It order to find f(5) and f ( -6 ) we just replace x on the equation with
x = 5 and x = -6
In the first case, x = 5
[tex]\begin{gathered} f(x)=2^x \\ f(5)=2^5 \\ =2\cdot2\cdot2\cdot2\cdot2 \\ =32 \end{gathered}[/tex]In the second case, x = -6
[tex]\begin{gathered} f(x)=2^x \\ f(-6)=2^{-6} \\ =\frac{1}{2^6} \\ =\frac{1}{2\cdot2\cdot2\cdot2\cdot2\cdot2} \\ =\frac{1}{64} \end{gathered}[/tex]Answer: f(5) = 32 and f(-6) = 1/64A pair of supplementary angles are in the ratio 4:5.Find the complement of smaller angle .
The complement of the smaller angle of supplementary angles in ratio 4:5 is given by 10 degree.
Given that the supplementary angles are in ratio 4:5.
Let the angles be 4x and 5x respectively.
We know that the sum of supplementary angles is 180 degree.
So, 4x+5x = 180
9x = 180
x = 180/9
x = 20
So the angles are = (20*4),(20*5) = 80,100.
So the smaller angle is 80 degree.
So the complement of the smaller angle is = 90-80 = 10 degree.
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(2+0.4 + 0.6)² I have been stuck on this problem for a while
what is the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence?
the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence is 1.65
A confidence interval is based on the sample statistics and is used to estimate a population parameter.
For example, a sample mean is used to build a confidence interval to estimate the population mean.
the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence is 1.65
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00:00 How many solutions does the equation below have? 2x – 7 + 19 = 6x - 4x + 12 No solution, 1 solution, 2 solutions, Infinitely many solutions
The last equallity is false! Because 0 IS NOT equal to 24, and thus the initial equation has no solution!!!
Un establecimiento vendía café a 5€/kg. Si ahora lo vende a 4,75€/kg, obtener el porcentaje de descuento aplicado. Porfavor es para dentro de 1 hora
El porcentaje del descuento aplicado es del 5%.
¿Como encontrar el porcentaje del descuento aplicado?
Recordar que si aplicamos un descuento de X (sería un porcentaje X) a un precio P, entonces el nuevo precio será:
P' = P(1 - X/100)
En este caso, sabemos que el precio origina es 5€ por kilo, y el precio nuevo es 4.75 € por kilo, reemplazando esos numeros en la ecuación de arriba obtenemos:
4.75 = 5*(1 - X/100%)
4.75/5 = 1 - X/100%
X/100% = 1 - 4.75/5
X = (1 - 4.75/5)*100%
X = 5%
Fue un descuento del 5%.
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Suppose the lake by your house as 198,000 gallons. But its volume grew by 3000 every weekWrite an equation modeling the number of gals in the lake after so many weeks
Given:
The current volume of the lake is 198,000 gallons.
Its volume grew by 3000 gallons every week
To find: An equation modeling the number of gallons in the lake after some weeks.
Explanation:
As we know,
If the growth or decay involves increasing or decreasing by a fixed number, then we must use a linear function.
Here, the increasing rate is 3000.
The current volume is 198,000 gallons.
Thus, the linear function that represents this situation is,
[tex]V=3000w+198000[/tex]Where w represents the number of weeks and V represents the volume.
Final answer:
The equation is,
[tex]V=3000w+198000[/tex]Write the percent as a decimal. Round to the nearest thousandth if the division does not terminate.5/40%=
ANSWER
[tex]0.001[/tex]Given;
[tex]\frac{5}{40}\%[/tex]Firstly, convert to decimal
we have;
[tex]\begin{gathered} \frac{5}{40}\% \\ =0.125\% \\ \end{gathered}[/tex]"Percent" means "per 100" or divide by 100
Hence, we have;
[tex]\begin{gathered} \frac{0.125}{100} \\ =0.00125 \\ \end{gathered}[/tex]now, converting to the nearest thousandth
[tex]\begin{gathered} =0.00125 \\ \equiv0.001 \end{gathered}[/tex][tex]\equiv0.001[/tex]The answer to the nearest thousandth is
[tex]0.001[/tex]what is linear functions and what is non linear functions
Linear functions: Are the ones represented by a line in a graph. Their characteristic is that their equation has the form:
[tex]f(x)=mx+b[/tex]Where m is the slope of the line, and b is the y-intercept of the line.
Some examples of linear functions:
[tex]\begin{gathered} f(x)=3x+2 \\ f(x)=-10x-5 \\ f(x)=9x \end{gathered}[/tex]And some examples of graphed linear functions:
Non-linear functions: Are the functions that have an exponent on the x different from 1, and they are not represented by lines.
Some examples of non-linear functions:
[tex]\begin{gathered} f(x)=x^3+1 \\ f(x)=\frac{1}{x} \end{gathered}[/tex]And some examples of graphed non-linear functions:
You can hike at an average rate of 3 miles per hour. your total hiking distance d (in miles) can be modeled by the function d = 3t where t is the time (in hours) you hike. you plan on hiking for 10 hours this weekend. what would the domain of this situation? (hint: compound inequality)
The domain of the given situation is 0≤t≤10.
Explain domainThe elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain. If a function f: A B exists that maps each element of A to an element of B, then A is the domain, and B is the co-domain. When (a, b) ∈ R, the image of element 'a' under the relation R is supplied by 'b'.
Given, the average hiking rate is 3 miles per hour.
The number of hours you plan hiking for is 10 hours.
Now, as we know that time can't be negative so we know that the domain must have t≥0.
And it is given that you plan to hike for 10 hours so the domain must also have t≤10.
Therefore, the domain of the given situation is 0≤t≤10.
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You deposit $1575 in a bank account that earns 3.75% interest per year for 5 years. How much will the balance be if it's compounded continuously?
the answer is $1899.81
Find the product a²b(2a³b-5ab).
Answer:
Multiply each term in the parentheses by a²b
2a⁵b²- 5a³b²
Answer:
Step-by-step explanation:
[tex]a^2b(2a^3b-5ab)=\\\\2a^3ba^2b-5aba^2b=\\\\2a^{3+2}b^{1+1}-5a^{1+2}b^{1+1}=\\\\2a^5b^2-5a^3b^2[/tex]
Towns K and L are shown on a map.
a) Work out the actual distance
between towns K and L.
b) A third town, M, is 150 km due
South of town K.
Mark M on the map with X.
c) Measure the bearing of town L
from town K.
A)The actual distance between towns K and L is 10 cm .
B) The bearing of town L from town k is 117 degree
What is mean by actual distance?The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.
The following list includes four distance metrics that are maybe the most often employed in machine learning: the Hamming Distance. Distance in Euclid. New York City distance
The distance a number is from 0 on the number line is its absolute value. Because -7 is 7 units away from 0, its absolute value is 7. Because it is 5 units away from 0, the number 5 has an absolute value of 5. Any number that is less than zero is considered to be negative.
Given ,
A)The actual distance between towns K and L is 10 cm .
B) check the photo of my work
C) The bearing of town L from town k is 117 degree
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What is the slope?
A) -5/4
B) 5/4
C)-4/5
D) 4/5
Answer:
A
Step-by-step explanation:
The slope is not increasing y as x is increasing, so you immediately know the slope is negative. The formula is rise/run so the change in y/rise is 5 and the change in x/run is 4. Which allows you to get -5/4
Dane is selling popcorn for a fundraiser. If each bag of popcorn
he sells costs $4.75, what equation can he use to calculate the
total amount of money he has raised if he has sold a number
of bags?
Answer:
Let the number of bags be 3 and the amount, x
1 bag = $4.75
1 bag = $4.753 bags = x
cross-multiply
x = $4.75 × 3
x = $14.25
hence,
3 bags = $14.25
Equation he can use:
Equation he can use:Since the amount for 1 bag is already stated, the number of bags sold is multiplied by the amount for 1 bag to get the amount.
Answer:y=4.72
Step-by-step explanation:
evaluate each sequence's related arithmetic series. 1, 2 and 3 please.
In order to evaluate the sequences, let's find the ratio of each one by subtracting the second term and the first one.
1)
[tex]\begin{gathered} 1,-5,-11,\ldots \\ r=-5-1=-6 \end{gathered}[/tex]Since the ratio is negative, the sequence is decrescent.
2)
[tex]\begin{gathered} 2.5,5.5,8.5,\ldots \\ r=5.5-2.5=3 \end{gathered}[/tex]The ratio is positive, so we have a crescent sequence.
3)
[tex]\begin{gathered} 4.7,8.7,12.7,\ldots \\ r=8.7-4.7=4 \end{gathered}[/tex]The ratio is positive, so we have a crescent sequence.
When 12 is added to half the sum of a number and 8, the result is 40. What is the number?
When 12 is added to half the sum of a number and 8, the result is 40, the number is 48.
Let the number be x.
According to question,
12 + (x + 8)/2 = 40
(x + 8)/2 = 40-12
(x + 8)/2 = 28
x + 8 = 28*2
x + 8 = 56
x = 56 - 8
x = 48
Hence, the number is 48.
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can yall help me with this
Answer:
A. 9 divided by -3
Step-by-step explanation:
-24/8= -3
the only other equation that is equal to -3 is a
Answer:
A
Step-by-step explanation:
This is actually a problem that can be solved without having to do the math for any of these expressions based on the rulings regarding negative numbers in division.
The expression that is provided, -24 / 8 features one negative number and one positive number. With this knowledge, we know the answer should be negative.
A also features just one negative number and one positive, meaning that the answer will be negative.
B and C feature two negative numbers, meaning that the negatives will cancel out and the answer would be positive
D features two positive numbers, meaning that the answer is positive!
With these comparisons, we can affirm that A is the correct answer.
1. The slope of the line
y = x + 17 is ___.
2. The slope of the line
y = x - 7/9 is ___.
Evaluate the numerical expression the quantity 2 to the power of five sixths end quantity over the quantity 2 to the power of one sixth end quantity.
cube root of 4
cube root of 2
square root of 8
square root of 6
2 is the numerical expression when 2 to the power of five sixths.
What are power and exponent?
Exponents and powers are two techniques for simplification of extremely big or extremely small numbers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner. It is claimed that the entire statement 34 has power.In multiplication, a number's power indicates how many times it should be used. Other names for powers include exponents and indices.[tex]2^{5/6} * 2^{1/6}[/tex]
[tex]2^{6/6}[/tex]
2¹
= 2
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|b-8|=2b solve the equation
The answer to the Equation (|b-8|=2b) is b = 8/3
Given Equation-
|b-8|=2b
Subtract 2b from both sides
|b-8|-2b = 2b-2b
Now we will simplify it by rearranging and combining like terms
we get,
-2b + |b-8| = 0
split the problem into two cases: one positive and one negative
-2b + b-8 = 0 --eqn 1
-2b - (b-8) = 0 --eqn 2
now solve equation 1 and combine like terms
we get,
-b - 8 = 0
b= -8
equation 2
we get,
-3b=-8
b=8/3
Remove invalid solution
that is b = -8
The answer to the Equation (|b-8|=2b) is b = 8/3
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A basketball player makes 95 out of 140 free throws. We should estimate the probability that the player makes the next free throw to be
Since the player makes 95 out of 140 free throws, the probability that he makes the next free throw is:
[tex]\frac{95}{140}\approx0.6786.[/tex]Answer: 67.86%
you invest $1500 for three years. find the amount of simple intrest you earn at an annual rate of 8.25%
Answer:
simple interest=371.25
Step-by-step explanation:
1500×8.25%×3
=123.75×3
=371.25
Answer:
371.25
Step-by-step explanation:
interest = principal x rate (expressed as a decimal, annual) x time (years)
our principal is 1500, and 8.25% as a decimal is 0.0825, and then its 3 years, multiply that all up and that equals 371.25
Amelia needs to buy some cat food. At the nearest store, 3 bags of cat food cost $13.50. How much would Amelia spend on 5 bags of cat food?
Amelia would spend $ on 5 bags of cat food.
PLEASEE HELPPP QUICK
Answer:
$22.50 for 5 bags of cat food
Step-by-step explanation:
$13.50 divided by 3 equals $4.50. Multiply this by 5 and you will end up with $22.50 for 5 bags of cat food
Can I get help with question 6-9For 6 I’ve already done it I just need assistance and see if I did it correctly
The scale factor is always the ratio of new image with respect to the old image.
6) The scale factor as per the image is 3:1 or 3.
7) The New image is P'Q'R'S' and old image is PQRS so the scale factor is given by:
Q'R':QR=3:6 or 1:2.
The scale factor is 1/2.
8) Here the pair of congruent angles is:
[tex]\begin{gathered} \angle G=\angle S=90 \\ \angle F=\angle R=35 \\ \angle H=\angle T=90-35=55 \end{gathered}[/tex]The proportional sides are:
[tex]\frac{HF}{TR}=\frac{HG}{TS}=\frac{GF}{RS}=\frac{2}{1}[/tex]So FG corresponds to RS, GH corresponds to TS, HF corresponds to TR.
dont guess please
Solve the equation below using the given domain, then enter the solution set. Be sure to use the {} properly and separate each entry with a comma. Finally, enter the solution set in the order that the domain is given.
Sample Answer: {(1, 2), (3 , 4), (5, 6), ...}
Equation: 2y = 6x - 10
Domain: {-1, 3, 8}
The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.
Define solution set and domain.The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set.
In mathematics, a function's domain is the collection of possible inputs it will accept.
Given equation is 2y = 6x - 10 and domain is {-1, 3, 8}
We can also write the given equation is
y =(6x-10)/2 ------------equation 1
As we know, domain is considered as the value of x,
Consequently, if we enter x = -1 in equation 1, we will receive
y = (-16)/2
y = -8
Similarly put x = 3 in equation 1, we will get
y = 8/2
y = 4
Similarly put x = 8 in equation 1, we will get
y = 38/2
y = 19
By combining the values of x and y, we get
The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.
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Molly has a $2500 down payment saved for this purchase. Molly assumes the $500 cash allowance will come straight off her total. How much loan does molly need?.
Answer:
Answer: $3000
Step-by-step explanation:
Based on the information given, the amount of loan that Molly needs will be the addition of the down payment and the cash allowance and this will be:
= Down payment + Cash allowance
= $2500 + $500
= $3000
Molly needs a loan of $3000
How to find the area of a semi-circle
The area of a circle is given by:
[tex]\begin{gathered} A=\pi r^2 \\ where \\ r=radius \end{gathered}[/tex]Therefore, the area of a semicircle is:
[tex]A_s=\frac{\pi r^2_{}}{2}[/tex]how do we do this one its one quiestion two parts
Answer:
Volume = 5861.64 cubic inches
Explanation:
We were given that we should make an open rectangular box from a cardboard of dimension 25 inches by 49 inches
We are to cut congruent squares from the corners and folding up the sides
The box is open at the top
We will proceed to solve as shown below:
[tex]\begin{gathered} Length=49in \\ Width=25in \\ \text{Taking a unit of square from each side, we have:} \\ New\text{ }Length=49-2x;x<24.5 \\ New\text{ }Width=25-2x;x<12.5 \\ Height=x \\ \text{So, the doamin of this is \lparen0, 12.5\rparen} \\ V(x)=x(49-x)(25-x) \\ V(x)=x^3-74x^2+1225x \\ \text{Taking the derivative of both sides, we have:} \\ V^{\prime}(x)=3x^2-148x+1225 \\ Equate\text{ }V^{\prime}(x)\text{ to zero, we have:} \\ 3x^2-148x+1225=0 \\ \text{Solving using quadratic formula, we have:} \\ x=38.81273011,10.52060321 \\ Either\text{ of these two values is either the maximum or minimum} \end{gathered}[/tex]We will proceed as shown below:
[tex]\begin{gathered} x=38.81273011,10.52060321 \\ \text{Take a second derivative. The maximum point is the point where x returns a negative value, we have:} \\ V^{\prime}(x)=3x^2-148x+1225 \\ V^{^{\prime}}^{\prime}(x)=6x-148 \\ \text{We substitute both values into this, we have:} \\ when:x=38.81273011 \\ V^{\prime}^{\prime}^(x)=6(38.81273011)-148 \\ V^{\prime\prime}(x)=84.87638066 \\ when:x=10.52060321 \\ V^{\prime\prime}(x)=6(10.52060321)-148 \\ V^{\prime\prime}(x)=-84.87638074 \\ \text{Therefore, the value of the height that gives the greatest volume is 10.52060321 inches} \end{gathered}[/tex]Hence, the maximum volume is given by:
[tex]\begin{gathered} x=10.52060321 \\ V(x)=x^3-74x^2+1225 \\ V(x)=5861.64in^3 \end{gathered}[/tex]Answer:
5.26 in × 14.48 in × 38.48 in
2930.82 in³
Step-by-step explanation:
You want the dimensions and volume of the maximum-volume open-top box that can be made from 25 in by 49 in stock when congruent squares are cut from the corners.
DimensionsIf the side length of the square is x, then the dimensions of the base of the box are (25 -2x) and (49 -2x) inches.
VolumeThe volume of the box is the product of the dimensions:
V(x) = x(25 -2x)(49 -2x) = 4x³ -148x² +1225x
Maximum volumeThe maximum volume will be had when x is such that the derivative of volume with respect to x is zero. The maximum value of x cannot be as great as 25/2 = 12.5 because that value gives a zero-width box.
V'(x) = 12x² -296x +1225 = 0
Final dimensionsUsing the quadratic formula, we find the relevant value of x to be ...
[tex]x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}=\dfrac{-(-296)-\sqrt{(-296)^2-4(12)(1225)}}{2(12)}\\\\=\dfrac{296-\sqrt{28816}}{24}=\boxed{\dfrac{74-\sqrt{1801}}{6}\approx 5.2603}[/tex]
Then the dimensions are ...
x ≈ 5.2603
25 -2x ≈ 14.4794
49 -2x ≈ 38.4794
The box is about 5.26 inches by 14.48 inches by 38.48 inches.
Largest volumeThe volume of the final box is about ...
(5.2603 in)(14.4794 in)(38.4794 in) ≈ 2930.82 in³
The volume of the finished box is about 2930.82 cubic inches.
__
Additional comment
As the attachment shows, a graphing calculator can show the extreme value(s) of the volume function, and the corresponding box dimensions.
Solve by factoring64x^2-1=0
Given:
[tex]64x^2-1=0[/tex]Required:
To solve the given equation by factoring method.
Explanation:
Consider
[tex]64x^2-1=0[/tex][tex]\begin{gathered} (8x)^2-1^2=0 \\ (8x+1)(8x-1)=0 \\ \\ 8x+1=0 \\ 8x=-1 \\ x=-\frac{1}{8} \end{gathered}[/tex]And
[tex]\begin{gathered} 8x-1=0 \\ 8x=1 \\ x=\frac{1}{8} \end{gathered}[/tex]Final Answer:
[tex]x=-\frac{1}{8},\frac{1}{8}[/tex]I need help with 7 please it says find the value of x round each answer to the nearest tenth
To find the value of x, we can work the two triangles separately; as follows:
So, according to the figures above:
x = y + z, and we can find y and z using Pythagoras theorem:
[tex]y\text{ = }\sqrt[]{14^2-12^2}=\text{ 2}\sqrt[]{13}[/tex][tex]z\text{ = }\sqrt[]{29^2-12^2}=\text{ }\sqrt[]{697}[/tex]Then:
[tex]x\text{ = 2}\sqrt[]{13\text{ }}+\text{ }\sqrt[]{697}=33.6[/tex]