The expression can be written as 5¹/₂₅.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the number is 5 and 1 over 25. The mixed fraction can be written as:-
E = 5 and 1 over 25
E = 5¹/₂₅.
Therefore, the expression can be written as 5¹/₂₅.
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A certain bacteria has a half-life of every 1.5 hours. If you start with 600 bacteria cells, how many will you have left after 6 hours?
Please include an explanation if you can!!!
The number of bacteria that is left is 38
How to determine the bacteria's leftThe half-life is the time it takes for half of the bacteria to reduce
The time is given as 1.5 hours
After 1.5 hours:
The number will have gone through 6 / 1.5 = 4 half-lives.
So, the number of bacteria cells after 6 hours will be 600 * (1/2)^4
Evaluate
600 * (1/2)^4 = 600 / 16 = 37.5
Approximate
600 * (1/2)^4 = 600 / 16 = 378
Since the number of bacteria cells is 37.
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what is -3/4 to the power of 3
Answer:
it is 2 minus six
2-6
Step-by-step explanation:
hdgeheksdiddh
Answer:
-27/64
Step-by-step explanation:
Exact form
-27/64
Decimal Form
-0.421875
(4.6x10^6)(1.1x10^7)
Answer:
[tex]5.06*10^{13}[/tex]
Step-by-step explanation:
[tex](4.6*10^6)(1.1*10^7)=(4.6*1.1)(10^6*10^7)=5.06*10^{13}[/tex]
the amount of taxes a city collects is proportional to the population of the city. in 2005 the population was million and it had increased to million by 2017. if billion dollars in taxes were collected in 2005, how much was collected in 2017?
If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.
In 2005 the population was 2 million and it had increased to 3 million by 2017.
If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.
The amount of taxes of the city is proportion to the population of that city.
Tax(T) = kP(Population)
where k is a constant.
In 2005 Population = 2 millions and T = 20 billion. So
20 = 2k
Divide by 2 on both side, we get
k = 10
In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:
t = 10 × 3
t = 30 billion
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The complete question is:
The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?
Thirty five divided by three
Answer: Thirty-five divided by three equals 11.67.
Step-by-step explanation:
Division is the mathematical operation that finds the number of times one quantity is contained within another. In this case, 35 is being divided by 3 to find the result.
To perform the division, we divide 35 by 3, which gives us a quotient of 11 with a remainder of 2. If we want to express this result as a decimal, we can add the remainder divided by the divisor, so the answer would be 11 + 2/3 = 11.67.
In summary, 35 divided by 3 equals 11.67, meaning that 3 goes into 35 a total of 11 times with a remainder of 2.
3. During arugby Contest; 54 342 People watched the first game while 49990 people watched the Second game. If 156 330 people watched all three games, How many watched the third game ?
Answer:
51998
Step-by-step explanation:
To solve the problem, we need to subtract the number of people who watched the first two games from the total number of people who watched all three games:
156330 - (54342 + 49990) = 156330 - 104332 = 51998 people watched the third game.
Therefore, 51998 people watched the third game.
Practice
1.
Three students wrote expressions for this diagram.
Explain or show why they are each correct.
Yolanda: 16 ÷8=2
Riku: 16 ÷ 2=8
Mariana: 8x2 = 16
All three expressions are correct based on the properties of arithmetic operations.
How to explain the expressionYolanda wrote 16 ÷ 8 = 2, which means she is finding how many times 8 fits into 16. The answer is 2, meaning 16 is divided into 8 equal parts and each part has a value of 2.
Riku wrote 16 ÷ 2 = 8, which means he is finding how many times 2 fits into 16. The answer is 8, meaning 16 is divided into 2 equal parts and each part has a value of 8.
Mariana wrote 8 x 2 = 16, which means she is finding the product of 8 and 2. The answer is 16, meaning 8 multiplied by 2 gives a total of 16.
All three expressions are correct.
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Find the value of X.
The value of x is 10
What are similar figures?Similar figures are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.
This shows that x-3/21 = x-1/27
21(x-1) = 27(x-3)
divide through by 3
= 7(x-1) = 9 ( x-3)
7x -7 = 9x-27
collect like terms
9x -7x = 27-10
2x = 20
divide both sides by 2
x = 20/2
x = 10
therefore the value of x is 10
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CAN SOMEONE PLS HELP MEE
Answer:
[tex]4\sqrt{3} - 4i = \boxed{\left(8, \dfrac{\pi}{6}\right)}[/tex]
Step-by-step explanation:
Given complex number is:
To plot this on polar coordinates use the fact that a complex number of the form [tex]z=x+yi[/tex] can be converted to polar form [tex](r, \theta)[/tex] using the relationship
[tex]r = \sqrt{x^2 +y^2) }\\\mathrm{and}\\\theta = cos^{-1}\left(\dfrac{x}{r}}\right)[/tex]
Comparing [tex]4\sqrt{3} - 4i[/tex] and [tex]z=x+yi[/tex]
we see that
[tex]r = \sqrt{(4\sqrt{3})^2 + (-4)^2}\\\\r = \sqrt{48 + 16}\\\\\\r = \sqrt{64} = 8\\\\\theta = cos^{-1} \left(\dfrac{4\sqrt{3}}{8}\right)[/tex]
[tex]\theta = \cos^{-1} \left(\dfrac{\sqrt{3}}{2}\right) = 30^\circ = \dfrac{\pi}{6} \;radians[/tex]
So in polar coordinates,
[tex]4\sqrt{3} - 4i = \left(8, \dfrac{\pi}{6}\right)[/tex]
a rectangle with area 1800 sq m is 3 times as long as it is wide. what is the sum of the diagonals? round to the nearest tenth.
The sum of the diagonals is 60, rounded to the nearest tenth.
Let's call the width of the rectangle "w". Then the length is 3 times the width or 3w. The area of the rectangle is 1800 square meters, so:
w * 3w = 1800
w^2 * 3 = 1800
w^2 = 600
w = √600 = √(600^(1/2)) = √(600^(1/2)) = 6 √(10^(1/2))
So the width is 6 √(10^(1/2)) and the length is 3 * 6 √(10^(1/2)) = 18 √(10^(1/2)).
The sum of the diagonals is the square root of the sum of the squares of the lengths of the two sides, so:
d = √(w^2 + (3w)^2)
d = √(w^2 + 9w^2)
d = √(10w^2)
d = √(10 * w^2)
d = √(10 * (6 √(10^(1/2)))^2)
d = √(10 * (6^2 * (10^(1/2)))^2)
d = √(10 * (36 * 10))
d = √(10 * 360)
d = √3600
d = 60
So the sum of the diagonals is 60, rounded to the nearest tenth.
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what is separate the population into non overlapping groups and then obtain a simple random sample from each group is called?
"Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.
Explain about the Stratified Sampling?Differentiated stratified sampling. By employing a characteristic to divide the population, we can then obtain a proportional randomized sample of each group.
The population is divided into non-overlapping groups, or strata, and a proportional simple randomized sample is taken from each stratum to create a stratified sample. Each group's members ought to have some things in common. Once the strata have been established, we must decide how many people will be chosen from each stratum. Here, proportionality of the chosen number is crucial.Thus, "Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.
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Find the length of YB
Answer:
YB = 11.2
Step-by-step explanation:
Δ AYZ and Δ ABCare similar by the AA postulate
then the ratios of corresponding sides are in proportion , that is
[tex]\frac{AY}{AB}[/tex] = [tex]\frac{AZ}{AC}[/tex] ( substitute values )
[tex]\frac{7}{7+YB}[/tex] = [tex]\frac{15}{15+24}[/tex] = [tex]\frac{15}{39}[/tex] ( cross- multiply )
15(7 + YB) = 7 × 39 = 273 ( divide both sides by 15 )
7 + YB = 18.2 ( subtract 7 from both sides )
YB = 11.2
The length of YB would be; 11.2
We know that proportion is a fraction of a total amount, and the measures are related using a rule of three.
Since Δ AYZ and Δ ABC are similar by the AA postulate
Then the ratios of corresponding sides are in proportion , that is
AY/AB = AZ/AC
cross- multiply ;
15(7 + YB) = 7 × 39 = 273
7 + YB = 18.2
Hence, YB = 11.2
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What is a residual? What does it mean when a residual is positive? Choose the correct answer below. A. A residual is the difference between an observed value of the response variable y and the value of the corresponding explanatory variable x. If it is positive, then the response variable is greater than the explanatory variable. B. A residual is the difference between an observed value of the response variable y and the average value of the response variable. If it is positive, then the response variable is greater than the mean. C. A residual is the difference between an observed value of the response variable y and the predicted value of y. If it is positive, then the observed value is greater than the predicted value. D. A residual is a data point that does not fit the pattern of the rest of the data. If it is positive, then the data point should still be included in the data set.
(C) The difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.
What is residual?The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.
A residual is a discrepancy between an observed and expected value for the response variable y.
In the event that it is positive, the observed value exceeds the expected value.
The information that was ignored throughout the (first) cycle of the modeling is contained in the residuals, which serve as a significant source of information.
They must thus divulge something to us.
It is possible to describe the residual plot to the students as a kind of magnifier for the modeling procedure.
Therefore, (C) the difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.
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The level of significance in hypothesis testing is the probability of?
The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).
In hypothesis testing, the level of significance is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true. It is also known as the p-value and is usually denoted by the symbol α (alpha). The formula for calculating the level of significance is:
α = P (Statistic ≥ Observed Statistic | H0 is true)
For example, suppose we are testing a hypothesis that the mean height of all people in a population is 160cm. We select a sample of 50 people and measure the mean height to be 162cm. Assuming the null hypothesis is true, the level of significance is calculated as follows:
α = P (Statistic ≥ 162 | H0 is true)
This p-value measures the probability of obtaining a result that is at least as extreme as the observed result (162cm), if the null hypothesis is true. If this p-value is less than the predetermined significance level (usually 0.05 or 0.01), then the null hypothesis is rejected and we accept the alternative hypothesis.
The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).
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Deandre's dog ate 8 cans of dog food this week. Each can contained 47.6 grams of protein. How much protein was this in all
Answer:
Step-by-step explanation:
380.8 grams
Answer:
Step-by-step explanation:
380.8
An angle measures 4.2° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
Step-by-step explanation:
If 2 angles are complementary, they are equal to 90 degrees. So, lets say that the measure of the first angle is x, and the measure of the second angle is y.
Since x measures 4.2 degrees more than its complementary angle (y), we can say that x - 4.2 = y
And, since they are complementary angles, x+y = 90.
We can now use a system of equations to solve. Since we know y = x-4.2, we can substitute y with x-4.2, making the equation x + x - 4.2 =90.
Simplify:
x+x-4.2=90
2x -4.2 =90
2x = 94.2
x= 47.1
Since y=x-4.2, we can now find y.
y = x-4.2
y= (47.1)-4.2
y=42.9
So, the measure of the angles is 47.1° and 42.9°.
Hope this helps!
An account with an initial balance of $2,000.00 and a 2.80% interest rate has a balance of $2,056.72 at the end of one year. What is the effective annual yield?
The effective annual yield (EAY) is 2.83%
How the answer was obtainedThe effective annual yield (EAY) is the true annual interest rate that an investor earns after taking into account the effect of compounding. To calculate the EAY, you need to find the interest rate that will make the formula (1 + r/n)^n = final balance/initial balance hold true, where r is the interest rate and n is the number of times compounding occurs in a year.
Given the initial balance of $2,000 and a final balance of $2,056.72 after one year, we can use the following formula to calculate the EAY:
(1 + r/n)^n = $2,056.72/$2,000
Since the interest rate is given as 2.80%, and the number of times compounding occurs in a year is not given, we'll have to assume n. A common assumption for n is 12, which represents monthly compounding. Plugging in the numbers, we have:
(1 + 0.028/12)^12 = $2,056.72/$2,000
Solving for r, we get:
r = 12 * (($2,056.72/$2,000)^(1/12) - 1)
r = 2.83%
So the effective annual yield (EAY) is 2.83%.
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at his school's spring carnival, bryant is in charge of the balloon-launcher contest. in this contest, each team builds a catapult to launch water balloons at a target. bryant gives a bucket of 14 water balloons to each team in the contest. in all, he gives out 70 water balloons.which equation can you use to find the number of teams t in the contest?
The equation 70 = 14t can be used to find the number of teams in the contest. By solving this equation, we found that there were 5 teams in the contest.
70 = 14t
To find the number of teams in the contest, we can use the equation 70 = 14t. This equation states that the total number of water balloons, 70, is equal to the number of teams, t, multiplied by the number of balloons each team gets, 14.
To solve this equation, we can divide both sides of the equation by 14. This will give us the equation t = 70/14. We can then simplify this equation by dividing 70 by 14. This gives us t = 5. This means that there are 5 teams in the contest.
Therefore, the equation 70 = 14t can be used to find the number of teams in the contest. By solving this equation, we found that there were 5 teams in the contest.
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pls help plssssss
it would really help
The length of side AC rounded to 1 decimal place is 17.3 cm.
What is the length of side AC?The figure on the image is a right triangle.
From the image;
Angle B = 68 degreesOpposite to angle B = AC = ?Adjacent to angle B = AB = 7cmusing the trigonometric ratio, we determine the length of side AC.
Tangent = Opposite / Adjacent
tan( 68 ) = AC / 7
AC = tan( 68 ) × 7
AC = 17.3 cm
Therefore, side AC has a length of 17.3 cm.
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what is 4/5x12 i need help please its so hard to do it
The simplification of the given fraction above would be = 9⅘
What is a fraction?A fraction is defined as the part of a whole value which is represented in the form of a numerator and a denominator.
The given fraction that requires simplification is as follows:
= 4/5 × 12
= 48/5
= 9⅘
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please help me in this duty
P(30)=3, If Ms. Crowley has 30 students in her class, she must buy 3 packs of red paper mate flair pens.
P(0)=0, and if she has 0 students, she does not need to buy any pens.
To find the number of packs of pens Ms. Crowley must buy, we need to divide the number of students by the number of pens in each pack and then round up to the nearest whole number.
This is because if Ms. Crowley has 30 students, for example, and each pack contains 12 pens, then 30 ÷ 12 = 2.5, which means she needs 3 packs of pens to ensure that every student has a pen.
Using this calculation, we can find the number of packs of pens Ms. Crowley must buy for each number of students:
P(30) = ceil(30 ÷ 12) = ceil(2.5) = 3
P(0) = ceil(0 ÷ 12) = ceil(0) = 0
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5(6-3)=6+13 simplified
Answer:
15=19
Step-by-step explanation:
5×3=6+13
15=19
so 15=19
how to find the possible values for theta where 0 degrees is greater than theta and 360 degrees is greater than theta
The possible values for theta, where 0 degrees is less than theta and 360 degrees is greater than theta, would correspond to an angle measure in the range 0 < theta < 360 degrees.
This range includes all angles greater than 0 degrees and less than 360 degrees, which correspond to a full revolution around a circle.
It's important to note that angle measures are typically represented in either degrees or radians, with 360 degrees corresponding to 2π radians. So, if you need the values of theta in radians, the range would be 0 < theta < 2π.
In general, the possible values for theta are dependent on the context in which they are used and the specific system of measurement being employed. For example, in some cases, the range of possible values for theta may be restricted to between 0 and 180 degrees, or between -180 and 180 degrees, depending on the application.
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Carter drove 210 miles in 7 hours. If he drove at a constant rate, how far did he travel each hour?
Answer: 30 miles
Step-by-step explanation:
We are given a constant rate of 210 miles in 7 hours. Since we are trying to find how far Carter travelled in 1 hour, we can set up a proportion.
[tex]\frac{210}{7} =\frac{x }{1}[/tex] [cross multiply]
[tex]210=7x[/tex] [divide both sides by 7]
[tex]x=30[/tex]
Therefore, Carter travelled 30 miles in one hour.
a cycle shop gave away 5000 miniature cycles and bumper stickers. the cycles cost 0.62 each and the bumper stickers cost 0.52 each. the cycle shop spent $2798 on the gifts. how many of each gift did they buy>
The cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.
Let's call the number of miniature cycles given away "x". The number of bumper stickers given away would then be 5000 - x.
The cost of the cycles is 0.62x, and the cost of the bumper stickers is 0.52 (5000 - x).
So we can write an equation to represent the total cost:
0.62x + 0.52 (5000 - x) = 2798
Expanding the second term:
0.62x + 2600 - 0.52x = 2798
Combining like terms:
0.10x = 198
Finally, solving for x:
x = 1980
So the cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.
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5.060 x 10 3rd power /km
Answer:
Step-by-step explanation:
charge it paigon
ou have an ordinary deck of 52 well-shuffled cards. you remove the cards one at a time until you get an ace. let the random variable x denote the number of cards removed. what is the probability mass function of x? make sure to specify where x can take values. recall that there are four aces in a standard 52-card deck.
The probability mass function of x is p(x) = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.
x indicates the number of cards removed
that means
x = 1, 2, ..., 52
The probability of picking an ace is
P(ace) = 4/52
that means:
P(Ace') = 48/51 ----- Cards are selected without replacement
If x Ace is chosen, remaining cards are 52 - x
Using the above as a guide, it looks like this:
For x = 1, 2, ..., 52, PMF = 4/52 * (48/51)^(x-1) * (1/51)^(52-x).
ABOUT PROBABILITYProbability is the magnitude of the chance (likelihood) of something events will occur. Based on the definition of probability, there are the important things are the magnitude of the opportunity and the event will occur.
The probability that an event will occur is between 0 and with 1. If an event has a chance of happening 0, then this event is definitely not going to happen. If an event has chance will occur 1, then the event will definitely occur. With thus it can be concluded that the smaller the probability of an event (the closer the probability is to 0), the smaller the chance of the event
it will happen.
Conversely, the greater the probability of an event (the closer the probability is to 1), the greater the chance of the event it will happen.
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how do i solve this asap
Answer:
Step-by-step explanation:
when there is a plus before a negative, ignore it, the negative makes it irrelavant.
-4-3=-7
-4y-7
A linear function is shown on the graph. A linear function beginning with an open circle at negative 4 comma negative 1 and ending with a closed circle at 6 comma 4. What is the domain of the function? {x | −4 < x < 6} {x | −4 < x ≤ 6} {y | −1 < y < 4} {y | −1 < y ≤ 4}
Any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.
What is linear function?I linear function is a mathematical expression involving variable that when craft create is straight line linear function are used to model relationship between two variable such is cost and revenue price in demand in distance and time linear function can also be used to solve equation and the specialily useful for predicting future outcomes.
The domain of the linear function is {x | −4 < x < 6}, which means that the x-values of the function are all real numbers greater than -4 and less than 6. This means that any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.
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Will Mark Brainlist!
Solve for x on the diagram below
Answer:
x = 20
Step-by-step explanation:
3x + 80 + 2x = 180
5x + 80 = 180
5x = 100
x = 20