The distance on the map where the scale is 1 inch to 40 miles is 1.75 inches.
How far will be the two cities on the other map?First we know that the cities are at 2.8 inches apart on a map whose scale is 1 inch to 25 miles, then the real distance between the two cities is:
D = (2.8)*25mi = 70 mi
Now we move to a map where each inch is 40 miles, to find the distance in inches, we can take the quotient between the real distance and the scale, it gives:
d = (70mi/40mi) inches
d = 1.75 inches
The distance on the other map is 1.75 inches.
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The distance on the map where the scale is 1 inch to 40 miles is 1.75 inches.
First we know that the cities are at 2.8 inches apart on a map whose scale is 1 inch to 25 miles, then the real distance between the two cities is:
D = (2.8)*25mi = 70 mi
Now we move to a map where each inch is 40 miles, to find the distance in inches, we can take the quotient between the real distance and the scale, it gives:
D = (70mi/40mi) inches
D = 1.75 inches
Therefore, distance on the other map is 1.75 inches. Learn more about map scales:
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Is any additional information needed to show △≅△GHJ by SAS? Explain.
Answer:
Yes
Step-by-step explanation:
The pair of congruent angles needs to be included between the congruent sides. Since this is not the case, more information is needed.
The correct response is yes, the additional information is needed to show that ΔDEF is congruent to ΔGHJ by SAS congruency rule is whether the sides DE and GH, are congruent
What is the SAS congruency postulate?The SAS (Side-Angle-Side) congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.
The specified information for each triangle, starting from the indicated angle, and calling the sides in a clockwise direction, we get;
∠E, side EF and side DF in triangle ΔDEF are congruent to angle ∠H, side HJ, and side GJ
Therefore, the information from the diagram in the question are a nonincluded angle and two sides, SSA, which is not a condition for congruency.
The additional information needed to prove ΔDEF is congruent to ΔGHJ, by SAS are the sides DE and GH, which makes the angle ∠E and ∠H included angles.
Therefore, additional information is required;
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Mr. Callaway needs to purchase enough grass seed to cover a 3000-square-foot lawn and a
4200-square-foot lawn. If 40 ounces of grass seed will seed a 2400-square-foot lawn, how many ounces
does he need to seed both lawns?
Answer:
Mr. Callaway needs 120 ounces of seed to seed both lawns
Step-by-step explanation:
2400/40 = 60 ounces per square foot
3000 divided by 60 = 50 ounces
So, Mr. Callaway needs 50 ounces to cover a 3000-square-foot lawn
4200 divided by 60 = 70 ounces
So, Mr. Callaway needs 70 ounces to cover a 4200-square-foot lawn
50+ 70 = 120 ounces
So, Mr. Callaway needs 120 ounces to seed both lawns.
If you can, please give me a Brainliest; thank you, and have a good day!
Answer:
120 ounces pf grass seed
Step-by-step explanation:
[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{3000}[/tex] Cross multiply and solve for x
120000 = 2400x Divide both sides by 2400
\[tex]\frac{120000}{2400}[/tex] = [tex]\frac{2400x}{2400}[/tex]
50 = x
It will take 50 ounces of grass seed to cover 3,000 square foot lawn.
[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{4200}[/tex] Cross multiply and solve for x
168000 = 2400x Divide both sides by 2400
70 = x
It will take 70 ounces of grass seed to cover 4200 square foot lawn.
50 + 70 = 120
Jack and Diane are jogging back and forth along a one-mile path. They started out at 9:00 A.M. from opposite ends of the path. They passed each other in 10 minutes when Diane has gone 1/3 mile. What time will they meet at the same end of the path? You have to assume they keep jogging at the same speeds.
Explain:
If they keep running at the same pace, they will eventually meet at the same end of the course after 30 minutes.
what is speed ?The rate at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial distance. The basic unit of distance with the basic unit of time are combined to form the SI unit of speed. This means that the SI unit of speed is the metre per second.
The way that the issue is described is vague.
I believe what is being said here is that they continue to jog at the same speed.
Half a mile per ten minutes is Diane's speed.
2/3 miles per 10 minutes is Jack's speed.
The numerator and denominator (top and bottom of the ratio) must be multiplied by the factor between 10 minutes and an hour (60 minutes) in order to convert this to a standard miles per hour format.
60/10 = 6.
In order to convert the above speeds to miles per hour, we must multiply both speeds by 6.
Diane: (1/3 divided by 6)/hour equals 2 miles/hour
Jack: (4 miles per hour) = (2/3 x 6) / hour
Diane will complete one length in the time it takes Jack to complete a round trip (back) because he runs twice as fast as she does.
Running a mile at a speed of two miles per hour takes Diane 30 minutes.
Running 2 miles (back and forth) at a speed of 4 miles per hour will take Jack 30 minutes.
So after 30 minutes they will meet again at his starting point.
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According to the Central Limit Theorem, the mean of the sampling distribution of means - \mu_{\overline{X}}μX‾ - will equal...
- the mean of the original population divided the square root of n.
- Cannot be predicted without additional information.
- the mean of the original population.
- the mean of the original population divided by n-1.
According to the Central Limit Theorem, the mean of the sampling distribution of means will be equal to The mean of the Original Population.
Central Limit theorem:
The central limit theorem (CLT) is a statistical concept that states that the sample mean distribution of a random variable assumes an approximately normal or normal distribution when the sample size is large enough. Simply put, the theorem states that the mean sampling distribution approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.
For example:
An investor wants to estimate the return on the ABC stock market index, which consists of 100,000 shares. Due to the large size of the index, the investor cannot analyze each stock individually and instead chooses to use a random his sample to obtain an estimate of the index's total his return. Investors select a sample of stocks. Each sample contains at least 30 strains. Samples should be random and previously selected samples should be replaced by subsequent samples to avoid bias.
If the average return of the first sample was 7.5%, the average return of the next sample could be 7.8%. Due to the nature of random sampling, each sample will produce different results. As you increase the sample size for each selected sample, the sample means begin to form their own distribution.
The distribution of the sample mean approaches a normal distribution as the value of n increases. The average return of the index example stocks estimates the return of the entire index of 100,000 shares, and the average returns follow a normal distribution.
According to the central limit theorem, if a large sample is chosen from an unknown population with mean μ and standard deviation σ, the sampling distribution of the sample mean follows a normal distribution.
The mean and standard deviation of this sampling distribution are:
μₐ = μ
σₐ = σ/√n
This standard deviation of the sampling distribution of the mean is called the standard error.
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For the following diagrams find the measure for all the Missing angles
The missing measures of the named angles are:
w = 62°
z = 57°
y = 57°
x = 61°
b = 24°
a = 132°
c = 156°
d = 156°
e = 132°
f = 24°
g = 24°
h = 156°
i = 156°
How to Find the Measure of Missing Angles in a Triangle?To find the measures of each of the named angles in the figure above, note the following:
Angles on a straight line = 180 degrees.Base angles of any isosceles triangle are congruent.Vertical angles are congruent.Sum of triangle = 180 degrees.Therefore:
w = 62° [alternate interior angles are congruent]
z = 180 - 123 = 57° [angles on a straight line]
y = 180 - 62 = 57° [angles on a straight line]
x = 180 - 62 - 57 = 61° [triangle sum theorem]
b = 24° [base angles of isosceles triangle]
a = 180 - 2(24) = 132°
c = 180 - 24 = 156°
d = 180 - 24 = 156°
e = a = 132°
f = g = 1/2(180 - e)
Plug in the value of e:
f = g = 1/2(180 - 132)
f = g = 24°
h = i = 180 - 24 = 156°
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The figures below show the length of a new pencil and its length after seema used it for a day. New pencil - 18 cm After seema used it - 15 cm
By what fraction of the original length of the pencil reduce that day?
A. 1/4
B. 1/5
C. 1/6
D. 1/18
The pencil was reduced by 1/6 of its original length. Hence, the correct option is Option C.
To calculate the fraction, you must divide the remaining length (15 cm) by the original length (18 cm). In order to get a fraction, you have to divide it by their highest common factor, which in this case is 3.
= \frac{15}{18}
= \frac{5}{6}
This is the length of the pencil left at the end of the day. To find the fraction used, you have to subtract this fraction from its whole.
= 1 - \frac{5}{6}
= \frac{5}{6} - \frac{5}{6}
= \frac{6-5}{6}
= \frac{1}{6}
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you are dealt five cards from a thoroughly shuffled standard deck of cards. what is the probability that you get a full house. (full house
The probability of getting a full house is 0.001441 or 0.14%.
When you dealt five cards from a thoroughly shuffled standard check of cards then for the probability of getting a full house we need to know the total number of full house combinations and possible cards hands.
This is calculated by taking the number of possible full house combinations (3,744) and dividing it by the total number of possible 5-card hands (2,598,960). This can be written as :
Mathematically, this can be expressed as:
P(Full House) = 3,744 / 2,598,960 = 0.001441 or 0.14%
Therefore the probability of getting a full house is 0.001441 or 0.14%
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How do you simplify 16^(2/3)?
Answer:
4(2)^(2/3) or 4∛(4)
Step-by-step explanation:
Rules of Exponents..
16^(2/3)
= (2^4)^(2/3)
= 2^(8/3)
= 2^(2 + 2/3)
= 2^2 · 2^(2/3)
= 4(2)^(2/3) or 4∛(4)
The original price of a sweatshirt is $50. The sale price is 75% of the original price. Find the sale price of the sweatshirt.
Group of answer choices
$45.25
$10
$12.50
$37.50
Answer:10
Step-by-step explanation:
Answer:
$37.50
Step-by-step explanation:
75% of $50:
0.75x50=$37.50
What is Graph y=-4
y = mx + b
y = -4
m = 0
b = -4
Since the slope (m) is 0, the line is horizontal. The y-intercept (b) is -4, meaning that the graph is a horizontal line at y = -4.
See the attached file for the graph.
Assuming Ash Ave. and Maple are parallel then the length of Ash Ave is ? mi. Enter a number answer only to the nearest tenth
Answer:
11.25. or 11.3 miles
Step-by-step explanation:
Because Ash Ave. and Maple are parallel, this means that you have a pair of similar right triangles. Therefore, you can set up a proportion and solve for the length of Ash Ave.
6 miles/9 miles = 7.5 miles/x miles
x=11.25 miles
Albert has $1,000 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will he earn in 4 years?
Answer:
$215.50
Step-by-step explanation:
To calculate the amount of interest that Albert will earn on his account over the course of 4 years, we can use the formula for compound interest:
Interest = principal * (1 + rate/n)^(n*t) - principal
Where:
principal is the initial amount of money in the account ($1,000 in this case)
rate is the annual interest rate (5% in this case)
n is the number of times that interest is compounded per year (annually in this case, so n=1)
t is the number of years the money is invested (4 years in this case)
Plugging these values into the formula, we get:
Interest = $1,000 * (1 + 0.05/1)^(1*4) - $1,000
= $1,000 * (1.05)^4 - $1,000
= $1,000 * 1.2155 - $1,000
= $215.50
To the nearest cent, the interest Albert will earn in 4 years is $215.50.
which category, groceries or dining out, has a higher population mean annual credit card charge? dining out what is the point estimate of the difference between the population means? round to the nearest whole number.
groceries has a higher population mean annual credit card charge
What is population mean?
A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.
The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.
Given that Bank of America’s Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment (US Airways Attache, December 2003).
Sample size n =42
Mean difference d = 850
Std dev s = 1125
Point estimate of the difference is 0
95% confidence level would be
= 0A ± tcritical * stderrror
= A ± 2.021*173.59
= (-350.83 , 350.83)
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referring to question 1, what is the predicted strength of a weld with a diameter of 51? a. -812.72 b. -503.16 c. -81.82 d. we should not use the least squares regression line to calculate this value
The predicted strength of a weld with diameter of 51 is -503.16.
Given that diameter of weld is 51.
And we have to find predicted strength of a weld.
We know that the equation of predicted strength is,
strength = -941.6 + (8.598 × D)
where D id diameter = 51
⇒ strength = - 941.6 + (8.598 × 51)
strength = -941.6 + 438.4
strength = -503.2
Therefore predicted strength of a weld is -503.2 i.e option (b) -503.16.
A prediction equation predicts a value of the response variable for given values of the factors. The Delphi Survey technique is a popular method used in prediction. There are two types of prediction methods: qualitative and quantitative.
The Least square Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It is called a "least squares" because the best line of fit is one that minimizes the variance.
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2(4x+3)+4=3x-(2x+4)?
The solution of the equation is -2.
What is the solution of an equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
What is distributive property?
The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.
Given equation is 2(4x+3)+4=3x-(2x+4).
Apply distributive property in 2(4x+3):
8x + 6 + 4 = 3x - (2x+4)
8x + 10 = 3x - (2x+4)
Open parenthesis on the right side:
8x + 10 = 3x - 2x - 4
Combine like terms:
8x - 3x + 2x = -4 -10
7x = -14
Divide both sides by 7:
x = -14/7
x = -2
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find the volume of the given solid. bounded by the cylinders z = 5x2, y = x2 and the planes z = 0, y = 4
1024/3 units³ is the required volume of the given solid using the triple integral theorem.
What is the triple integral formula?As the name implies, triple integrals are 3 sequential integrations, used to determine a volume or to integrate into a 4th dimension, over 3 other independent dimensions.
∭Ef(x,y,z)dV=∬D[∫u2(x,y)u1(x,y)f(x,y,z)dz]dA.
So, we must use the triple integral formula in rectangular coordinates to get the volume of the solid (v):
[tex]V=\iiint d y d x d z[/tex] ...(1)
The solid is restricted by the following intervals:
[tex]y \in\left[x^2, 16\right], x \in[-4,4], z \in[0,4][/tex]
Then, this triple integral is now characterized as:
[tex]V=\int_0^4 \int_{-4}^4 \int_{x^2}^{16} d y d x d z[/tex]
Now we continue to integrate again to get the volume:
[tex]\begin{aligned}& V=\int_0^4 \int_{-4}^4\left(16-x^2\right) d x d z \\& V=\left.\int_0^4\left(16 \cdot x-\frac{x^3}{3}\right)\right|_{-4} ^4 d z \\& V=\frac{256}{3} \int_0^4 d z=\frac{1024}{3}\end{aligned}[/tex]
Therefore, 1024/3 units³ is the required volume of the given solid using the triple integral theorem.
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Complete question:
Use a triple integral to find the volume of the given solid. The solid is bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.
Factorise xsquared+ 5x + 6
Answer:
[tex](x+2)(x+3)[/tex]
Step-by-step explanation:
⭐What does factorisation mean?
factorisation is the process of writing a number or a polynomial in terms of its factors⭐What are factors?
factors are the terms that multiply together to create a number or a polynomialThus, we have to write [tex]x^2+5x+6[/tex] in terms of its factors.
I have a picture attached to this response to show you how factorisation works, but I will also explain it here.
How to factorise:
Look at the constant in your polynomial (the term without a variable). In this problem, the constant is 6. Look at the coefficient middle term in your polynomial (the number next to the variable). In this problem, the middle coefficient is 5. Find what numbers multiply together to have a product of 6, and add together to have a sum of 5.The numbers +2 and +3 multiply together to have a product of 6, and add together to have a sum of 5. In the next line, write the polynomial again, but write 5x in terms of the numbers we found.You'll get: [tex]x^2 + 2x +3x + 6[/tex]Now, we can factorise the binomials we see here.⭐What are binomials?just as "bi" means 2, binomials are equations with 2 termsThe binomials are [tex]x^2 + 2x[/tex] and [tex]3x + 6[/tex]To factorise the binomials, find the GCF for both terms of each binomial.The GCF for [tex]x^2 + 2x[/tex] is x.The GCF for [tex]3x+6[/tex] is 3.Now, write the GCFs outside of the parentheses for each binomial and rewrite what's in the parentheses.You'll get: [tex]x(x+2) +3(x+2)[/tex]You should have the same expression in both parentheses.Now, we have to rewrite this expression by keeping what's inside of the parentheses, and putting the terms outside of the parentheses inside parentheses.You'll get: [tex](x+2)(x+3)[/tex]That's it!The picture of factorisation is attached to this response.
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There are 20 grams of protein in 3 ounces of sauteed fish. If the answer is 9 hours whats the question?
There are 60 grams of protein in 9 ounces of sauteed fish.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have been given that there are 20 grams of protein in 3 ounces of sauteed fish.
Let's assume that 9 ounces of sauteed fish contain x grams of protein.
As per the given information, we can write the ratio would be as:
20 grams of protein : 3 ounces = x grams of protein : 9 ounces
20/3 = x/9
x = (20 × 9)/3
x = 180/3
x = 60
Hence, there are 60 grams of protein in 9 ounces of sauteed fish.
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The question seems to be incomplete the correct question would be:
There are 20 grams of protein in 3 ounces of sauteed fish. If 3 ounces of sautéed then, what are the grams of protein fish has?
what is s for the following function
Step-by-step explanation:
you just need to put the value for t into the equation and then solve for s.
t = 3s + 2
t = 11
11 = 3s + 2
3s = 11 - 2 = 9
s = 3
t = 17
17 = 3s + 2
3s = 17 - 2 = 15
s = 5
t = 23
23 = 3s + 2
3s = 23 - 2 = 21
s = 7
t = 29
29 = 3s + 2
3s = 29 - 2 = 27
s = 9
Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 pictures. What is the percent of increase in yearly sales?
Therefore the percentage of increase in yearly sales is 35% by last year.
What is percentage?
Percentage refers to a number that is "out of one hundred." As with fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When utilizing percentages, the total is regarded as being composed of 100 equally sized components. In addition to the abbreviation "pct," which is used less frequently, the symbol "%" is used to denote percentages in numbers.
Here,
the company sold a total of 720,460 pictures Last year.
This year, they sold 972,621 pictures
therefore first we have to find the difference between the last year and this year pictures sold
it comes out to be,
=>972,621-720,460=252,161
Therefore the increase in percentage this year=
=> 252,161/720460 * 100
=>0.35*100
=> 35%
Therefore the percentage of increase in yearly sales is 35% by last year.
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Last week, the price of apples at a grocery
store was $1.60 per pound. This week,
apples at the same grocery store are on sale
at a 10% discount. What is the total price
of 4% pounds of apples this week at the
grocery store?
A. $4.77
B. $6.48
C. $6.75
D. $6.93
The total price of 4 pounds of apples this week at the grocery store is $5.76
What is the total price after discount?Last week price of apples per pound = $1.60Discount = 10%Quantity of apples = 4 poundsTotal price of apples this week = Last week price of apples per pound × Quantity of apples
= $1.60 × 4
= $6.4
Actual price paid = Total price of apples this week - (Discount × Total price of apples this week)
= $6.4 - (10% × $6.4)
= 6.4 - (0.1 × 6.4)
= 6.4 - 0.64
= $5.76
In conclusion, 4 pounds of apples cost $5.76 this week at the grocery store.
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the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection. For each binomial experiment described, find the mean, the variance and the standard deviation!
Mean = 54.52
V(X) = 3.2712
S.D = 1.8086
To calculate the mean (expected value) of a binomial distribution B(n, p) you need to multiply the number of trials n by the probability of successes p , that is: mean = n × p
Where, n= 58
p = 0.94
Therefore, mean = 54.52
To find the Variance of the given binomial distribution
Variance = np(1-p)
=58 X 0.94 ( 1- 0.94)
= 54.52 X 0.06
V(X) = 3.2712, when we know the variance and the mean then we can calculate the standard deviation easily
To find the standard deviation of the given binomial experiment = [tex]\sqrt{np(1-p)}[/tex]
= [tex]\sqrt{3.2712}[/tex]
S.D = 1.8086
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Select the correct answer.
Which expression is equivalent to this quotient?
Answer:
[tex]$\frac{5}{8}$[/tex]
Step-by-step explanation:
evaluate the double integral y^2/(x^2 y^2) where is the region that lies between the circles and by changing to polar coordinates.
The value of the double integral ∫∫[tex]\frac{y^{2} }{x^{2} +y^{2} }[/tex] dA is 131.95.
We know that in polar coordinates, the circle become r = 4 and r = 16. These are the limits on the radius. Clearly the limits on the angle are
0 ≤ θ ≤ 2π.
Therefore we get,
∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = ∫ ∫ r²sin²θ / r² dr dθ
= ∫ sin²θ dθ ∫ r dr
= [ [tex]\frac{1}{2}[/tex]θ - [tex]\frac{1}{4}[/tex]sin(2θ)]₀²ⁿ[ [tex]\frac{1}{2}[/tex] r²]₄¹⁰
= [tex]\frac{1}{4}[/tex] (2π)(10² - 4²)
= 42π
∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = 131.95.
What is Polar coordinates?
When each point on a plane of a two-dimensional coordinate system is decided by a distance from a reference point and an angle is taken from a reference direction, it is known as the polar coordinate system.
Polar coordinates are useful in calculating the equations of motion from a lot of mechanical systems. Polar coordinate means the magnitude and direction of a vector.
Polar coordinate system of locating points in a plane with reference to a fixed point O and a ray from the origin usually chosen to be the positive x-axis.
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. on average, 21 pairs of twins are born per year in montgomery county. a) calculate the probability that exactly 18 pairs of twins will be born in the county in 2015
The probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.
Given that,
Poisson (2.)
Let x = The number of pairs of twins
That will be born in the Country in 2015
To find : Calculate the probability that exactly 18 pairs of twins will be born in the country in 2015.
We know that
Here,
The probability mass function (pmt of x) is given by
P ( X = x ) = e⁻²¹ x 21ˣ / x!
where x = 0,1,2 , . . .
Substitute x = 18 in above equation,
Then we get,
P ( x = 18 ) = e⁻²¹ x 21¹⁸ / 18!
P( x = 18 ) = 0.07472
P ( x = 18 ) = 0.07472
Therefore, the probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.
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Last year, 160 new houses were built in a neighborhood. So far this year, 3/8 of them have been sold. How many new houses have been sold this year?
Write your answer in simplest form.
Answer:
The answer is 60
Step-by-step explanation:
160 × 3/8 = 480/8 = 60
Thus, 60 new houses have been sold this year.
Please help!!! Mathematics uhhhh.
If the bookstore sells 15 pencils, the ratios of pens to pencil written as fraction is 2 / 3.
How to solve for variables in proportional graph?Proportional relationships are relationships between two variables where their ratios are equivalent.
A proportional relationship is one in which two quantities vary directly with each other.
Therefore, proportional relationship can be represented as follows:
y ∝x
y = kx
where
k = constant of proportionalityx = number of pencilsy = number of pensTherefore,
4 = 6k
k = 4 / 6
k = 2 / 3
Therefore, let's find the number of pen sold when the bookstore sells 15 pencils.
y = 15 × 2 / 3
y = 30 / 3
y = 10
Therefore, if the bookstore sell 15 pencils the ratio of pen to pencil is 10 / 15 = 2 / 3
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how do i round 13856 to the nearest hundred
Answer: 13,900
Step-by-step explanation:
To round numbers to the nearest hundred, you always look at the place one down which is the tens place. The tens place is 5.
The options for 856 to round to is either 800 or 900.
The rule is that 0-4 rounds down, 5-9 rounds up. Since the tens place is 5, it will round up to 900.
Therefore, the answer would be 13,900.
Hope This Helps djoodlys!:)49 POINTS ANSWER AND SHOW WORK,, Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day. Draw a graph to represent this situation.
The graph of the linear function y = 36 - 4x that represents this situation is given by the image shown at the end of the answer.
How to graph the linear function?To graph the linear function, these three steps are taken:
First, the function is defined.Then, the two intercepts are obtained.Finally, a line is traced connecting the two intercepts.The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are detailed as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable x.b is the intercept, representing the numeric value of the output variable y when the input variable assumes as value of 0.Initially, he has 36 overdue activities, hence the intercept is of:
b = 36.
And thus the coordinates of the y-intercept are given as follows:
(0,36).
Each day, he can do 4 activities, meaning that the number of remaining activities decays by 4, and thus the slope is of:
m = -4.
Thus the definition of the function is presented as follows:
y = -4x + 36.
The x-intercept of the function is the value of x when the output variable assumes a value of 0, hence it is obtained as follows:
-4x + 36 = 0
4x = 36
x = 9.
Thus the coordinates of the x-intercept are given as follows:
(9,0).
Finally, a line is traced connecting the y-intercept (0,36) and the x-intercept (36,0).
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How do we dilute a bacterial culture 50-fold, 100-fold, and 200-fold?
The dilutions in one step, or have to do serial dilutions.
There is a limit to how much can dilute a sample in one step.
Dilute by more than a factor of 100 in a single step, because that a large volume of dilute solution.
Rather, use the serial dilution technique.
Remember the formula for dilution factor (DF):
DF =Vf /Vi
, where
Vi = aliquot volume
and Vf = final volume = aliquot volume + diluent volume
a) DF = 50
For a single dilution.
This time add 0.2 mL of sample to 9.8 mL of saline.
Vf = 0.2 mL + 9.8 mL= 10.0 mL
DF = Vf/Vi = 10.0mL 0.2mL= 50
b) DF = 100
For a single dilution.
This time add 0.1 mL of sample to 9.9 mL of saline.
Vf = 0.1 mL + 9.9 mL=10.0 mL
DF =Vf/Vi = 10.0mL/0.1mL = 100
c) For a serial dilution.
The formula for serial dilutions is
DF =DF1×DF2×DF3×…
about a 1:100 dilution followed by a 1:2 dilution
(1) Add 0.1 mL of sample to 9.9 mL of diluent.
DF1 = 100 Call this "Solution 1".
(2) Add 5 mL of Solution 1 to 5 mL of saline. Call this "Solution 2".
Vi = 5 mL
Vf = 5 mL + 5 mL= 10 mL
DF2 = Vf/Vi = 10mL/5mL=2
DF = DF1×DF2 = 100 ×2= 200
DF = 50
DF = 100
DF = 200
The dilutions in one step, or have to do serial dilutions.
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