Answer:
Below
Step-by-step explanation:
2^3 / 2^7 = 2^(3-7) = 2^(-4) = 1/ (2^4) = 1/16 = .0625
~~~~pick your poison
The required expression [tex]2^3/2^7[/tex], after simplification is equivalent to 1/16.
To simplify the expression [tex]2^3/2^7[/tex], we can apply the rule of exponentiation that states when dividing two numbers with the same base, we subtract the exponents.
In this case, the base is 2.
Using the rule, we subtract the exponent of the denominator from the exponent of the numerator:
[tex]2^3/2^7 = 2^{7} = 2^{-4}[/tex]
The expression [tex]2^{-4}[/tex] can be further simplified by using the rule that states any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent:
[tex]2^{-4} = 1/2^4[/tex]
= 1/16
Therefore, the expression [tex]2^3/2^7[/tex] is equivalent to 1/16.
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HelpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss WILL GIVE 20 POINTS EASY
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.
What's meant by rate?
A rate in calculation displays how numerous times one number is contained in another. The rate of oranges to failures, for case, is eight to six if there are eight oranges and six failures in a coliseum of fruit. The proportions of oranges to the overall quantum of fruit are 814 for oranges and 68 for failures, independently. An equation in which two rates are made equal is known as a chance. As an illustration, you could express the rate as 1 3 if there's 1 joe and 3 girls( for every one boy there are 3 girls)Areas If the scale factor of the sides of two analogous polygons is m/ n
also the rate of the areas is (m/n)^2.
Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.
It's given that, the rate of peripheries of two analogous quadrilateral is 2 4
now,
to find the rate of area, we can take two quadrilaterals, say square.
Square ABCD of side 2 units and Square PQRS of side 4 units.
now rate of areas,
[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]
[tex]=\frac{2 \times 2}{4 \times 4}[/tex]
= 4/16
= 1/4
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Amy has three times as many Star Wars toys as Carly. Total they have 312 Star Wars toys. how many Star Wars toys does Amy have?
Answer:
the answer to this question is 936
Sean M(2,5) el punto medio de P(a,-2) y Q(-5,b) ¿como hallar el valor de (a+2b)
Solving the provided question, we can say that equatiοn of slope intercept will me as y -y1 = m(x-x1) => 3x - y = -1
What is slope intercept?In mathematics, the intersectiοn point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crοsses on a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equation fοr the straight line to show this.
The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept fοrm. When an equatiοn has the intercept form (y=mx+b), the slοpe is m and the y-intercept is b. Sοme equations can also be rewritten such that they seem to be slοpe intercepts. If y=x is rewritten as y=1x+0, fοr instance, the slοpe and y-intercept are bοth changed to 1.
Here,
coordinates are
M(2,5) and P(a,-2)
equation of slope intercept will me as
y -y1 = m(x-x1)
y - 5 = 3x-4
3x - y = -1
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A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution. How many liters
of the 10% and how many liters of the 70% solutions will be used?
Liters of 10% solution =
Liters of 70% solution=
Liters of 10% solution = 1 liters
Liters of 70% solution = 5 liters
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x +3 = 8 is an equation.
We have,
10% solution = x
70% solution = y
Now,
A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.
This means,
We can make two equations.
0.10x + 0.70y = 6 x 0.20
0.10x + 0.70y = 1.2 ______(1)
x + y = 6 ______(2)
Solve for x and y.
From (2),
x = 6 - y
Substituting in (1) we get,
0.10x + 0.70y = 1.2
0.10 (6 - y) + 0.70y = 1.2
0.6 - 0.10y + 0.70y = 1.2
0.6 + 0.60y = 1.2
0.60y = 1.2 - 0.6
0.60y = 0.6
y = 1
And,
x = 6 - y
x = 6 - 1
x = 5
Thus,
10% solution = 1 liter
70% solution = 5 liters
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89392i÷5×5+788 what is the answer
Answer:
89392i + 788
Step-by-step explanation:
The divide by 5 and the multiply by 5 cancel out, and we cannot simplify 89392i + 788 any further, since we don't know what i is. Therefore the answer is 89392i + 788.
Hope that helps!
pls help
About 3,500 tourists visit the Granite Falls overlook each year. After the construction of a new nature center with exhibits and hands-on activities, that number is expected to increase 5% each year. Assuming the same growth continues, you can use a function to approximate the number of annual visitors to the overlook x years after the nature center is built.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:
Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:
y0 = 3,500
Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:
r = 0.05
Write the equation for exponential growth. The formula for exponential growth is given by:
y = y0 × (1 + r)^x
where x is the number of years after the nature center is built.
So, the equation for the function in this case would be:
f(x) = 3,500 × (1 + 0.05)^x
This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.
One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that ______.
One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that quantify the strength and direction of the correlation in a precise and standardized way..
When we have two variables that are related, we say that there is a correlation between them. The most common way to visually represent a correlation is by plotting the data on a scatter plot, where each point represents a pair of values for the two variables.
While a scatter plot is a useful tool to visualize the relationship between two variables, it doesn't tell us how strong or weak the correlation is. For instance, two variables might show a positive correlation, but the scatter plot might be quite dispersed, indicating that there is a lot of variability in the data. In this case, we would say that the correlation is weak. On the other hand, if the scatter plot is tightly clustered around the line, we would say that the correlation is strong.
This is where the correlation coefficient comes in. The correlation coefficient is a mathematical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.
To compute the correlation coefficient, we first need to calculate the covariance between the two variables. Covariance is a measure of how much the two variables vary together, and it is defined as the sum of the products of the deviations of the values from their respective means. Once we have the covariance, we can divide it by the product of the standard deviations of the two variables to get the correlation coefficient.
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5 Practice
6a of 6
Question 6a
If a truck carrying 3 tons of wheat unloads 1, 000 pounds, what is the weight of the
wheat still in the truck?
Answer: the weight of the wheat still in the truck is 5000 pounds.
Step-by-step explanation:
Here are the steps to calculate the weight of the wheat still in the truck:
Convert the weight of the unloaded wheat to tons. To convert from pounds to tons, divide by 2,000:
1000 lbs / 2000 lbs/ton = 0.5 tons
Subtract the weight of the unloaded wheat from the original weight:
3 tons - 0.5 tons = 2.5 tons
Convert the answer back to pounds:
2.5 tons * 2000 lbs/ton = 5000 lbs
Therefore, the weight of the wheat still in the truck is 5000 pounds.
The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. Express the APR algebraically.
The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. APR algebraically is: 12f/a.
What is APR algebraically?Finance charge = Monthly interest rate · Average daily balance
Monthly interest rate = APR/12
Where:
Finance charge = f
Average daily balance = a
f= Monthly interest rate · a
f = APR/12 · a
f/a = APR/12
12.f/a = APR
Therefore APR algebraically is: 12f/a.
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I need help on solving for "B"
The y-intercept b of the equation of the line is 30.
How to find the equation of a line?The graph represent a linear relationship between the temperature in degree farad and time in minutes.
Therefore, let's find the y-intercept b of the equation.
Hence, using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = 20x + b
where
b = y-interceptUsing (6, 150) let's find b as follows:
y = 20x + b
150 = 20(6) + b
150 - 120 = b
Therefore,
b = 30
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What is the probability of obtaining twelve heads in a row when flipping a coin? Interpret this probability The probability of obtaining twelve heads in a row when flipping a coin is________
In this question you're given that a coin is flipped 12 times. Now I'll make some assumption here. The first assumption is that the coin is fair. That means the probability of getting ahead in a trial in the toss is the same as probability of getting a deal in the toss and that would be half And second. The all the 12 flips or tosses are independent of each other. And thirdly that the probability of getting ahead, it's the same in each toss and you can see that in each talks there's only two outcomes ahead or not ahead which is a so this is considered a success and this is a failure. It just happened to be the probability of the success and the probability of failure is the same at heart. So this actually follows a binomial distribution model. But in the event that you have not learned by normal distribution we can just go by simple probability multiplication rule. So in probability and it's times or is plus. But the assumption of independent trials and the coin is fair is still the same whether you're using binomial distribution or just simple probability multiplication rule, no Probability of obtaining 12 heads in a row when flipping a coin would be the first pulse, you get a hit. And the second course you also get ahead. And the third toss you get ahead. So on so forth. Up to the last toss, which is the 12th toss, you also get a hit. So it's hit for every toss. So what this means is that probability of first courses ahead is half so that's half now. N and in probability means multiple execution. So just times and second hand is second thoughts is also ahead. So there's a half and so N. S. A. Terms enter is ahead, so that's another half, so so on, so forth. All the way to the last end here. Mr toms And the 12 is also a hit. So this times, how so what we have here is half to the power of 12 since half is multiplying itself 12 times. And so the answer is 1/4 oh 96 Or 0.0002, 44 six, decimal places. Now, if you are using binomial distribution to solve this problem, you will be after this part here. You will be letting X be the number of heads. Oh 12 courses. Right, So X follows the binomial distribution Number of trials is 12, 12 horses. And probability of success in this case is probability of getting ahead in a in a toss is half, so probability of X equals two. R. Where r is the number of heads in 12 courses will be 12, choose our half to the power of our and one minus half is also half To the power of 12 minus are so probability of obtaining 12 heads in a role. So we will be looking at probability of X equals 2, 12. So just suck 12 into the arm. So is this and you will get the same answer of 0.000244
Equation: -140
Answer: x =
= -10x
=
If it takes 6 people 8 hours to finish the job, how long would it take 4 people?
12 hours
If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours
Answer:
5.333 hours.
Step-by-step explanation:
Put this on a chart:
6 people = 8 hours
4 people = ? hours
To find ? Use crisscross multiplication and solve:
? = (4 * 8) / 6
? = 32 / 6
? = 5.333
Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.
Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.
What is meant by budget?
Budget is a planning and monitoring tool used by management to coordinate all of the company's activities. Budgeting is the process of estimating income and expenses for a given time frame.For any individual, group of people, organisation, or government. A budget is a plan for financial calculations for a specified time period, usually a month or a year, but not always.Budgeting is the process of estimating a company's revenues and expenses for a given time period.Examples of budgets prepared for this purpose include the sales budget, which makes a projection of the company's sales, and the production budget, which makes a projection of the company's production, among others.Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.
We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.
So we can set up the following system of equations:
x + y = 168 (total amount of punch)
1.57x + 2.41y = 1.66(168) (total cost of punch)
Simplifying the second equation:
1.57x + 2.41y = 278.88
Now we can use substitution or elimination method to solve for x and y.
Using substitution:
x = 168 - y
1.57(168 - y) + 2.41y = 278.88
264.36 - 1.57y + 2.41y = 278.88
0.84y = 14.52
y = 17.29
So Hannah needs 17.29 gallons of fruit drink.
Using x + y = 168, we can find that she needs 150.71 gallons of soda.
Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.
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2-step Word problemas please help my
Answer:
1: 9 polar bears and 38 penguins
2: 47 snowglobes
3: 130 snowballs
4: 97 penguins
Step-by-step explanation:
i did the math
what is the total population if 15% is 36,000 people
Suppose ABC Inc Can Produce 20 Units of Output Using any of the 4 Techniques Below TECHNIQUE TI 12 13 Т4 LAND LABOR CAPITAL 10 18 12 10 20 8 10 22 6 10 24 3 Further Suppose That The Output sells for $20 Per Unit In The Market. And the prices of land, labor, And capital are $8, $6, & $4, respectively.
11. Which technique should this firm use to maximize profit?
12. This firm will earn a profit equal to ________ dollars.
13. This firm will earn a Revenue equal to _____ dollars.
14. The profit associated with T1 is equal to _______ dollars.
15. If the price of labor falls to $2, ceteris paribus, this firm will earn a profit of
______dollars.
-4x - 15y = -10
x + 3y = 1
Answer:
This system of equations can be solved using substitution or elimination methods.
Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.
Solving for x in the second equation:
x + 3y = 1
x = 1 - 3y
Substituting this expression for x into the first equation:
-4(1 - 3y) - 15y = -10
Expanding and solving for y:
-4 + 12y - 15y = -10
12y - 4 = -10
12y = -6
y = -1/2
Now that we know y = -1/2, we can substitute this value back into the expression for x:
x = 1 - 3(-1/2) = 1 + 3/2 = 7/2
So the solution to the system of equations is (7/2, -1/2).
Checking the solution in both equations:
-4(7/2) - 15(-1/2) = -4(7/2) + 15/
Step-by-step explanation:
Can someone please help me with this question please
Answer:
77.5°
Step-by-step explanation:
You want the measures of the angles formed when ray OX bisects the 155° angle AOB.
BisectorThe angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...
155°/2 = 77.5°
A hiker is starting a hike to his destination. There are four trails (Trail no. 1, 2, 3, and 4) that lead
to his destination. However, each trail divides into two sub-trails along the way and only one of
the two sub-trails leads to hiker’s destination. The hiker has no map available. The hiker decides
to choose one of the four trails by rolling a fair 4-sided die. The hiker also decides to choose
between two sub-trails by flipping a fair coin. What is the probability that the hiker will reach his
destination.
The probability that the hiker will reach his destination is, 1/2
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,
the probability of taking any one trail is 1/4.
Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.
The probability of taking the correct sub-trail is 1/2.
P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)
P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)
P(reaching destination) = 4/8
P(reaching destination) = 1/2
Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.
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Please help me with my following homework problem
The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.
How to make the decisionThe test statistic for this hypothesis test can be calculated as follows:
t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)
Plugging in the values, we get:
t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36
Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.
Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.
Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.
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How did you calculate the total mass of boys
**Image **Find the value of x. Show your steps.
The value of x is 9 by using the concept of corresponding angles.
What are corresponding angles?Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.
From the information given:
(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.
Using the sum of angles on a straight line.
Step 1: (8x + 9)° + 99 = 180°
Step 2: 8x + 108 = 180
Step 3: 8x = 72
Step 4: x = 9
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The height of a triangle is 8 m more than twice the length of the base. The area of the triangle is 21 m². Find the height of the triangle.
Answer:
The height of the triangle is 14 m,
Step-by-step explanation:
Let the base be x, then the height is:
2x + 8The area is half the product of base and height.
Set up equation and solve for x:
x(2x + 8)/2 = 21x(x + 4) = 21x² + 4x = 21x² + 4x - 21 = 0x² + 7x - 3x - 21 = 0x(x + 7) - 3(x + 7) = 0(x + 7)(x - 3) = 0x = - 7 or x = 3The first root is discarded as negative. The second root is the answer.
The base is 3 m, so the height is:
2*3 + 8 = 14 mAnswer:
The height of the triangle is 14 m.
Step-by-step explanation:
The area of a triangle can be found by using the following formula:
[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]
where:
b is the base of the triangle.h is the height of the triangle.If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:
[tex]h = 2b + 8[/tex]
Rewrite this equation to make b the subject:
[tex]\implies 2b=h-8[/tex]
[tex]\implies b=\dfrac{1}{2}h-4[/tex]
Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:
[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]
To find the height of the triangle, solve the equation for h.
[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]
[tex]\implies h^2-8h=84[/tex]
[tex]\implies h^2-8h-84=0[/tex]
[tex]\implies h^2-14h+6h-84=0[/tex]
[tex]\implies h(h-14)+6(h-14)=0[/tex]
[tex]\implies (h+6)(h-14)=0[/tex]
Apply the zero-product property:
[tex]h+6=0 \implies h=-6[/tex]
[tex]h-14=0 \implies h=14[/tex]
As length cannot be negative, the height of the triangle is 14 m.
How many millimeters long is 3 inches
Answer:
3 inches is approximately equal to 76.2 millimeters.
Step-by-step explanation:
Answer:
3 inches = 76.2 millimeters
Step-by-step explanation:
rj and is 2 brother are given php2000 weekly allowance they have allocoted 60% for food 8% for fare 15% for school needs and the remaining 17% for savings how much is allocoted for the following
Answer:
RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.
For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.
For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.
For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.
For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.
So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340
a 17 meter ladder leans against a building the base of the ladder from the building is 6 meters.Find the angle in degrees
The angle of the base and the ladder is 69. 34 degrees
How to determine the valueNote that the six trigonometric identities are;
sinetangentcosinecotangentcosecantsecantFrom the information given, we have that;
Hypotenuse = 17 meters
Adjacent = 6 meters
The identity to use is the cosine
cos θ = adjacent/hypotenuse
Substitute the values
cos θ = 6/17
cos θ =,0. 3529
Take inverse of cos
θ = 69. 34 degrees
Hence, the value is 69. 34 degrees
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A farmer wants to fence a rectangular area of 288 square feet next to a river. Find the length and width of the rectangular which uses the least amount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river
What is the solution of the system
of equations?
y = __
2
3 x + 5
7x − 3y = 15
(0, 5)
B (2,19/3)
(4, 23/3)
(6, 9)
Answer:
2,19/3 this is answer this is correct
Express the following in the form; a+jb
1. Cos(e^j)
2.exp(e^j)
3.(sqrt(j))^sqrt(j)
Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively
What is the expression in a + jb1.
Cos(e^j) can be expressed using Euler's formula as:
Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2
= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))
Re = cos(e^j) + cosh(1)
Im = sin(e^j) - sinh(1)
2.
exp(e^j) can also be expressed using Euler's formula as:
exp(e^j) = e^(cos(1) + j*sin(1))
3.
(sqrt(j))^sqrt(j) can be written as:
(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]
where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.
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