/tex]rewrite knowing 2⁵ = 32, (-2)⁵ = -32
[tex]\sf -\left(\sqrt[5]{(-2)^5}\right)[/tex]simplify, ⁿ√xⁿ = x
[tex]\sf -\left(-2}\right)[/tex]distribute inside parenthesis
[tex]\sf 2[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]
{ Pisces04 }Let [] denote the operation a [] b = a+b - [tex]\frac{ab}{2}[/tex] ....
The only statement that holds for the given operation is Statement II
Operations and numbersGiven the following operartions
a [] b = a+b - ab/2
We need to check the true statement
For the expression x [] (y+z) = x [] y + x [] z
x [] (y+z) = x+y+z - x(y+z)/2
x [] (y+z) = x+y+z - (xy+xz)/2
x [] y +x [] z = x+y - xy/2 +[x+z - xz/2 ]
x [] y +x [] z = x+y+x+z -xy/2 - xz/2
x [] y +x [] z = 2x+y+z - (xy+xz)/2
This shows that the statement I is incorrect
For the second statement
y [] z = y+z - yz/2
x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2
x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4
For the other expression
x [] y = x+y - xy/2
(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2
(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4
This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)
For the third statement
x [] z = x+z - xz/2
y [] z = y+z - yz/2
z [] 0 = z+0 - z(0)/2
z [] 0 = z
x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z
x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2
For the expression (x+y)[] z
(x+y)[] z = (x+y)+z - (xyz)/2
Hence the statement III is not valid
Based on the explanations above, the only statement that holds for the given operation is Statement II
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Which of the following is a true statement
5/6 > 10/12
8/16=1/4
3/4<4/6
11/15<4/5
Answer:
11/15 < 4/5
Step-by-step explanation:
1. 5/6 = 10/12, so the first answer is not correct
2. 1/4 = 4/16, so the second answer is not correct
3. 3/4 = 9/12 and 4/6 = 8/12, so the third answer is not correct
4. 4/5 = 12/15 > 11/15, so this answer is correct
a survey of 504 citizens found that 378 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? (Round to 3 decimal digits)
The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
What is a confidence interval?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We have:
A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
Sample proportion = p = 378/504 = 0.75
q = 1 - p = 1 - 0.75 = 0.25
[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]
[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]
SD = 0.01928
For 95% confidence interval Z value = 1.96
Lower limit = 0.75 - 1.96(0.01928)
= 0.712
Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
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Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire. O14 ft 15 ft 20 ft 29 ft Jason planted and staked a tree . The stakes are 21 ft from the base of the tree . They are connected to wires that attach to the trunk at a height of 20 ft . Find the length of a wire . O14 ft 15 ft 20 ft 29 ft
Answer:
29 ft
Step-by-step explanation:
The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.
a² + b² = c²
(21 ft)² + (20 ft)² = c²
c² = 841 ft²
c = √(841 ft²)
c = 29 ft
Answer: 29 ft
Find the following sums ( for letter C)
Each number in the sum is even, so we can remove a factor of 2.
2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)
Use whatever technique you used in (a) and (b) to compute the sum
1 + 2 + 3 + 4 + ... + 39 + 40
With Gauss's method, for instance, we have
S = 1 + 2 + 3 + ... + 38 + 39 + 40
S = 40 + 39 + 38 + ... + 3 + 2 + 1
2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41
S = 20×21 = 420
Then the sum you want is 2×420 = 840.