A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?

Answers

Answer 1

Assume that there are 100 students in the class.

(Working with numbers is easier than working with percentages).

There are 27 students who passed both tests, and 51 who passed only the first test.
The 27 students who passed both tests are included in the 51 who passed the first test.

We are asked "What percent of those who passed the first test also passed the second test?"

so we are asked "what percent of 51 is 27?"

let 51 be 100%
then 27 is [tex] \frac{27*100}{51} [/tex]%=52.941%

Answer: 52.941%

Related Questions

Simplify 3 - (2 - 8).

Answers

3 - ( 2 - 8 ) =
3 - ( -6 ) =
3 + 6 =
9

44^4 = 22^4 * ? find the missing factor in exponential form. How would you solve this?

Answers

[tex]\bf 44^4=22^4\cdot x\implies (2\cdot 22)^4=22^4x\implies (2^4\cdot 22^4)=22^4x \\\\\\ \cfrac{2^4\cdot \underline{22^4}}{\underline{22^4}}=x\implies 2^4\implies 16=x[/tex]

Answer:

Step-by-step explanation:

An open rectangular box has volume 32 cm3. find the lengths of the edges giving the minimum surface area

Answers

Final answer:

An open rectangular box with a volume of 32 cm³ would have its minimum surface area when it takes the form of a cube. In this case, each side of the box would be approximately 3.174 cm.

Explanation:

To minimize the surface area of an open rectangular box given a constant volume, the box should take the shape of a cube. This is because a cube is the three-dimensional shape that has the minimum surface area for a given volume. The volume V of the box is given as 32 cm³. Since for a cube, the volume V = a³ where a is the side length of the cube, we need to find the value of a such that the volume is equal to 32cm³.

To do this, we use the cube root function as follows: a = ∛V = ∛32 = 3.174 cm.

So, for a rectangular box with a volume of 32 cm³, the lengths of the edges that would give the minimum surface area would all be approximately 3.174 cm.

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An open rectangular box with a volume of 32 cm³ would have its minimum surface area when it takes the form of a cube.

In this case, each side of the box would be approximately 3.174 cm.

To minimize the surface area of an open rectangular box given a constant volume, the box should take the shape of a cube.

This is because a cube is the 3-dimensional shape that has the minimum surface area for a given volume.

The volume V of the box is given as 32 cm³.

Since for a cube, the volume V = a³ where a is the side length of the cube, we need to find the value of a such that the volume is equal to 32cm³.

To do this, we use the cube root function as follows:

a = ∛V

= ∛32

= 3.174 cm.

So, for a rectangular box with a volume of 32 cm³, the lengths of the edges that would give the minimum surface area would all be approximately 3.174 cm.

If f(x) = 5x – 6, what is the equation for f–1(x)?

Answers

Answer:

5x-2+^3 hole

Step-by-step explanation:

The inverse of f(X) = (x +6 ) /5

What is inverse function?

The inverse of a function f is denoted by f^-1 and it exists only when f is both one-one and onto function. Note that f^-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x.

(f o f^-1) (x) = (f^-1 o f) (x) = x

Steps To Find An Inverse Function

The following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps.

For the given function f(x) = ax + b, replace f(x) = y, to obtain y = ax + b.Interchange the x with y and the y with x in the function y = ax + b to obtain x = ay + b.Here solve the expression x = ay + b for y. And we obtain y = (x - b/aFinally replace y = f^-1(x), and we have f^-1(x) = (x - b)/a.

Given:

f(x) = 5x – 6

let y= f(x) = 5x – 6

Now, Interchange the x with y and the y with x.

x= 5y -6

x+6 = 5y

y = (x +6 ) /5

So, f^-1(x) = (x +6 ) /5

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making use of Archimedes’s Principle, displacements, and buoyancy, explain why some objects float on water, but others do not.

Answers

Archimides' Principle states that any body immersed in a fluid receives a vertical pushing force upwards equal to the weight of the fluid displaced by the body.

Then, there are two forces acting on the body, its weight (vertical downwards) and the bouyancy (vertical push upwards).

There are three possibilities:

1) The buoyancy is greater than the weight of the body => the body will float (move upward, toward the surface if it is a liquid)

2) The buoyancy is equal than the weight of the boy => the body wll remain quite (also floating but not moving either upwards or downwards)

3) The buoyancy is less than the weight of the body => the body will sinkl.

So, a body will float on water when the buoyancy from the liquid is overcomes its weight.

Buoyancy is related with density because:

buoyancy = weight of the liquid displaced = mass o fliquid * g = density of the liquid * Volume of the liquid * g

Weight of the body = mass of the body * g = density of the body * Volumen of the body * g

When the body is completely immersed in the liquid its volume es equal to the volume of the liquid displaced =>

So we can compare the weight of the body and the buouancy force

density of liquid * volume of liquid * g vs density of body * volume of liquid * g

where the difference is the densities of liquid and body.

That is why it is deduced that the bodies float when their densities are smaller than the densities of the liquid where they are.

Answer:

If the weight is equal to the buoyant force, it will float. The same is true for if the weight is less than the buoyant force. However, if the weight is greater than the buoyant force, it will sink.

What are the zeros of f(x)=4x^3-13x^2-37x+10

Answers

In this question there are 3 points of intersection on the x-axis. Of which are: (5,0), (1/4,0), and (-2,0). Hope this is right!

Write a function rule for the table. (2, $16.00), (4, $32.00), (6, $48.00), (8, $64.00)

Answers

The answer to this question is (1, $8.00)

The answers 80kg, 88 divided by 110 then times by 100

Answers

137.5 because first you divide 110 by 80 and then mupilty the answer by 100

Final answer:

The student is completing a two-step mathematical operation to find a percentage by dividing 88 by 110 and then multiplying the result by 100. The '80kg' mention seems to be unrelated. Without more context, it's difficult to relate this to the given references, though they involve calculations and conversions in physics.

Explanation:

The student seems to be performing a two-step operation where they are first dividing 88 by 110 and then multiplying it by 100. This is a common way of finding percentages. To get the result first, divide 88 by 110 which equals 0.8. Secondly, multiply 0.8 by 100 to get 80%. The '80kg' seems irrelevant to this operation if no further context is provided, it could be a weight measurement in physics.

In terms of any associations with the provided references, it seems that the question might be related to converting some measurements or calculating kinetic energy ('K'). However, without additional information, it's hard to ascertain the exact nature of the task.

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Armando has a baseball card that is worth $45. The value of the card is increasing at a rate of 1.5% per year. How much will the card be worth in 15 years?

Answers

What you need to do is I=PRT, which stands for interest=principle*rate*time. So it would be I=45*1.5*15. The answer is $10.13

Evaluate the line integral where f(x,y,z)=3sin(x)i−(cos(y))j−5xzk and c is given by the vector function r(t)=t5i−t4j+t3kr(t)=t5i−t4j+t3k , 0≤t≤10≤t≤1.

Answers

[tex]\mathbf f(x,y,z)=3\sin x\,\mathbf i-\cos y\,\mathbf j-5xz\,\mathbf k[/tex]

[tex]\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=t^5\,\mathbf i-t^4\,\mathbf j+t^3\,\mathbf k[/tex]
[tex]\implies\mathrm d\mathbf r(t)=(5t^4\,\mathbf i-4t^3\,\mathbf j+3t^2\,\mathbf k)\,\mathrm dt[/tex]

[tex]\displaystyle\int_C\mathbf f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}f(x(t),y(t),z(t))\cdot\mathbf r'(t)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(3\sin(t^5)\,\mathbf i-\cos(t^4)\,\mathbf j-5t^8\,\mathbf k)\cdot(5t^4\,\mathbf i-4t^3\,\mathbf j+3t^2\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(15t^4\sin(t^5)+4t^3\cos(t^4)-15t^{10})\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1\bigg(3\sin(t^5)\,\mathrm d(t^5)+\cos(t^4)\,\mathrm d(t^4)-15t^{10}\,\mathrm dt\bigg)[/tex]
[tex]=-3\cos(t^5)+\sin(t^4)-\dfrac{15}{11}t^{11}\bigg|_{t=0}^{t=1}[/tex]
[tex]=-3\cos1+\sin1+\dfrac{18}{11}[/tex]

A 20-year, $148,000 mortgage is taken out with a 4.9% APR. If payments are scheduled monthly and there are no additional costs, determine the balance on the account after the first month's payment has been made.

Answers

so.... the account is at 0 at the beginning, after the 1st payment made to the account, the only balance it'd have, is the first payment amount, so namely, what's the monthly amortized payment

[tex]\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right][/tex]

[tex]\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to & \begin{array}{llll} 148,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\to &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &20 \end{cases} \\\\\\ pymt=148000\left[ \cfrac{\frac{0.049}{12}}{1-\left( 1+ \frac{0.049}{12}\right)^{-12\cdot 20}} \right][/tex]

if f(x)=x-3/x, g(x)=x+3, and h(x)=2x+1, what is (g*h*f)(x).

A. 3x-6/x
B. 6x-6/x
C. 2x+4/2x+7
D. 4x-3/x

Answers

Answer = (g*h*f)(x) = 4x-3/x

Answer:

Option B - 6x-6/x

Step-by-step explanation:

Given : If [tex]f(x)=\frac{x-3}{x}, g(x)=x+3,h(x)=2x+1[/tex].

To find : What is the value of [tex](g(h(f)))(x)[/tex]

Solution :

[tex](g(h(f)))(x)=g(h(f(x)))[/tex]

i.e, substitute the value of f(x) in h(x) and then put that h(x) in g(x).

[tex]g(h(f(x)))=g(h(\frac{x-3}{x}))[/tex]

[tex]g(h(f(x)))=g(2(\frac{x-3}{x})+1)[/tex]

[tex]g(h(f(x)))=(2(\frac{x-3}{x})+1)+3[/tex]

Solving the RHS,

[tex]=(2(\frac{x-3}{x})+1)+3[/tex]

[tex]=(\frac{2x-6}{x})+1)+3[/tex]

[tex]=(\frac{2x-6+x}{x})+3[/tex]

[tex]=\frac{3x-6}{x}+3[/tex]

[tex]=\frac{3x-6+3x}{x}[/tex]

[tex]=\frac{6x-6}{x}[/tex]

Therefore, The value of [tex](g(h(f)))(x)=\frac{6x-6}{x}[/tex]

Hence, Option B is correct.

The number of bagels sold daily for two bakeries is shown in the table. Bakery A Bakery B 53 34 52 40 50 36 48 38 53 41 47 44 55 40 51 39 Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below.

Answers

You are given the number of bagels sold daily for bakeries A and B and are shown in the table above. Based on the above data, it is better to describe the centers of distribution in terms of the mean than the median. This is because all of the data from bakery A and B have values that are near the average and no data sample have possible outliers. For instance,

bakery A
mean (A) = [53 + 34 + 52 + 40 + 50 + 36 + 48 + 38]/8 = 43.88

Bakery B
mean (B) = [53 + 41 + 47 + 44 + 55 + 40 + 51 + 39]/8 = 46.25

Even if bakery A and B has the 38 and 39 as the lowest data respectively, they are still near the average data.

Considering the information about the asymmetry in Bakery B's distribution, the median would be a more appropriate measure of central tendency for both Bakery A and B. It would provide a better representation of the "typical" number of cupcakes sold in each bakery, even if there might be outliers in the data.

Understanding Mean and Median:

Mean: The mean, also known as the average, is calculated by adding all the values in a dataset and dividing by the number of values. It's a good measure of central tendency when the data is symmetrical and free from outliers.Median: The median is the 'middle' value when the data is ordered from least to greatest. It's less sensitive to extreme values (outliers) compared to the mean.

Why Median is More Appropriate (Considering the Information):

The information mentions that the distribution for Bakery B is not symmetric. This suggests that the data points in Bakery B might be skewed towards one side, with a few possibly higher or lower values compared to the majority.

Reasoning:

Option A (Mean): The mean is easily influenced by outliers. If Bakery B has outliers, the mean might not accurately represent the "typical" number of cupcakes sold for Bakery B.Option B (Mean for Perfect Symmetry): This option specifies the mean if the distributions are perfectly symmetrical. Since we know Bakery B's distribution isn't symmetrical, the mean wouldn't be the best choice.Option C (Median for Bakery B Asymmetry): This correctly identifies that the median is a better choice for Bakery B due to the asymmetry in its data.Option D (Median for Outliers): While outliers can be present in both Bakery A and B, the key factor is the asymmetry in Bakery B's distribution. The median is generally more resistant to the influence of outliers, making it a better choice in this case, even if outliers exist in both datasets.

complete question:

The number of bagels sold daily for two bakeries is shown in the following table: Uchange Bakery A Bakery B 53 34 52 40 50 36 48 38 53 41 47 44 55 40 51 39 Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below. (3 points)

a. Mean, because there are no outliers to affect the data

b. Mean, because the distribution is perfectly symmetric for both bakeries

c. Median, because the distribution for Bakery B is not symmetric

d. Median, because there are outliers that affect both data sets

In the x -y plane, the line 3x + 2y =72 intersects the x -axis at x=b,for some number b. What is the value of b?

Answers

Since it is specifically stated that the line intersects the x-axis, then this means that y = 0. Therefore substituting y = 0 into the given equation will us the value of x.

Substituting y = 0:

3 x + 2 * 0 = 72

3 x = 72

x = 24

Therefore this means that the line intersect the x-axis at point (24, 0).

an architect designs a rectangular flower garden such that the width is exactly two thirds of the length if 320 ft of the antique picket fencing are to be used to enclose the garden find the dimensions of the garden

Answers

check the picture below.

what's the width? well, w = (2/3)l.

The dimensions of the garden where 320 ft of the antique picket fencing are to be used to enclose the garden are 96 feet and 64 feet.

Given that:

A garden is in rectangular shape.

The length of the antique picket fencing used to enclose the garden is 320 feet.

The perimeter defines the enclosing length.

So, the perimeter is 320 feet.

Let P = 320.

Let l represent the length and w represents the width of the garden.

The width is exactly two-thirds of the length.

So, [tex]w=\frac{2}{3} l[/tex].

The perimeter of the garden is:

P = 2(l + w)

= 2 (l + [tex]\frac{2}{3} l[/tex])

= [tex]\frac{10}{3} l[/tex]

So, substitute P = 320.

[tex]\frac{10}{3} l=320[/tex]

Simplifying,

l = 96 feet

So, w = 64 feet

Hence, the dimensions are 96 feet and 64 feet.

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The product of (n^2-6n+3)and -4 is

Answers

[tex](n^2-6n+3)( -4)= \\ (-4)(n^2)+(-4)(-6n)+(-4)(3)= \\ -4n^2+24n-12[/tex]

-4(n^2-6n+3)

-4n^2+24n-12

A map has a scale of 1 in. 4 mi. You measure 3 inches between your house and the movie theatre. How many miles is it from your house to the Movie Theatre

Answers

Hi!

1in:4m
3in:xm

3/1 = 3
4 x 3 = 12

1in:4m
3in:12m

The answer is 12

Hope this helps! :)

Answer: x = 12

Step-by-step explanation:

1/3 = 4/x

1x = 12

X = 12

can someone please explain proportions?

Answers

proposition is

A statement or assertion that exppresses a judment or opinion

The volume of 10,000 drops of a liquid is 1 fluid ounce.
What is the volume of 10
drops?

Answers

1/100th of a fluid ounce because to get 10,000 to 10 you divide by 100 so you would divide 1 by 100 to get 1/100th of a fluid ounce.

Given line L = ax + by + c = 0, b(its suppose to be the equal sign with the slash going thru it) 0

What is the slope of this function?

-a/b
a/b
b/a

Answers

ax + by + c = 0
by = - ax - c
y = -a/b (x) - c/b

so slope = -a/b

answer
-a/b

G for exercises 13 and 14, assume the sample populations do not have equal standard deviations and use the .05 significance level: (a) determine the number of degrees of freedom, (b) state the decision rule, (c) compute the value of the test statistic, and (d) state your decision about the null hypothesis.

Answers

I believe it isC. Not fully sure

EASY 5 POINTS!!! You have a new pool and want to know its volume. The pool is 5 feet deep and has a radius of 7 feet. About how much water can the pool hold? Use 3.14 for pi.

Answers

the answer is 770cc. I.e. option D

Answer:

The volume of water that can be hold by the pool is approximately 770 cubic feet.

Step-by-step explanation:

To calculate it we have to use the volume formula for a cylinder. This is:

[tex]Volume=pi*r^{2}*h\\pi=3.14\\r=radius\\h=deep[/tex]

Solving the equation with the given values:

[tex]Volume=3.14*7^{2} *5\\Volume=769.3 cubic feet \\Aprox.Volume= 770 cubic feet[/tex]

The volume of water that can be hold by the pool is approximately 770 cubic feet.

You and two friends (Adam and Alana) will only play a game if it is fair for all three of you. The game your friend has proposed is to roll two number cubes (numbered 1-6) and find the sum. If the sum. If the sum is from 1-4 you get the point, 5-8 Adam gets the point, and 9-12 Alana gets the point.

Answers

Yes, the game was fair and no one had a better advantage.

Answer:

yes!

Step-by-step explanation:

no one had a better advantage.everyone had the same amount of advantage.

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – x = 25

Answers

x^2 - x = 25
Add c in both side
c = (b/2a)^2 = (1/2)^2 = 1/4
x^2 - x + 1/4 = 25 + 1/4
(x - 1/2)^2 = 101/4
(x - 1/2) = √101/4
x - 1/2 = 5.02
x = 5.52 &
x = 4.52

5.52, –4.52

is the correct answer,never forget negatives!

the sum of two numbers is 8 and their difference is 2. find the numbers

Answers

5 and 3. 5+3=8 and 5-3=2

A 5-foot ladder is leaning against a 4-foot wall. How far must the bottom of the ladder be from the base of the wall so that the top of the ladder rests on the top of the wall?

Answers

Using the pythagorean theroem to solve this problem (a squared plus b squared equals c squared)
C would be the hypotenuse, which in this case is the five ft ladder.
The other known length of the leg is 4 ft.
5^2-4^2=25-16=9
9 must equal a^2 and a must equal 3
The correct answer is 3 ft

you need to use pythogoras theorem for this. imagine the leaning ladder as the hypotenuse, the wall as the height and the bottom of the ladder to the wall's base as the length.

so for now the length is the unknown. therefore,

length = sqrt (5^2 - 4^2)
length = sqrt 9
length = 3 foot

3ft is the answer

Is this less than
Greater than
Or equal too?

Answers

The values are equal.

Root 5.76= 2.4

-2.4=-2.4

Choose the polynomial that is written in standard form. 2x3y2 + 4x4y + 8x7 −3x4y2 + 4x4y5 + 10x2 6xy2 + 4x3y8 + 9x2 −2x5y3 + 4x2y2 + x2

Answers

The first thing that should be considered is alphabetical precedence.
If a term has x in it, it should be considered before y.
Then sort by powers. For example, x^3 should go before x^2.
Finally sort by coefficient if the variables and their powers are the same.
A is incorrect because 8x^7 should go before all else.
B is incorrect because 4x^4 should go before -3x^4.
C is incorrect because the order should be 4x^3, then 9x^2, then 6x
D is correct.

It is D because of the order of the exponents

Lori rented a car for one day. The daily rental rate was $12.50 plus 25 cents per mile. The total cost of her rental was $46. How many miles did she drive that day?

Answers

46=12.5+.25x
33.5=.25x
x=134
Final answer: 134 miles

2/3 (5 x 4) ÷ 3 + 6/7 I divided 3/2 is 1.5*(20)=30/3=10+1.16=11.16 is that correct not so good in math

Answers

2/3 (5 × 4) ÷ 3 + 6/7 = 334/63

Further explanation

Order of Operations in Mathematics follow this following rule :

ParenthesesExponentsMultiplication and DivisionAddition and Subtraction

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem.

Let's write down the problem that is wanted to be solved:

[tex]\frac{2}{3} ( 5 \times 4 ) \div 3 + \frac{6}{7}[/tex]

[tex]\frac{2}{3} ( 20 ) \div 3 + \frac{6}{7}[/tex] → Parentheses First

[tex]\frac{40}{3} \div 3 + \frac{6}{7}[/tex] → Multiplication

[tex]\frac{40}{9} + \frac{6}{7}[/tex] → Division

[tex]\frac{280}{63} + \frac{54}{63}[/tex] → Match the denominator of the fraction

[tex]\frac{334}{63}[/tex] → Final Answer

From the results above, it can be concluded that the results of this operation 2/3 (5 × 4) ÷ 3 + 6/7 is 334/63

Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576

Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Order of Operations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS

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