The equivalent expression of (7)⁵ x (7)⁸ x (7³)² is (7)¹⁹
How to rewrite the expression?The expression is given as
(7)⁵ x (7)⁸ x (7³)²
The base of the above expression are the same
i.e. Base = 7
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
(7)⁵ x (7)⁸ x (7³)² = (7)⁵⁺⁸⁺³ˣ²
Evaluate the product in the equation
(7)⁵ x (7)⁸ x (7³)² = (7)⁵⁺⁸⁺⁶
Evaluate the sum in the above equation
So, we have
(7)⁵ x (7)⁸ x (7³)² = (7)¹⁹
Hence, the simplified expression of the expression given as (7)⁵ x (7)⁸ x (7³)² is (7)¹⁹
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Formula?
$268 is deposited into savings account at 4% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $427?
Answer: 12 years
A, taken two at a time 4) a. ** Evaluate each expression. 5) P2
we have
4P2
the formula is equal to
n!/(n-r)!
n=4
r=2
substitute
4!/(4-2)!
4!/2!=(4*3*2!)/2!
simplify
4*3=12
answer is 12V =Y(r+ B) solve for r
Suppose that the age of all of a country's vice presidents when they took office was recorded. The collection of the ages of all the country's vice presidents when they took office is a A. PopulationB. ParameterC. Sample D. Statistic
Answer:
Population
Explanation:
A population is a complete group that has a common feature. A Sample is a part of that population and a statistic or parameter are measures of the sample or population.
In this case, we have the ages of all the country's vice presidents, so it is a population.
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 7)(0,7) and (2, 112)(2,112).
An exponential function in the form y=abˣ is y = 7×4ˣ .
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Write the equation of the function:
y = abˣ
For point (0 , 7)
7 = ab⁰
for point (2 , 112)
x = 2
y = 112
Substitute:
112 = ab²
Swap the sides:
ab⁰ = 7
ab² = 112
Find the quotient of the equations:
ab²/ ab⁰ = 112/7
Simplify the equations:
b² = 16
b = ±√16
Split into two equations: b = +√16 or b = -√16
Simplify the radical expression:
b = 4
b = -4
Combine the results: b = 4 or b = -4
Any fraction with a denominator of 1 is equal to its numerator:
a = 7
7 = a (±4)°
Substitute into one of the equations:
a = 7
b = ± 4
y = 7×4ˣ
Hence , y =7×4ˣ is an exponential function with the formula y=abˣ.
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A group of 15 people are ordering pizza.each person want 2 slices and each pizza has 15 slices.how many pizzas should they order
Which degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone?
Circle
Parabola
One line
Two lines
One line is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone.
A rhombus's three-dimensional surface of rotation around one of its symmetry axes is known as a bicone or dicone in geometry. A bicone is a surface made by uniting two right circular cones that are congruent at their bases.
A 3D representation of a double cone {not shown indefinitely stretched). A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.
The part that intersects the plane is only the bus of the cone.
As a result, when a double cone's apex is cut by a plane parallel to the cone's slant edge, one line is created.
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Answer: one line
Step-by-step explanation:
SHOW ALL WORK PLEASE!
Sarah has two similar regular pyramids with pentagon-shaped bases. The smaller has a scale factor of 2:3 when compared to the larger. Only the smaller pyramid is shown.
She calculates the area of the base of the pyramid (through long, hard work) to be 110.11 square units. The height of the pyramid is 15 units. Now she needs to calculate the volume of the pyramid.
(a) Calculate the volume of the pyramid for Sarah.
(b) "Oh, no!" Sarah exclaims. "Now I have to go through all this hard work again to find the volume of the larger pyramid!" Does she? Explain.
(c) Calculate the volume of the larger pyramid for Sarah.
Answer: a) The volume of the pyramid 440.44 cube units
(b) No she doesn't
(c) The volume of the larger pyramid is 1,486.485 cube units
Step-by-step explanation: The given parameters are;
The scale factor of the pyramids, S.F. = 2:3
The base area of the small pyramid, = 110.11 square units
The height of the small pyramid, h₁ = 12 units
(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid
Therefore;
The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units
V₁ = 440.44 cube units
The volume of the small pyramid, V₁ = 440.44 cube units
(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid
She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid
The volume scale factor = (The linear scale factor)³
(c) The linear scale factor of the pyramids = 2:3 = 2/3
Therefore;
The volume scale factor of the pyramids = (2/3)³ = 8/27
To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;
V₂ = V₁ × (27/8)
Therefore;
The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units
The volume of the larger pyramid, V₂ = 1,486.485 cube units.
PLS GIVE ME BRAINLIESTA DN FRIEND REQUEST ME PLS AND THANK YOU
Which of these is the northern-most countries? Responses
A Colombia
B Brazil
C Ecuador
D Peru
true or false√3^(3√2) =(108)^1/6
False
Explanations:For the Left Hand side of the expression:
[tex]\sqrt[]{3}^{(3\sqrt[]{2})}[/tex]This can be simplified as:
[tex]\begin{gathered} 3^{\frac{1}{2}(3\sqrt[]{2})} \\ =3^{1.5\sqrt[]{2}} \\ =3^{2.12} \\ =\text{ }10.27 \end{gathered}[/tex]For the Right Hand Side of the expression:
[tex]\begin{gathered} (108)^{\frac{1}{6}} \\ =(108)^{0.167} \\ =\text{ }2.19 \end{gathered}[/tex]Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true
Just need a simple explanation.
The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:
x = -3 or x = 9.
Are the steps correct?The equation in Step 6 is given as follows:
[tex]\sqrt{(x - 3)^2} = \sqrt{36}[/tex]
Simplifying the square roots, the variable x can be isolated, as follows:
x - 3 = 6.x - 3 = -6.Both -6 and 6 are correct results for the square root of 36, because:
6² = 36.(-6)² = 36.His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:
x - 3 = 6. -> x = 9.x - 3 = -6. -> x = -3.From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;
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Use the equation A=Pe^rt to answer each question. Show all work. First question
Answer:
$7209.78
Explanation:
To find the amount in the account after 6 years, we will use the following equation
[tex]A=Pe^{rt}[/tex]Where P is the initial amount, r is the interest rate and t is the time in years.
So, replacing P = $5000, r = 6.1% = 0.061, and t = 6 years, we get
[tex]\begin{gathered} A=5000e^{0.061t} \\ A=5000e^{0.061(6)} \\ A=5000e^{0.366} \\ A=5000(1.44) \\ A=7209.78 \end{gathered}[/tex]Therefore, the answer is $7209.78
an insurance company claims the probability of surviving a certain type of cancer is 20%. what are the odds of surviving? express your answer in the form a:b
The probability of surviving is given as 20%.
It is required to find the odds of surviving.
Let the event "surviving a certain type of cancer" be X.
It follows that the probability can be written as:
[tex]\begin{gathered} P(X)=20\%=\frac{20}{100}=\frac{\cancel{20}^1}{\cancel{100}^5} \\ \Rightarrow P(X)=\frac{1}{5} \end{gathered}[/tex]Recall that for an event X, the odds in favor of the event happening are given by the ratio:
[tex]\begin{gathered} \frac{P(X)}{P(\overline{X})} \\ \text{Where }P(\overline{X})\text{ is the probability of the event not happening} \end{gathered}[/tex]The probability of event X not happening is given as:
[tex]\begin{gathered} P(\overline{X})=1-P(X) \\ \text{Substitute }P(X)=\frac{1}{5}\text{ into the equation:} \\ P(\overline{X})=1-\frac{1}{5}=\frac{4}{5} \\ \Rightarrow P(\overline{X})=\frac{4}{5} \end{gathered}[/tex]Substitute the probabilities into the odds formula:
[tex]\frac{P\mleft(X\mright)}{P(\overline{X})}=\frac{\frac{1}{5}}{\frac{4}{5}}=\frac{1}{4}[/tex]The odds of surviving is 1:4.
The odds of surviving in the ratio from is 4 : 1.
What are odds in favor and odds against?The odds in favor is the ratio of the number of ways that an outcome can occur compared to how many ways it cannot occur.
The odds against is the ratio of the number of ways that an outcome cannot occur compared to in how many ways it can occur.
Given, An insurance company claims the probability of surviving a certain type of cancer is 20%.
So, The probability of not surviving a certain type of cancer is 80%.
∴ The odds of surviving is 2/8 = 1/4.
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The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 19 people are combined. What is the probability that
the combined sample tests positive for the virus? ls it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least or person has the virus.
The probabilty that the combined sample wil test posiltive is 1.
(Round to three decimal places as needed.)
Answer: there is a 0.095% chance that one of the adults tests positive
Step-by-step explanation:
what is the slope of the line through (-9, 6) and (-3,9)
Solution
For this case we have the following points:
(-9, 6) and (-3, 9)
and we can find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{9-6}{-3+9}=\frac{3}{6}=\frac{1}{2}[/tex]Then the solution would be:
B ) 1/2
Please help with these two problems.
Answer:
7. x = 25
8. x = 28
Step-by-step explanation:
7. Alternate interior angles are congruent.
[tex]x + 25 = 2x[/tex]
[tex]x = 25[/tex]
8. Consecutive angles add up to 180°.
[tex]4x + 2x + 12 = 180[/tex]
[tex]6x + 12 = 180[/tex]
[tex]6x = 168[/tex]
[tex]x = 28[/tex]
Lana has a three-year lease that requires her to pay $395 rent permonth. What is the total amount she will pay for rent during the term ofher lease?a. $1,185b. $14,220c. $4,740d. $1,422
Step 1. Since Lana Pays the rent monthly, and the lease is for a 3 year period, the first step will be to calculate the number of months that are in 3 years.
Since there are 12 months in just 1 year, we multiply 12 by 3 to get the number of moths in 3 years:
[tex]12\times3=36[/tex]There are 36 months in 3 years.
Step 2. Multiply the number of months by the monthly payment of the rent.
We multiply $395 by the 36 months:
[tex]395\times36[/tex]And the result is:
[tex]395\times36=14,220[/tex]$14,220 is the total amount she will pay for rent during the term of her lease.
Answer:
b. $14,220
1) Bob’s frog can travel 7 inches per jump, Kim’s frog can travel 9 inches, and Jack’s frog can travel 13 inches. If the 3 frogs start off at point 0 inches, how many inches will it be to the next point that all 3 frogs touch?
2) Two runners run around a circular track. The first runner completes a lap in 6 minutes. The second runner completes the track in 13 minutes. If they both start at the same place and the same time and go in the same direction, after how many minutes will they meet again at the starting place?
Answer:
See below
Step-by-step explanation:
LCM of 7 9 13
Prime factorization
9 = 3 x 3
7 = 7
13 = 13
LCM = 3 x 3 x 7 x 13 = 819 in
LCM of 6 and 13 is similarly 78 min
There are 2 buses. Bus A can travel 125 miles in 3 hours, and bus B can travel 85 more miles than bus A within the same time what is the speed of bus B?
Answer:
70 miles an hour
Step-by-step explanation:
First, you want to know how fast bus A can go. So you want to do 125/3 since the bus travels 3 hours. you get 41.6666667. keep that number. then you want to divide 85 by 3 since bus B is going for 3 hours. you get 28.3333333. then you add those numbers to get how fast bus B is going and you get 70 miles per hour for bus B
help please for my homework
A. The similar triangles are: B. ΔABC ~ ΔDBE
B. AC = 16
What is the Angle-Angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if two angles in one triangle are congruent to two corresponding angles in the other triangles.
The side lengths of two similar triangles are proportional to each other, which means they have ratio that is equal to one another.
Part A:
In the given diagram, triangles ABC and DBE have two pairs of corresponding angles that are congruent to each other which are: angle ABC ≅ DBE, and angle BCA ≅ BED.
Therefore, based on the AA similarity theorem: B. triangle ABC ~ triangle DBE.
Part B:
Since triangles ABC and DBE are similar triangles, therefore, BC/BE = AC/DE
Substitute
12/15 = (x + 1)/(x + 5)
Cross multiply
12(x + 5) = 15(x + 1)
12x + 60 = 15x + 15
Combine like terms
12x - 15x = -60 + 15
-3x = -45
-3x/-3 = -45/-3
x = 15
AC = x + 1 = 15 + 1
AC = 16
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express in simplest form: sec 0 • cot 0 • sin 0
Note that;
secθ = 1/cosθ cotθ= cosθ/sinθ
substitute into into the expression
[tex]\sec \theta.\cot \theta.\sin \theta=\frac{1}{\cos\theta}.\frac{\cos \theta}{\sin \theta}\text{. sin}\theta[/tex]cosθ at the numerator will cancel out the cosθ at the denominator, also sinθ at the numerator will cancel out the sinθ at the denominator
[tex]=1[/tex]How do you write 6.01 × 10^2 in standard form?
which is more 95 fluid ounces or 3 quarts
95 fluid ounces or 3 quarts.
To solve htis problem, convert the ounces to quarts and compare the results.
1 ounce ----------------------- 0.03125 quart
95 ounces ------------------- x
x = (95 x 0.03125) / 1
x = 2.97 quarts
2.97 ounces < 3 quarts
Three quarts is more
Given the following sets, find the set (A UB) n (AUC).U={1, 2, 3, ...,9}A = {1, 2, 4, 8}B = {3, 7, 9)C={1, 2, 3, 4, 6}Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. (AUB) n (AUC)=0(Use a comma to separate answers as needed. Use ascending order.)O B. (A UB) n (AUC) is the empty set.
From the data sets given
(A U B) = ( 1, 2 ,3 ,4 , 7, 8 , 9)
(A U C) = (1, 2 ,3 ,4 ,6 ,8)
(A U B) n ( A U C) = ( 1 ,2, 3, 4 ,8)
Learning Diagnostic Analytics Recommendations Skill plans Fifth grade > AA.12 Describe relationships among quadrilaterals SZT Complete the sentence below. A rhombus is a rectangle. always sometimes never Submit
A rectangle has 4 right angles.
A rhombus does not have 4 right angles,
So, A rhombus is sometimes a rectangle
Let X be a discrete random variable for the outcome of a toss of a coin with sides 0 and 1,with P(X = 0) = 0.5 and P(X = 1) = 0.5. Moreover let Y be another variable associatedwith a biased coin with sides 1 and 2, such that P(Y = 1) = 0.4 and P(Y = 2) = 0.6. IfZ = X + Y , what is P(Z < 3)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
[tex]\begin{gathered} P(X=0)=0.5,P(X=1)=0.5 \\ P(Y=1)=0.4,P(Y=2)=0.6 \\ Z=X+Y \end{gathered}[/tex]STEP 2: Write the formula for calculating the required probability
[tex]P(Z<3)=P(Z=1)+P(Z=2)[/tex]STEP 3: Find P(Z=1)
[tex]\begin{gathered} P(Z=1)=P(X=0)\text{ and }P(Y=1) \\ =0.5\times0.4=0.2 \end{gathered}[/tex]STEP 4: Find P(Z=2)
[tex]\begin{gathered} P(Z=2)=P(X=0)\cdot P(Y=2)\text{ or }\times P(X=1)\cdot P(Y=1) \\ (0.5\times0.6)+(0.5\times0.4) \\ =0.3+0.2=0.5 \end{gathered}[/tex]STEP 5: Find the P(Z<3)
[tex]P(Z<3)=0.5+0.2=0.7[/tex]Hence, the answer is 0.7
2. Which of the following represents a quadratic function? (Circle all that apply!) (2 pts)a, y = 9x2 + 4x - 6b. y = 3x + 8c. y = 1223 - 6x2 + 4x - 9
A quadratic function is a function in the form,
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{where a, b, c are real } \\ a\ne0 \end{gathered}[/tex]Option A is a quadratic function,
Option B, is not a quadratic function because it is not the form of the equation written above and also,
[tex]a=0[/tex]Option C is also not a quadratic function because it has the highest degree of x to be 3.
In option D the function is given by the function is defined by
[tex]\begin{gathered} y=x^2 \\ \text{thus} \\ a=1\ne0 \end{gathered}[/tex]This implies that the function in option D is a quadratic function
Option E is not a quadratic function
Find the inverse
g(x) =
10 –5x
2
The most appropriate choice for inverse of a function will be given by-
[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]
What is inverse of a function?
At first, it is important to know about function
A function from A to B is a rule that maps to each element of A a unique element of B.
A is called the domain of the function and B is called the co domain of the function.
[tex]f^{-1}[/tex] is said to be the inverse of [tex]f[/tex] if [tex]f[/tex] [tex]o[/tex] [tex]f^{-1}[/tex] = [tex]f^{-1} o[/tex] [tex]f[/tex] = [tex]I[/tex], I is the identity function.
Let g(x) = y
[tex]\frac{10-5x}{2} = y\\10 - 5x = 2y\\5x = 10-2y\\x = \frac{10 - 2y}{5}[/tex]
[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]
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3 thousandths times 0.001
the answer would be 3
5. A ja contains 11 green marbles, 7 red marbles, and 6 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability ofselecting a blue marble followed by a green marble?
Answer: 11/92
Explanation:
Probability is expressed as
number of favorable outcomes/number of total outcomes
From the information given,
number of green marbles = 11
number of red marbles = 7
number of blue marbles = 6
Total number of marbles = 11 + 7 + 6 = 24
Probability of selecting a blue marble = 6/24 = 1/4
Since the marble is not replaced, total number of marbles left = 24 - 1 = 23
Probability of selecting a green marble = 11/23
The probability of selecting a blue marble followed by a green marble is
1/4 x 11/23
= 11/92
