Using exponent properties, the equivalent expression is given as follows:
\(\left(\frac{2}{3}\right)^14\)
What is the equivalent expression?Two thirds to the fourth power is given by:
\(\left(\frac{2}{3}\right)^4\)
Two thirds to the third power is given by:
\(\left(\frac{2}{3}\right)^3\)
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
\(\left(\frac{2}{3}\right)^4 \times \left(\frac{2}{3}\right)^3 \left(\frac{2}{3}\right)^{4 + 3} = \left(\frac{2}{3}\right)^7\)
Then, this entire expression is raised to the second power, meaning that:
\(\left[\left(\frac{2}{3}\right)^7\right]^2 = \left(\frac{2}{3}\right)^7 \times \left(\frac{2}{3}\right)^7 = \left(\frac{2}{3}\right)^{7+7} = \left(\frac{2}{3}\right)^14\)
\(\left(\frac{2}{3}\right)^14\) is the equivalent expression.
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helppp just number 1 :,(
Answer:
9
Step-by-step explanation:
The distance is the positive difference in the coordinates.
\(BD=|-6-3|=9 \)
66. The quadrilaterals below are similar.
What is the length of FG?
Answer: 9
Step-by-step explanation:
18/6 = 3
3 x 3 = 9
using the line of best fit
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
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Can someone pls help 15 POINTS!!!
Answer:
Step-by-step explanation: Just so you know we need to see the whole problem and l am actually already learned this im just finished with the Ratios
Write a unit rate for the situation please. 20 meters in 4 seconds
Answer: 20/4 = 5 m/s
Step-by-step explanation:
A unit rate is a number over 1. 20/4 is the answer not simplified. Divide both 20 and 4 by 4. 20=5; 4=1. Therefore, it is 5 m/s.
Hope this helps! :)
Can someone help with vectors?
Answer:
Wait, the vector from despicable me or the math vector?
Step-by-step explanation:
If its the math vector than here: The correct answer is a vector
Maria purchased a car for $8599. If the rate of depreciation is 2.5%, what will the value of the car be after four years? Round your answer to the nearest hundredth.
Answer:
$ 7770.81
Step-by-step explanation:
2.5 % each year means the car retains 97.5 % ( or .975 in decimal) of its value per year
8599 ( .975) ^4 = $ 7770.81
Work out the volume of the prism height of 12 4 and five
The calculated volume of the prism is 702 cubic cm
Finding the volume of the prismFrom the question, we have the following parameters that can be used in our computation
The trapezoidal prism (see attachment)
The formula of the volume of a trapezoidal prism is
Volume = Base area * Height
Where we have
Base area = 1/2 * (8 + 10) * 6
Evaluate the sum of 8 and 10
Base area = 1/2 * 18 * 6
Evaluate the products of 1/2, 18 and 6
Base area = 54
Also, we have
Height = 13
So, the volume is calculated as
volume = 13 * 54
Evaluate
volume = 702
Hence, the volume of the prism is 702 cubic cm
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Solve for x using
cross multiplication.
4x - 4
4x - 4
7
x + 3
x = [?]
Answer:
x = 29
Step-by-step explanation:
Multiply both sides by 7:
\(4x-4=\frac{7x+21}{2}\)
Multiply both sides by 2:
\(8x-8 = 7x+21\)
Subtract 7x from both sides:
\(x-8=21\)
Add 8 to both sides
\(x=29\)
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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find the values of y and x
Step-by-step explanation:
180-66=y | 6x-102=66
y=114
x=(66+102)/6-->x=168/6-->x=28
To turn 2/5 into a decimal what operation must you preform
Answer:
2/5 =0.4
Step-by-step explanation:
Decimals are one of the method of representation of fractions in which there is power of 10 in the denominator of the fraction. They are 10,100,1000,10,000 ,100,0000 and so
Example = 1/10 = 0.1
1/100 = 0.01
1/1000 = 0.001
In 2/5 we have to make the denominator 10
since in denominator there is five , can be made 10 by multiplying it by 2
2/2 = 1 and 1* x = x , hence if we multiply numerator and denominator by 2 it won't change the fraction.
2/5×2/2=2×2/5×2=4/10=0.4
Thus, 2/5 =0.4 in decimal form.
The product of five and a number plus 10 is at least thirty
Answer: Greater of equal sign
Step-by-step explanation:
5+10+x is greater than or equal to 30 ( use the greater of equal to sign)
AThe number that is used to multiply thevariable is called the coefficient. In thisexpression, what is the coefficient?2 + 4yBC4y2PH
Answer:
4
Step-by-step explanation:
Since the number that is used to multiply the variable is called the coefficient, identify the number that goes with the variable ''y'', in this case, it is 4.
Please help me on my homework
the correct answer is $948
Can someone help me pleaaaaaaaaaaaaase
Answer:
x=4y-284
Step-by-step explanation:
Hope this helped!!!
Triangle A is a scaled version of triangle B. The dimensions of triangle A are twice the dimensions of triangle B. The area of triangle B is 40.5 sq cm. What is the area of triangle A?
Step-by-step explanation:
the lengths of any line (side, height,...) in A is twice as long as in B.
now, the area of a triangle is
baseline × height / 2
so, two lines are multiplied. that means the factor 2 gets multiplied in 2 times. and that means the area increases by the factor 2×2 = 4
therefore, the area of A is
40.5 × 4 = 162 cm²
HELP NEEDED ASAP
2. Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid. [1mark]
b) State the following for the transformed function [2marks]
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
The five key points of the parent function are:
Domain: Set of all real numbersRange: Set of all real numbers from -1 to 1 (inclusive)No vertical asymptoteNo horizontal asymptoteMaximum: (π/2 + 2πn, 1)The five key points of the parent functionThe function is given as:
y = -2 sin[2(x - 45)] + 1
The above function is a sine function, and the parent function of a sine function is
y = sin(x)
The properties of the above function are:
Domain: Set of all real numbersRange: Set of all real numbers from -1 to 1 (inclusive)No vertical asymptoteNo horizontal asymptoteMaximum: (π/2 + 2πn, 1)The transformed functionThe transformed function is given as:
y = -2 sin[2(x - 45)] + 1
A sine function is represented as:
y = A sin[Bx + C] + D
Where:
A represents the amplitudePeriod = 2π/BC represents horizontal phase shiftUsing the above representations, we have:
Amplitude = -2Period = 2π/2 = πHorizontal phase shift, C = 2 * -45 = -90Equation of the axis, y = 1The graph of the functionSee attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1
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A nine-month old baby drank an average of 7 1/4 oz during each of four feedings. If the baby drank 7 1/2oz, 7 3/8oz, & 6 3/8oz in the first three feedings, how many ounces were taken during the fourth feeding?
A) 7 3/8
B) 6 3/8
C) 6 3/4
D) 7 3/4
Show work please
Answer: D) 7 3/4
Step-by-step explanation:
With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.
7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4
Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses
29 = 21 1/4 + x
Now we can isolate x by subtracting 29-21 1/4
so
x = 7 3/4 thus the answer is D
Answer:
D) 7 3/4
Step-by-step explanation:
Let x = amount of last feeding.
7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4
4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x
28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x
29 = 20 10/8 + x
(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)
29 = 21 2/8 + x
29 = 21 1/4 + x
x = 29 - 21 1/4
x = 28 4/4 - 21 1/4
x = 7 3/4
Answer: 7 3/4
How many solutions does this system of equations have y = -1/3x + 7. y = -2x^3 + 5x^2 + x - 2
The system of equations has one solution.
How many solutions does this system has?To check this, we can graph the two equations of the system:
y = (-1/3)x + 7
y = -2x³ + 5x² + x - 2
On the same coordinate axis, and check how many times do the graphs intercept.
The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.
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LOOK AT PIC, ASAP, ROGHT ANSWER GETS BRAINLIEST !
Answer:
Step-by-step explanation:
The teacher has 7/8 pounds of clay given.
gives out 1/16 per station
7/8= 0.875 pound
7/8 / 1/16 pound= 14 maximum stations
14 stations divided by 2 classes = 7 in each room
from information find out measure of angle ABF
Answer:
if 9x = 180 degree
Step-by-step explanation:
one x equal to 20 degree
and if 3x= 60 degree the ? = 120 degree
Answer:
∠ ABF = 120°
Step-by-step explanation:
HCI is a straight line , so
3x + 2x + 4x = 180 , that is
9x = 180 ( divide both sides by 9 )
x = 20
∠ ABF and ∠ BCI are corresponding angles and are congruent , so
∠ ABF = 2x + 4x = 6x = 6(20) = 120°
ap stats on average, how many people from the region will need to be selected to find one person who carries the genetic trait
On an average, about 2.13 people region will need to get selected in order to find that one person who carries the genetic trait.
Random selection is a very important process in research methodology. The purpose of random selection is to increase the generalizability of the results as when we draw a random sample from a large population, it is less likely to be subject to bias.
Since 47 percent of the people in the population are carrying the gene, the probability of random selection will be 0.47. But we need to also consider how many trials will be unsuccessful. Therefore, we will use the mean,
1/0.47 = 2.127 ≅ 2.13
--The given question is incomplete, the complete question is
"According to a recent survey, 47 percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?"--
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can x³+4x²-2x=0 be solved if so solve it
On solving the provided question we can say the root of the given cubic equation are - x= 0, 4.449 and -0,449
What does "cubic equation" mean?A cubic equation is one that has degree three. All cubic equations have roots that are either one real root and two imaginary roots or three real roots in nature. Three-degree polynomials are referred to as cubic polynomials.
What is cubic quadratic equation?An algebraic equation known as a cubic equation has a polynomial with a greatest degree of three. These are a few instances of cubic equations. 2x3 - 4x2 + 5 = 0, etc., where x3 - 4x2 + 15x - 9 = 0 A cubic equation has the generic form ax3 + bx2 + cx + d = 0, where a 0.
\(x = \frac{4-\sqrt{24} }{2} = 2 - \sqrt{6} = -0.449\\ x = \frac{4+\sqrt{24} }{2} = 2 - \sqrt{6} = 4.449\\\\x = 0\)
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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.
2.66; The line of best fit overpredicts the temperature change.
2.66; The line of best fit underpredicts the temperature change.
1.94; The line of best fit underpredicts the temperature change.
−1.94; The line of best fit overpredicts the temperature change.
The correct statement regarding the residual in this problem is given as follows:
2.66; The line of best fit underpredicts the temperature change.
What are residuals?For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:
Residual = Observed - Predicted.
For a rain amount of 0.4 inches, the predicted temperature change is given as follows:
y = -1.4 x 0.4 + 0.2
y = -0.36.
Then the residual is given as follows:
R = 2.3 - (-0.36)
R = 2.66 -> underpredicts the change.
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Answer:
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sofiapenaloza
05/31/2023
Mathematics
College
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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.
2.66; The line of best fit overpredicts the temperature change.
2.66; The line of best fit underpredicts the temperature change.
1.94; The line of best fit underpredicts the temperature change.
−1.94; The line of best fit overpredicts the temperature change.
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joaobezerra
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The correct statement regarding the residual in this problem is given as follows:
2.66; The line of best fit underpredicts the temperature change.
What are residuals?
For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:
Residual = Observed - Predicted.
For a rain amount of 0.4 inches, the predicted temperature change is given as follows:
y = -1.4 x 0.4 + 0.2
y = -0.36.
Then the residual is given as follows:
R = 2.3 - (-0.36)
R = 2.66 -> underpredicts the change.
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Step-by-step explanation:
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The first bend is made 6 inches from one end. Describe two ways you could complete the triangle.
The two ways of forming isosceles triangle by bending the metal strip using length by length by base are
6 by 6 by 87 by 7 by 6What is an isosceles triangle?A triangle that have the two sides equal is referred to as an isosceles triangle.
Using a strip of 20 inches long to construct an isosceles triangle means that the perimeter of the triangle is 20 inches
the perimeter is equal to base + length + length
bending 6 inches already means one of the dimensions is gotten then fo the other is based on if
the 6 is base the 6 is lengthif the 6 is base then minus the 6 from 20 and divide the rest for the length
20 - 6 = 14
the two lengths is 14 one length is 7. so we have 6 + 7 + 7 = 20
If the 6 is length then get another 6 and the rest is base
20 - 6 = 14
14 - 6 = 8
therefore we have 6 + 6 +8 = 20 inches
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If the lengths of two adjacent sides of a parallelogram area a and b, and if the acute angle formed by these two sides is theta, show that the product of the lengths of the two diagonals is given by the expression (a^2 + b^2)^2 - 4a^2b^2cos^2theta
√(a² + b²)² - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.
An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.
we have AB as a, AD as b and the angle between them is theta.
So using the cosine rule, we have
BD = √a² + b² - 2abcosθ
So now consider the triangle ABC
Here AB is a, BC is b and the angle is 180-theta
So using cosine rule, we get AC as
AC = √a² + b² - 2abcosθ( 180 - θ )
AC = √a² + b² - 2ab(-cosθ )
AC = √a² + b² - 2abcosθ
Now we have the two diagonals AC and BD. So multiplying, we get
AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ
Simplifying, we get
AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)
AC × BD = √(a² + b²)² - (2abcosθ)²
AC × BD = √(a² + b²)² - 4a²b²cos²θ
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i need help again omf im so sorry
Answer:
I'm pretty sure Dave is correct
Step-by-step explanation:
Ashley made 85% of her free throws. Emma made 7/8 of her free throws. who has the better average?
We need to compare two numbers, so we need to put them in the same format. In this case, we will choose the decimal form
\(\begin{gathered} 85\text{ \%=0.85} \\ \frac{7}{8}=0.875 \end{gathered}\)Then, Emma has a better average than Ashley.
Suppose that the length of a confidence interval is 0.06 when the sample size is 400. Determine how the sample size must change to decrease the length of the confidence interval to 0.03 (Use decimal notation. Give your answer as a whole number:) new sample size:
We use Z-Distribution for large sample sizes, The reduced sample size is 200.
What do you mean by probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
What do you mean by Z-distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
confidence interval = 0.06
Sample size= 400
new interval of confidence = 0.03
new sample size = 400/0.06 * 0.03
=200
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