25 percent of 60 students in a class failed in the test. how many students failed the test​

when x = 4, the value of y is 1.

In an inverse variation, the product of the variable and its corresponding value remains constant. Let's denote the constant of variation as k.

According to the given problem, we have the inverse variation equation:

y = k/x^3

To find the value of k, we can substitute the given values for y and x:

8 = k/2^3

8 = k/8

k = 8 * 8

k = 64

Now that we have the constant of variation, we can find the value of y when x = 4:

y = 64/4^3

y = 64/64

y = 1

Therefore, when x = 4, the value of y is 1.

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Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

Answer:

g=1.5

Step-by-step explanation:

1. simplify both sides of the equation,

2. flip the equation,

3.add 0.9 to both sides,

4. multiply both sdes by 3.

Answer:

-78

Step-by-step explanation:

Zinc group :

Mean, x1 = 3328

σ1 = 640

Sample size, n1 = 28

Placebo group :

Mean, x2 = 3406

σ2 = 851

Sample size, n2 = 31

The point estimate for the true difference between the population means is obtained as :

Mean difference between population :

x1 - x2 = 3328 - 3406 = - 78

The function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ

An average rate measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

The functions are given as:

f(x) = x² --- quadratic

g(x) = 2ˣ --- exponential

The exponential function has the same base as the power of the quadratic function.

This means that the exponential function would increase faster from the point where f(x) = g(x)

This is illustrated using the following table

x      0   1   2   3   4    5

f(x)  0    1   4   9   16   25

g(x)  1   2    4   8   16   3

Hence, the function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ

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Answer:

c ≥ 8

Step-by-step explanation:

1/4c − 1 + 1/4c ≥ 3

Step 1: Add 1/4 to 1/4, since they are on the same side of the equation

1/4 + 1/4c - 1 ≥ 3

1/4 + 1/4 = 1 + 1 / 4

= 2/4

= 1/2

Step 2: Put together the equation

1/2c - 1 ≥ 3

Step 3: Add 1 to both sides.

1/2c − 1 + 1 ≥ 3 + 1

1/2c ≥ 4

Step 4: Multiply both sides by 2.

2 × 1/2c ≥ 2 × 4

c ≥ 8

Answer:

The answer is 24 cracks will be filled

Step-by-step explanation:

hope it helps :3

16 ounces in a pound.  convert pounds  to ounces

calculate the amount of cement we have. That would be 3 x 16 = 48 ounces of cement.

The amount of cracks to be filled : 48 /2  = 24 cracks

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

Answer:

x = 16.2

Step-by-step explanation:

Using trig functions:

cos theta = adjacent side/ hypotenuse

cos 72 = 5/x

Solving for x

x = 5 /cos 72

x=16.18033

Rounding to the nearest tenth

x = 16.2

Answer: x = 16.2 units

Step-by-step explanation:

     We are given an angle (72°), the adjacent side (5), and the hypotenuse (x). We will use the cosine function to solve.

cos(θ) = \(\frac{adjacent}{hypotenuse }\)

cos(72°) = \(\frac{5}{x }\)

xcos(72°) = 5

x = \(\frac{5}{cos(72\°)}\)

x = 16.1803398 ≈ 16.2

Answer:

42.9%

Step-by-step explanation:

If 16 are men, this means 12 of the students are women (28 - 16 = 12)

So, 12 out of 28 are women = 12 ÷ 28 = 0.42857... = 42.857...% = 42.9%

Answer: 50,388,480

just keep multiplying or use a calculator

Answer:

The events are  independent.Their conditional probability is equal to the  probability of an event .

2) The probability that there is line spoilage given that there is transformer spoilage=0.08

- Transformer spoilage but not line spoilage=0.046

Transformer spoilage given that there is no line spoilage = 0.05

- Neither transformer spoilage nor there is no line spoilage =0.03

v- Either transformer spoilage or there is no line spoilage  = 0.97

Step-by-step explanation:

Let A be an event that the spoilage is due to transformers so

P(A) = 5% = 5/100 or 0.05

Let B be an event that the spoilage is due to line so

P(B) = 8% = 8/100 or 0.08

Let C be an event that the spoilage is due to both then

P(C) = 3% = 3/100 or 0.03

1)  Independence

For events to be independent their joint probability is given by

P(A) = P(A∩B)/ P (B)  By Law of independence

P(A∩B)= P(A/B)P(B)

P(A∩B) = 5/100 *8/100=40/10000= 4/1000

P(A) = 5/100  

P(A/B) =P(A∩B)/ P (B)

= 4/1000/8/100= 1/20  

P(A)= P(A/B)

5/100 is equal to  1/20

The events are independent.Their conditional probability is equal to the probability of an event

2) The probability that there is line spoilage given that there is transformer spoilage

P(B/A)= P(A∩B)/ P (A) = 4/1000/5/100= 4/50= 2/25=0.08

Which is again equal to probability of event B.

- Transformer spoilage but not line spoilage

P(A∩1-B)= 5/100*92/100= 460/10000=0.046

Transformer spoilage given that there is no line spoilage

P(A/1-B) =P(A∩1-B)/ P (1-B)

= 5/100*92/100/92/100= 5/100 = 0.05

- Neither transformer spoilage nor there is no line spoilage

1-P(A) +P(1-B)= 1-(5/100+92/100)= 3/100= 0.03

v- Either transformer spoilage or there is no line spoilage  

P(A)+P(1-B)= 5/100+92/100= 97/100= 0.97

The (C) solution of the equation is the value of the variable that causes an equation to be a true statement.

So, the Root or solution of the equation is the value of the variable that turns an equation into a true statement. ​

For instance,

The equation's solution in this case is x = - 2.

Here, the equation's roots or solutions are x = 1 and -1.

Therefore, the (C) solution of the equation is the value of the variable that causes an equation to be a true statement.

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The complete question is given below:

The value of the variable which makes an equation a true statement is called the ________ of the equation.​

A. Coefficient

B. Equation

C. Solution

D. Algebraic expression

E. Constant

F. Variable

Answer:

-5x=35            divide both sides by 5

-x=7                multiply both sides by -1

x=-7

Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

Answer:

v = -3w

Step-by-step explanation:

water level/volume = -3 x weeks

v = -3w

Answer:

0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

153 voters:

This means that \(n = 153\)

Assume the probability that a given registered voter will vote in the presidential election is 63%.

This means that \(p = 0.63\)

Mean and standard deviation:

\(\mu = E(X) = np = 153(0.63) = 96.39\)

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.63*0.37} = 5.97\)

Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election.

Using continuity correction, this is: \(P(X \geq 88 - 0.5) = P(X \geq 87.5)\), which is 1 subtracted by the p-value of Z when X = 87.5.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{87.5 - 96.39}{5.97}\)

\(Z = -1.49\)

\(Z = -1.49\) has a p-value of 0.0681.

1 - 0.0681 = 0.9319

0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.

Answer:

for some reason i cant see ur attachment. lo siento

Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

Answer:

0.512xx

Step-by-step explanation:

100% - 36% = 64%

64% = 0.64

thus after 1st yr, she is left with the value of 0.64xx

100% - 20% = 80%

80% = 0.8

thus after 2nd yr, she is left with the value of 0.8 x (0.64xx) = 0.512xx

Answer:

slope = 7/2 or 3.5 as a decimal.

y-intercept = 1 or (0, 1) in coordinate form.

Answer:

Distance between points = 8.6

Step-by-step explanation:

Formula :

Distance between two points = √(xB−xA)2+(yB−yA)2(xB-xA)2+(yB-yA)2

Solution :

Distance between two points = √(−2−−9)2+(−6−−1)2(-2--9)2+(-6--1)2

= √72+(−5)272+(-5)2

= √49+2549+25

= √7474 = 8.6023

Distance between points (-9, -1) and (-2, -6) is 8.6023

The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

Answer:

3

Step-by-step explanation:

The line is at 3 when x is -2

Answer:

A = $174,742.21

A = P + I where

P (principal) = $100,000.00

I (interest) = $74,742.21

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 100,000.00(1 + 0.08/12)(12)(7)

A = 100,000.00(1 + 0.006666667)(84)

A = $174,742.21

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $100,000.00 at a rate of 8% per year compounded 12 times per year over 7 years is $174,742.21.

Answer:

The amount of water in the reservoir at the beginning of second week

\(w_{2} = 299.8800\)

Step-by-step explanation:

Step(i):-

Given equation

  w₀ = 300  and

\(w_{n} = (0.9993) w _{n-1} + 0.15\)

Put n =1

\(w_{1} = (0.9993) w _{1-1} + 0.15\)

\(w_{1} = (0.9993) w _{0} + 0.15\)

\(w_{1} = (0.9993) X 300 + 0.15\)

\(w_{1} = 299.94\)

Step(ii):-

Put n =2

\(w_{2} = (0.9993) w _{2-1} + 0.15\)

\(w_{2} = (0.9993) w _{1} + 0.15\)

\(w_{2} = (0.9993) X (299.94) + 0.15\)

\(w_{2} = 299.8800\)

Conclusion:-

The amount of water in the reservoir at the beginning of second week

\(w_{2} = 299.8800\)

The four equivalent expressions that gives the number of tickets Simphiwe has left in terms of x, where x is the number of meals she has already bought are;

Four equivalent expressions that gives the number of tickets Simphiwe has left in terms of x are;

In the expression 14−2x

In the expression 2(7−x),

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