In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
1,5,25,125,..
Step 02:
[tex]an=5^{n-1}[/tex]if n = 8
[tex]a_8=5^{8-1}=5^7=78125[/tex]The answer is:
8th term is 78125
help in this question
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
A vertex example is what?f(x)=3(x−1)2
Find the given parabola's characteristics.
Lessen the steps you tap...
Vertex form is to be used, y=a(x−h)2+k,
to calculate the values of a, h, and k.
a=3
h=1
k=0
The parabola widens because the value of an is positive.
opens up
Find the (h,k) vertex. ( 1 , 0 )
Calculate p, the distance between the focus and the vertex.
To continue, tap...
1/ 12
Locate your focus.
To continue, tap... ( 1 , 1/ 12 )
By identifying the line that connects the vertex with the focus, you may determine the axis of symmetry.
x = 1
The horizontal line that results from deducting p from the vertex's y-coordinate k depends on whether the parabola opens up or down. This line is known as the directrix.
y = k − p
Simplify the formula after substituting the known p and k values.
y = − 1 /12
Analyze and graph the parabola using its characteristics.
Direction: opens up
vertices: ( 1, 0 )
Focus: ( 1 , 1 /12 )
x = 1 is the symmetry axis.
Direction: y = /1 12.
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If a price changes from $105,300 to $104,399 will that be a percentincrease or decrease?
If the price changes from $105,300 to $104,399, It means that there is a decrease in price.
Decrease = 105,300 - 104,399 = $901
The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes
[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]By rounding up to the nearest whole number, it becomes 1%
The percent decrease is 1%
Endpoint: (1,3) Midpoint: (-2,5) Please I need help ASAP
I need help on thisChange the equation into a equivalent equation written in the Slope-intercept form. x -7y + 5 =0
The slope-intercept form is an equation as follows:
[tex]y=mx+b[/tex]Then, we need to change the original equation in this equivalent:
[tex]-7y=-5-x\Rightarrow-7y=-x-5\Rightarrow7y=x+5[/tex]Dividing the total equation by 7, we have:
[tex]\frac{7}{7}y=\frac{x}{7}+\frac{5}{7}\Rightarrow y=\frac{1}{7}x+\frac{5}{7}[/tex]Therefore, the slope-intercept form is:
[tex]y=\frac{1}{7}x+\frac{5}{7}[/tex]Multiply.4y=2y3v2.4v7
Let's recall one of the properties of exponents:
[tex]x^4\ast x^5=x^{4\text{ + 5}}=x^9[/tex]Therefore, in our exercise we have:
[tex]4y\text{ }\ast2y^3=8y^{4\text{ }}andv^2\ast4v^7=4v^9[/tex][tex]8y^4\ast4v^9=32y^4v^9[/tex]Hey I need help with my homework help me find the points on the graph too please Thankyouu
Given the function:
g(x) = 3^x + 1
we are asked to plot the graph of the function.
Using the table:
x y
-2 10/9
-1 4/3
0 2
1 4
2 10
The graph:
The expomential functions have a horizontal asymptote.
The equation of the horizontal asymptote is y = 1
Horizontal Asymptote: y = 1
To find the domain is finding where the question is defined.
The range is the set of values that correspond with the domain.
Domain: (-infinity, infinity), {x|x E R}
Range: (1, infinity0, {y|y > 1}.
A test was given to a group of students. The grades and gender are summarized below A B C TotalMale 5 9 2 16Female 7 11 12 30Total 12 20 14 46If one student is chosen at random from those who took the test, find the probability that the student got a 'C' GIVEN they are female.
Probability that the student got a 'C' GIVEN they are female = number of females that got a C in the test/number of females
From the information given,
number of females that got a C in the test = 12
number of females = 30
Thus,
Probability that the student got a 'C' GIVEN they are female = 12/30
We would simplify the fraction by dividing the numerator and denominator by 6. Thus,
Probability that the student got a 'C' GIVEN they are female = 2/5
The proof below shows that sin theta -sin^3 theta=sin2theta cos^2 theta/2cos theta
Given:
Given the steps of the proof of the equation
[tex]\sin\theta-\sin^3\theta=\frac{2\sin2\theta\cos^2\theta}{2\cos\theta}[/tex]Required: Expression missing on the thrd step
Explanation:
The second step is
[tex]\sin\theta-\sin^3\theta=\sin\theta(1-\sin^2\theta)\frac{2\cos\theta}{2\cos\theta}[/tex]from which leads to
[tex]\sin\theta-\sin^3\theta=\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]The expression missing on the third step is
[tex]\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]Option D is correct.
Final Answer:
[tex]\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]May I please get help with this math problem it’s so confusing
We have to find the value of z and x.
We assume that lines g and h are parallel.
Then, z and the angle with measure 85° are consecutive interior angles.
As they are conscutive interior angles, their measures add 180°.
Then, we can write:
[tex]\begin{gathered} z+85\degree=180\degree \\ z=180-85 \\ z=95\degree \end{gathered}[/tex]Then, we can relate the angle with measure z with the angle with measure (6x-109). They are vertical angles and, therefore, they have the same measure.
Then, we can write:
[tex]\begin{gathered} z=6x-109 \\ 95=6x-109 \\ 95+109=6x \\ 204=6x \\ x=\frac{204}{6} \\ x=34 \end{gathered}[/tex]Answer: z = 95 and x = 34.
Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.
Given
A graph of a polynomial with the real coefficients.
To find:
a) The intervals in which the function is increasing is,
[tex]\begin{gathered} (-\infty,-5) \\ (-2,2) \\ (6,\infty) \end{gathered}[/tex]b) The value of x at which the unction has local minima.
From the graph shown in the figure, there is only one local minimum at x=-2.
c) The sign of the functions leading coefficient is positive.
Since the graph is moving upwards.
d) The degree of the function is 5.
2. A wooden cube with volume 64 is sliced in half horizontally. The two halves are then glued together to form a rectangular solid which is not a cube. What is the surface area of this new solid? A.128 B. 112 C. 96 D. 56
we have that
the volume of the cube is equal to
V=b^3
64=b^3
b^3=4^3
b=4 unit
see the attached figure
the surface area of the new figure is equal to
SA=2B+PH
where
B is the area of the base
P is the perimeter of the base
H is the height
we have
B=4*8=32 unit2
P=2(4+8)=24 unit
H=2 unit
so
SA=2(32)+24*2
SA=64+48
SA=112 unit2
the answer is option BUsing the Rational Roots Theorem which of the values shown are potential roots of ) = 32-132-3x + 457 Select all that apply. +1/3 +5 +5/3 +9 +1 +15 +3 +45
To solve this problem, you find the value of x that will make the function to be = 0 by substituting the likely values from the option into the eqaution and checking if after the simplification the value is 0
so checking
[tex]\begin{gathered} \text{The factors betwe}en\text{ }3\text{ and 45 are } \\ 1,3,5,9,15,45 \\ \text{factors of 3 are 1,3} \end{gathered}[/tex]we have
[tex]\begin{gathered} =3x^{^3}-13x^2-3x\text{ +45} \\ \pm1,\text{ 3, 5,9, 15,45} \\ \pm\frac{1}{3},\text{ 1, 5/3, 3, 5 , 15} \\ \text{values that apply are +3 twice and -5/3} \end{gathered}[/tex]help meee pleaseeee pleasee
Two containers designed to hold water are side by side, both in the shape of acylinder. Container A has a diameter of 8 feet and a height bf 16 feet. Container B hasa diameter of 10 feet and a height of 8 feet. Container A is full of water and the wateris pumped into Container B until Conainter B is completely full.To the nearest tenth, what is the percent of Container A that is empty after thepumping is complete?
Okay, here we have this:
Considering the provided information, we are going to calculate what is the percent of Container A that is empty after the pumping is complete, so we obtain the following:
First we will calculate the volume of each cylinder using the following formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]Applying:
[tex]\begin{gathered} V_A=\pi\cdot4^2\cdot16 \\ V_A=\pi\cdot16\cdot16 \\ V_A=256\pi \end{gathered}[/tex][tex]\begin{gathered} V_B=\pi\cdot5^2\cdot8 \\ V_B=\pi\cdot25\cdot8 \\ V_B=200\pi \end{gathered}[/tex]After pumping the water from container A to container B, the following amount remains in container A:
Remaining amount of water in A=256π-200π
Remaining amount of water in A=56π
Now, we obtain that the empty percentage that results in A is:
Empty percentage that results in A=200/256*100
Empty percentage that results in A=78.125%
Empty percentage that results in A≈78.1%
How many liters of paint must you buy to paint the walls of a rectangular prism-shaped room that is 20 m by 10 m with a ceiling height of 8 m if 1 L of paint covers40 m2? (Assume there are no doors or windows and paint comes in 1-L cans.)
17 Liters
Explanation
Step 1
find the total area to paint
we need to assume the floor wont be painted, so the total are to paint is
the are of a rectangle is gieven by:
[tex]Area=length*width[/tex]so, the total area will be
[tex]\begin{gathered} total\text{ surface area=\lparen20*10\rparen+2\lparen20*8\rparen+2\lparen10*8\rparen} \\ total\text{ surface area=200+2\lparen160\rparen+2\lparen80\rparen} \\ total\text{ surface area=200+320+160} \\ total\text{ surface area=680 m}^2 \end{gathered}[/tex]so , the area to paint is 680 square meters
Step 2
finally, to know the number of Liters need , divide the amount ( total area) by the rate of the paitn, so
[tex]\begin{gathered} paint\text{ needed=}\frac{total\text{ area}}{rate\text{ paint}} \\ paint\text{ needed=}\frac{680m^2}{40\frac{m^2}{L}}=17Liters \end{gathered}[/tex]so, the total paint needes is 17 Liters, and paint comes in 1-L cans, so
[tex]\begin{gathered} 17\text{ Liters} \\ 17\text{L}\imaginaryI\text{ters\lparen}\frac{1\text{ Can}}{1\text{ L}})=17cans \end{gathered}[/tex]therefore, the answer is
17 Liters
I hope this helps you
See the attached for the math problem
1. If the cake rises by ¹/₃ as it bakes, the number of cups of cake batter needed for the four cakes is 140.
2. If ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides, the number of cups of icing needed for the four cakes is 47.
How are the numbers determined?The number of cups of cake batter and icing can be determined using the mathematical operations of multiplication, addition, division, and subtraction.
First, the volumes of each cake and its batter are calculated using the given dimensions and the rise.
Using the division operation, the number of cups of cake batter for each cake is determined and multiplied by four.
We understand that the normal volume of the cake will increase with the icing, helping us to calculate the increased volume after the icing.
The difference between the two volumes becomes the volume of the icing required, which is divided by 14.4 in³ to get the number of cups of icing required.
a) Cups of Cake Butter:The volume of each cake = Length x Width x Height
Length = 14 inches
Width = 12 inches
Height = 4 inches (2 x 2)
= 12 x 14 x 4
= 672 in³.
Rise of the cake as it bakes = ¹/₃
The normal volume before rising = 1
Risen volume = 1¹/₃
1¹/₃ = 672 in³
The normal volume of cake batter before the ¹/₃ rise = 504 in³ (672/1¹/₃).
1 cup = 14.4 in³, the total cups for each cake = 35 cups (504 in³/14.4 in³).
The total cups of cake batter for the 4 cakes = 140 cups (35 x 4).
b) Cups of Icing:The total quantity of icing = 1¹/₄ (¹/₄ + ¹/₂ + ¹/₂).
The new volume after the icing = 840 in³ (672 x 1¹/₄)
The difference in volume after the icing = 168 in³ in (840 in³ - 672 in³)
If 1 cup = 14.4 in³, the cups of icing for each cake = 11.67 cups (168 in³/14.4 in³).
The total cups of icing for the 4 cakes = 47 cups (11.67 x 4).
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Question Completion:Four double-layered cakes, each 12.0 in. x 14.0 in., have been ordered for a special event. Each layer is 2.0 in. high.
a) If the cake rises by ¹/₃ as it bakes, how many cups of cake batter are needed? (1 cup = 14.4 in³. Hint: The ¹/₃ rise should be treated as a constant.)
b) How many cups of icing are needed if ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides? (Assume icing is not layered on top of the icing. 1 cup = 14.4 in³.)
please help need answer asap
Answer:
x = 34 degrees, y = 73
Step-by-step explanation:
Since the triangle is isosceles, the base angles are congruent (equal). First, find the supplement angle by doing 180-107, which gives you 73 for the base angles, which include y. Now there is a theorem that states the 2 remote interior angles are equivalent to the exterior angle, which means 107 = 73 + x. This gives us x = 34
I hope this helps!
Use the same process for the second one.
Answer question number 20. The question is in the image.Reference angle is the angle form by the terminal side and the x-axis.
Answer: We have to sketch the angle and find the reference angle for the 20:
[tex]\frac{8\pi}{3}[/tex]The reference angle is an angle between the terminal side of the angle and the x-axis.
[tex]\theta_R=180^{\circ}-\theta[/tex]The provided angle is:
[tex]\begin{gathered} \theta=\frac{8\pi}{3}=480^{\circ} \\ \\ 480^{\circ}=480^{\circ}-360^{\circ}=120^{\circ} \\ \\ \theta=120^{\circ} \end{gathered}[/tex]Sketch of the angle:
Therefore the reference angle is:
[tex]\begin{gathered} \theta_R=180^{\circ}-\theta \\ \\ \theta_R=180^{\circ}-120^{\circ} \\ \\ \theta_R=60^{\circ} \end{gathered}[/tex]2. Factor completely
2x^2 + 8x + 6
The factors are -3 and -1
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
2x² + 8x + 6
Put it equal to 0 so that we can solve for 'x'
2x² + 8x + 6 = 0
Now, its factors are 6x and 2x
2x² + 6x + 2x + 6 = 0
2x(x + 3) + 2(x + 3) = 0
To cross check your solution is correct or not. You've to just see the the brackets value should be same after taking common. Here the bracket value is (x+3) which is same.
(2x + 2) (x+3) = 0
split the values to solve further,
2x + 2 = 0 | x + 3 = 0
2x = -2 | x = -3
x = -2/2
x = -1
Hence, the factors are -3 and -1
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Solve the following and give the interval notation of the solution and show the solution on a number line. 6x-12(3-x) is less than or equal to 9(x-4)+9x
The Solution:
The given inequality is
[tex]6x-12(3-x)\leq9(x-4)+9x[/tex]Clearing the brackets, we get
[tex]6x-36+12x\leq9x-36+9x[/tex]Collecting the like terms, we get
[tex]\begin{gathered} 6x+12x-9x-9x\leq-36+36 \\ \end{gathered}[/tex][tex]\begin{gathered} 18x-18x\leq0 \\ 0\leq0 \end{gathered}[/tex]So, the solution is true for all real values of x.
The interval notation of the solution is
[tex](-\infty,\infty)[/tex]the variable w varies inversely as the cube of v. if k is the constant of variation, which equation represents this situation?a: qv^=kb: q^3 v= kc: q/v^3=kd: q^3/v=k picture listed below
Solution
Given that:
[tex]\begin{gathered} q\propto\frac{1}{v^3} \\ \\ \Rightarrow q=\frac{k}{v^3} \\ \\ \Rightarrow k=qv^3 \end{gathered}[/tex]Option A.
The width of a rectangle is 6x + 8 and the length of the rectangle is 12x + 16 determine the ratio of the width to the perimeter.Supply the following:Perimeter = 21 + 2w = Ratio= w/p Final answer in simplest form:
Solution:
For this case we know that the width is given by:
w = 6x +8
The lenght is given by:
l= 12x +16
And the perimeter would be given by:
P= 2l +2w = 2(12x+16)+ 2(6x+8)= 24x+32 +12x+16=36x + 48
And then the ratio would be:
[tex]\text{ratio}=\frac{6x+8}{36x+48}=\frac{3x+4}{18x+24}[/tex]Teresa is participating in a 4day cross-country bike challenge. She biked it for 61, 67, and 66 miles on the first three days. How many miles does she need to bike on the last day so that her average (mean) is 63 miles per day?
The number of miles that she need to bike on the last day so that her average (mean) is 63 miles per day is 62 miles.
What is a mean?The mean is the average of a set of numbers. Let the biking of the last day be represented as x. This will be:
(61 + 67 + 66 + x) / 4 = 64
(194 + x) / 4 = 64
Cross Multiply
194 + x = 64 × 4
194 + x = 256
Collect like terms
x = 256 - 194
x = 62
The miles is 62 miles.
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find the unit price of a 3 pack of bottle juice for $6.75 fill in the amount per bottle of juice
EXPLANATION
Let's see the facts:
Unit price = $6.75
Number of packs = 3
The unit price is given by the following relationship:
[tex]\text{Unit price= }\frac{6.75}{3}=2.25\frac{\text{dollars}}{\text{pack}}[/tex]The unit price is 2.25 $/pack
the table shows the number of miles people in the us traveled by car annually from 1975 to 2015
In the year 2022, the predicted number of miles of travels would be 3.601 trillion miles.
What is a model?
The term model has to do with the way that we can be able to predict the interaction between variables. In this case, we can see that there is a line of best fit as we can see from the complete question which is in the image that have been attached to his answer.
The question is trying to find out the number of miles that people are going to travel in the year 2022 based on the line of best fit that have been given in the question that we have attached here.
We know that; y = 0.048x + 1.345. Recall that x here stands for the number of years that have passed since the year 1975. We now have 47 years passed since 1975 thus;
y = 0.048(47) + 1.345
y = 3.601 trillion miles
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Which of the following are equations for the line shown below? Check all that apply. 5 (1,2) (3-6) I A. y + 6 = -4(x-3) B. y + 3 = -4(X-6) I C. y1 = -4(x-2) D. y - 2 = -4(x - 1)
We have the next points (1,2) and (3,-6)
The residence of a city voted on whether to raise property taxes the ratio of yes votes to no votes was 5 to 8 if there were 4275 yes both what was the total number of votes
The ratio of votes has been given as;
[tex]Yes\colon No\Rightarrow5\colon8[/tex]This means the ratios can be expressed mathematically as;
[tex]\begin{gathered} \text{Yes}=\frac{5}{5+8}\Rightarrow\frac{5}{13} \\ No=\frac{8}{5+8}\Rightarrow\frac{8}{13} \end{gathered}[/tex]If there were 4275 YES votes, then this means the number 4275 represents 5/13.
Therefore,
[tex]\frac{5}{13}=\frac{4275}{x}[/tex]Where x represents the total number of votes. Therefore,
[tex]undefined[/tex]I need to find two sets of coordinates and graph them. Please help?!
Answer
The two coordinates on the line include
(0, -1.5) and (-4.5, 0)
The graph of the line is presented below
Explanation
We are asked to plot the grap of the given equation of a straight line.
To do that, we will obtainthe coordinates of two points on the line.
These two points will preferrably be the intercepts of the line.
y = (-x/3) - (3/2)
when x = 0
y = 0 - (3/2)
y = -(3/2)
y = -1.5
First coordinate and first point on the line is (0, -1.5)
when y = 0
0 = (-x/3) - (3/2)
(x/3) = -(3/2)
x = (-3) (3/2)
x = -(9/2)
x = -4.5
Second coordinate and second point on the line is thus (-4.5, 0)
So, to plot the line, we just mark these two points and connect them to each other.
The graph of this line is presented under 'Answer' above.
Hope this Helps!!!
The half-life of a radioactive isotope is the time it takes for quantity of the isotope to be reduced to half its initial mass. Starting with 175 grams of a radioactive isotope, how much will be left rafter 5 half-lives? Round your answer to the nearest gram
Exponential Decay
The model for the exponential decay of a quantity Mo is:
[tex]M=M_o\cdot e^{-\lambda t}[/tex]Where λ is a constant and t is the time.
The half-life of a radioactive isotope is the time it takes to halve its initial mass. It can be calculated by making M = Mo/2 and solving for t:
[tex]\begin{gathered} \frac{M_o}{2}=M_o\cdot e^{-\lambda t} \\ \text{Simplifying:} \\ e^{-\lambda t}=\frac{1}{2} \\ \text{Taking natural log:} \\ -\lambda t=-\log 2 \\ t=\frac{\log 2}{\lambda} \end{gathered}[/tex]It's required to calculate the remaining mass of an isotope of Mo = 175 gr after 5 half-lives have passed, that is. we must calculate M when t is five times the value calculated above.
Substituting in the model:
[tex]M=175gr\cdot e^{-\lambda\cdot\frac{5\log 2}{\lambda}}[/tex]Simplifying (the value of λ cancels out):
[tex]\begin{gathered} M=175gr\cdot e^{-5\log 2} \\ \text{Calculating:} \\ M=175gr\cdot0.03125 \\ M=5.46875gr \end{gathered}[/tex]Rounding to the nearest gram, 5 grams of the radioactive isotope will be left after the required time.
please answer this question
Answer:
3
Step-by-step explanation:
Given expression:
[tex]\dfrac{(14^2-13^2)^{\frac{2}{3}}}{(15^2-12^2)^{\frac{1}{4}}}[/tex]
Following the order of operations, carry out the operations inside the parentheses first.
Apply the Difference of Two Square formula [tex]x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
to the operations inside the parentheses in both the numerator and denominator:
[tex]\implies \dfrac{((14+13)(14-13))^{\frac{2}{3}}}{((15+12)(15-12))^{\frac{1}{4}}}[/tex]
Carry out the operations inside the parentheses:
[tex]\implies \dfrac{((27)(1))^{\frac{2}{3}}}{((27)(3))^{\frac{1}{4}}}[/tex]
[tex]\implies \dfrac{(27)^{\frac{2}{3}}}{(81)^{\frac{1}{4}}}[/tex]
Carry out the prime factorization of 27 and 81.
Therefore, rewrite 27 as 3³ and 81 as 3⁴:
[tex]\implies \dfrac{(3^3)^{\frac{2}{3}}}{(3^4)^{\frac{1}{4}}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{3^{(3 \cdot \frac{2}{3})}}{3^{(4 \cdot \frac{1}{4})}}[/tex]
[tex]\implies \dfrac{3^2}{3^1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 3^{(2-1)}[/tex]
[tex]\implies 3^1[/tex]
[tex]\implies 3[/tex]
Given that,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
Evaluating the problem,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
→ ((196 - 169)^⅔)/((225 - 144)^¼)
→ (27^⅔)/(81^¼)
→ ((3³)^⅔)/((3⁴)^¼)
→ (3²)/3
→ 9/3 = 3
Therefore, the solution is 3.