Solve the quadratic inequality
4x^2-25<0

Answer:

if you help me, i help you

Answer:

x = 2.5

Step-by-step explanation:

2.4x - 6 = 0

2.4x - 6 + 6 = 0 + 6

2.4x = 0 + 6

2.4x = 6

2.4x ÷ 2.4 = 6 ÷ 2.4

x = 6 ÷ 2.4

x = 2.5

I am unable to solve this problem.

Answer:

78

Step-by-step explanation:

First we want 9 3/4 into an improper fraction.

(9 * 4) + 3 / 4 = 39 / 4

Then we want to change 39 / 4 into the same denominator as 1/8

39 / 4 * 2 = 78 / 8

And there is your answer, 78!

(hopefully this is correct, have a nice day!)

Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function

Riley has collected approximately 22.7 grams of the trace element in his sample.

To calculate the amount of trace element collected by Riley, we first need to find the volume of the cylinder-shaped container that he used. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

Plugging in the values given in the problem, we get:

V = π(5.7 cm)²(13.6 cm)

V ≈ 1338.6 cubic centimeters

Since the sample contains 0.017 grams of the trace element per cubic centimeter of water, we can find the total amount of trace element collected by multiplying the volume of the sample by the concentration of the trace element:

0.017 grams/cubic centimeter × 1338.6 cubic centimeters ≈ 22.7 grams

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Answer:

The intercept of the line perpendicular to the line \(y = x + 1\) is 5.

Step-by-step explanation:

The line \(y = x + 1\) has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:

\(m_{\perp} = -\frac{1}{m}\) (1)

Where:

\(m\) - Slope of the original line.

\(m_{\perp}\) - Slope of the line perpendicular to the original line.

If we know that \(m = 1\), then the new slope is:

\(m_{\perp} = -\frac{1}{1}\)

\(m_{\perp} = -1\)

A line is defined by the following expression:

\(y = m\cdot x + b\) (2)

Where:

\(x\) - Independent variable.

\(y\) - Dependent variable.

\(m\) - Slope.

\(b\) - Intercept.

If we know that \((x,y) = (4,1)\) and \(m = -1\), then the intercept of the line perpendicular to the original line:

\(b = y - m\cdot x\)

\(b = 1+4\)

\(b = 5\)

The intercept of the line perpendicular to the line \(y = x + 1\) is 5.

The depth of the water of the fish tank based on the mentioned details and after addition of glass of water will be 4150 ml.

Firstly calculating the volume of the fish tank to find the total amount of water it can contain.

Volume = length × breadth × height

Keep the values in formula

Volume = 25 × 20 × 30

Performing multiplication

Volume = 15000

Amount of water in fish tank = 15000×1/4

Amount of water in fish tank = 3750 ml

Amount of water added = 3750 + 400

Amount of water added = 4150 ml

So, the depth of the water will be 4150 ml.

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The complete question is attached in the figure.

Part A: Each block will have an area of 128 square inches (8 in. x 16 in.), but the outside border of each block will be covered with blue paint.

Area is the measurement of the space contained within a two-dimensional surface.

The outside border of each block is 8 in. long and 16 in. high, for a total of 128 square inches of each block that is covered in blue paint.

Part B: The entire mural will have 25 identical blocks, so the total number of square inches of the entire mural that will be covered by white paint is 3,200 square inches (25 blocks x 128 square inches per block).

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Answer:

4.56, so he should expect between 4 and 5 of them to contain fewer than 34 nuts.

Step-by-step explanation:

Normal Probability Distribution:

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean 42 and standard deviation 4.

This means that \(\mu = 42, \sigma = 4\)

Proportion with fewer than 34 nuts:

p-value of Z when X = 34. So

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

\(Z = \frac{34 - 42}{4}\)

\(Z = -2\)

\(Z = -2\) has a p-value of 0.0228.

Out of 200 bags:

0.0228*200 = 4.56.

4.56, so he should expect between 4 and 5 of them to contain fewer than 34 nuts.

Answer:

52

Step-by-step explanation:

52 is a bigger number than 33?

Answer:

28

Step-by-step explanation:

Ratios are like fractions. Since you're finding an equivalent ratio, u can set them up like equivalent fractions and put an x where the missing number would go:

\(\frac{1}{7} = \frac{4}{x}\)

You can either cross multiply and then solve for x, but it's easier to just think about it. The fractions are equivalent, right? So for them to be the same you'd have to do to the bottom what u do to the top.

To get from 1 to 4, you multiply by 4. By that logic, to get from 7 to x you'd have to multiply by 4 as well. Therefore x = 7x4, which is 28.

So x = 28

Here, the 11.5 oz of vinegar ingredient is needed in order to make 46 oz of furniture polish .

So in this problem it says a furniture polish can be made containing or combining vinegar and olive oil and the amount of oil should be three times the amount of vinegar. So I'm gonna make vinegar X. And oil three X. How much of each ingredient is needed in order to make 46 oz of furniture Polish. So I'm gonna go ahead and add these together. Okay. Yes. Which means that four x. equals 46 and divide by four So X. is 11.5. So that means that for vinegar we need 11.5 oz. And then I'm going to multiply that by three to get 34.5 oz for the oil. And if you can find those together just to check you get 46. So this would be the amount of both ingredients.

To make 46 oz of furniture polish, you will need 3 times as much olive oil as vinegar.

So, you need 46 oz / 4 = 11.5 oz of vinegar.

And 11.5 oz * 3 = 34.5 oz of olive oil.

Therefore,the 11.5 oz of vinegar ingredient is needed in order  to make 46 oz of furniture polish .

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Step-by-step explanation:

Equation to find the sum of the first n terms :

\(S_{n}\) = \(\frac{n}{2}\) x (2\(a_{1}\) + (n - 1)d)

- where n is the first n terms

- where \(a_{1}\) is the first term in the sequence

- where d is the difference (To find the difference: \(a_{1}\) - \(a_{2}\))

How to find n for the given sum :

1. Using the previous equation, plug in all the numbers that you know

2. PEMDAS then combine all like terms

3. Distribute what's on the outside to the inside of the parenthesis

4. Move  \(S_{n}\) to the other side to make a quadratic equation

5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)

Question 1:

Sum of first 10 terms : \(S_{10}\) = \(\frac{10}{2}\) ( 2 x 2 + (10 - 1)6)

 \(S_{10}\) = \(\frac{10}{2}\) (4 + (9)6) = (4 + 54) = 58

 \(S_{10}\) = \(\frac{10}{2}\) x 58

Answer : 290

Find n for the given sum : 1704 =  \(\frac{n}{2}\) x (2 x 2 + (n - 1)6)

distribute 6 into (n-1)

1704 =  \(\frac{n}{2}\) x ( 4 + 6n - 6)

combine like terms

1704 =  \(\frac{n}{2}\) x ( -2 + 6n )

Distribute  \(\frac{n}{2}\) to ( -2 + 6n )

1704 = \(\frac{-2n}{2}\) - \(\frac{6n^{2} }{2}\)

Simplify fractions and move 1704 to the other side

-3\(n^{2}\) - n + 1704 = 0

Use a quadratic calculator to find the answer and use the answer with the whole number

Answer : -24

Question 2:

(i'm just gonna show you the answers for the rest of them-)

Sum of the first 14 terms: 490

Find n for the given sum: 33.65 (I'm gonna round it to 34)

Question 3:

Sum of the first 21 terms: 483

Find n for the given sum: 11.48 (rounded: 11)

Question 4:

Sum of the first 32 terms: -1328

Find n for the given sum: -9.34 (rounded -9)

really hope this helps in any way :D

Answer:40

Step-by-step explanation:

look at the number of lions at 22 which should be one line after 20, if you use a ruler to connect that line to the best-fit green line you can find the answer 40 as the side on the number of hyenas (number 40) is directly aligned with the part of the green line you previously connectec

c = -1/4

Given the line y = -x and the parabola y = c - x²

Slope of tangent, m = - 1

Now, slope of tangent from curve, y' = -2x

∴ - 1 = -2x

⇒ x = 1/2

∴ y = -1/2

(1/2, -1/2) passes through the curve.

Putting x = 1/2 and y = -1/2 in the equation of curve, y = c - x²

⇒ -1/2 = c - (1/2)²

⇒ -1/2 = c - 1/4

⇒ c = 1/4 - 1/2

⇒ c = -1/4

∴ Value of c is -1/4.

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The probability that Jack and Jill will end up in the same class is 19/59.

The principles of probability and counting are fundamental concepts in probability theory and combinatorics. They are used to solve problems that involve uncertain events and counting arrangements of objects, respectively.

The principles of probability include:

Sample space: The set of all possible outcomes of a random experiment.

Event: A subset of the sample space.

Probability: A measure of the likelihood of an event, expressed as a number between 0 and 1.

Here we have

A group of 60 students is randomly split into 3 classes of equal size.

All partitions are equally likely. jack and jill are two students belonging to that group

Let's assume that Jack is assigned to a class, say the first class.

There are 20 students in that class, and the remaining 40 students are split evenly between the second and third classes.

Since all partitions are equally likely, each of the 59 remaining students has an equal chance of being assigned to any of the two remaining classes.

Now, we want to know the probability that Jill is assigned to the same class as Jack. There are 19 other students in the first class besides Jack, so there are 19 possible students in that class that Jill can be assigned to.

Out of the remaining 59 students, there are 40 in the other two classes, so Jill has 40 possible students she can be assigned to if she is not in Jack's class.

Hence,

The probability that Jill is assigned to the same class as Jack

= 19/59

Therefore,

The probability that Jack and Jill will end up in the same class is 19/59.

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Cutting 6-inch squares from each corner of a 20x12-inch tin sheet creates an open box with dimensions 8x0x6 inches.

By cutting 6-inch squares from each corner of a 20x12-inch tin sheet, you can create an open box.

The box's dimensions will be 8x0x6 inches. The width of 0 inches indicates that the tray has no width, resembling a line segment.

The explanation involves finding the maximum volume by taking the derivative of the volume function and setting it to zero.

The critical points are obtained by solving the resulting cubic equation, which yields two possible values: x = 10 and x = 6.

However, since x cannot exceed half the width or length of the sheet, the smaller value, x = 6 inches, is chosen.

Thus, the tray dimensions are determined, and it can be visualized as an open box with a length of 8 inches, no width, and a height of 6 inches.

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Answer:

32 and 25

Step-by-step explanation:

Answer:

30 in

Step-by-step explanation:

18^2 + 24^2 = x^2

324 + 576 = x^2

900 = x^2

30 = x

Answer:

30 in

Step-by-step explanation:

With maths problems, first thing to do is to identify clearly the information that you have (from the question) and what you want to find;

Here, we have a right-angle triangle and given 2 of the sides, we are asked to find the other;

Considering this, if you've learnt it well and done plenty of practice, then you should realise pythagoras theorem can be applied to get the unknown side;

The square of the two given sides added will give the square of the unknown side:

(24)² + (18)² = x²

576 + 324 = x²

x² = 900

x = sqrt(900)

x = 30

False. The student t distribution may be used to construct a confidence interval for the mean of a population that is normally distributed, so long as the sample size is small.

The student t distribution may be used to construct a confidence interval for the mean of any population, so long as the sample size is small. The student t distribution is a probability distribution that is used to estimate the population mean when the sample size is small and the population standard deviation is unknown. The student t distribution is also used to construct confidence intervals for the population mean.

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The angle between v and w is tan (inverse(0.8)).

In this problem, we are given two vectors v and w where v×w=(−4,−3,−5) and v⋅w=2. The angle between these two vectors is theta, which ranges from 0 to 180 degrees. We want to find tan(θ) which will be 180-90 degrees.

The problem can be solved by applying elementary trigonometry. For example, if we have tan(θ)=tan(−4)*sin(−3)+(tan(−5)*cos(−2)), then tan(θ)=2 and so v×w= −4+4i+5; also v⋅w= 1/i, so w×v= −3/i

The two vectors are perpendicular to each other. So if theta is between v and w, then the line segment with length 2 must pass through (0,−1). So tan(θ)=2/5=0.8.

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Answer:

is a function that reverse another function if de function apply to an input x gives a result of a y den applying its inverse function g to y gives de result of x nd opposite eg f (x )=y nd if g (y )=x

Answer:

21

Step-by-step explanation:

Answer:

The first one I think joe is right, the answer to part 2 is = kx + 3x^2 − 8

Step-by-step explanation:

Answer:

These are confusing Beth , b/c you have to remember that they will add to 100%

Step-by-step explanation:

so

green = 3*  yellow

100% = green + yellow + 35% + 25%

100% = 3* yellow + yellow +60%

40% = 4* yellow

10% = yellow

30% = green

there are 14 purples in the bag , which is 35% of total

14/.35 = 40

there are a total of 40 pins

so

4    are yellow  (10% of 40  or 40* 0.1)

12 are green    (30% of 40  or 40*0.3)

14  are purple  (35% of 40 or 40*0.35)

10  are grey  (25% of 40  or 40*0.25 )

see?  : |

a) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] b) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] c) p(x) = a + bx + cx² as a linear combination of the polynomials in C can be defined as p(x) = a + b + c(x - 1)²

(a) Finding the transition matrix from C to B

To find the transition matrix from C to B, we need to express the vectors in the basis C as linear combinations of the vectors in basis B.

Let's express each vector in basis C in terms of basis B

1 = 1(1) + 0(x) + 0(x²)

(2 - 1) = 0(1) + 1(x) + 0(x²)

(x - 1)² = 0(1) + 0(x) + 1(x²)

The coefficients of the linear combinations are the entries of the transition matrix from C to B. Thus, the transition matrix is

[1 0 0]

[0 1 0]

[0 0 1]

(b) Finding the transition matrix from B to C:

To find the transition matrix from B to C, we need to express the vectors in the basis B as linear combinations of the vectors in basis C.

Let's express each vector in basis B in terms of basis C

1 = 1(1) + 0(2 - 1) + 0((x - 1)²)

x = 0(1) + 1(2 - 1) + 0((x - 1)²)

x² = 0(1) + 0(2 - 1) + 1((x - 1)²)

The coefficients of the linear combinations are the entries of the transition matrix from B to C. Thus, the transition matrix is

[1 0 0]

[0 1 0]

[0 0 1]

(c) Writing p(x) = a + bx + cx² as a linear combination of the polynomials in C

To write p(x) = a + bx + cx² as a linear combination of the polynomials in C, we need to express the polynomial p(x) in terms of the basis C.

We have the basis C = {1, (2 - 1), (x - 1)²}

p(x) = a + bx + cx² = a(1) + b(2 - 1) + c((x - 1)²) = a + b(2 - 1) + c((x - 1)²)

Thus, the polynomial p(x) = a + bx + cx² can be written as a linear combination of the polynomials in C as

p(x) = a + b(2 - 1) + c((x - 1)²)

Simplifying further

p(x) = a + b + c(x - 1)²

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Answer:

False

Step-by-step explanation:

No we can't find the square root of negative number.

Hope it helped you

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Answer:

143. Divide 91/7 = 13, then take the number of oil changes per day and times it by 11. 13 x 11 = 143.

Step-by-step explanation:

Answer:

113.75

Step-by-step explanation:

Since 11 days is only 4 days away from 11, divide 91 / 4 = 22.75. Add this number to 91 to get the answer.