9.215
627
How to work the problem

Answer:

  reflect over the x-axis and shift down 3

Step-by-step explanation:

The leading coefficient of -1 means the graph is reflected over the x-axis. The addition of -3 to the function means each graphed point is shifted down 3 units from the original.

The graph of y = -x^2 -3 is the result of the transformation ...

  reflect over the x-axis and shift down 3

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

The Selling Price of The Book before discount will be 20

The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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Answer:*FIND THE SQAURE ROOT OF 1054729 BY DIVISION METHOD*.

Step-by-step explanation:

what? you said to tell you that

Answer:

A. 7.5%

B. 68.26%

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 of 52.5 mm and a standard deviation of 2.5 mm.

This means that \(\mu = 52.5, \sigma = 2.5\)

A. Less than 48.9 mm

The proportion is the pvalue of Z when X = 48.9. So

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

\(Z = \frac{48.9 - 52.5}{2.5}\)

\(Z = -1.44\)

\(Z = -1.44\) has a pvalue of 0.075

0.075*100% = 7.5%, which is the answer.

B. Between 49 and 55

The proportion is the pvalue of Z when X = 55 subtracted by the pvalue of Z when X = 49. So

X = 55

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

\(Z = \frac{55 - 52.5}{2.5}\)

\(Z = 1\)

\(Z = 1\) has a pvalue of 0.8413

X = 49

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

\(Z = \frac{49 - 52.5}{2.5}\)

\(Z = -1\)

\(Z = -1\) has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826*100% = 68.26%, which is the answer.

The percent of the butterflies had the given wingspans are;

A) 7.5%

B) 76.64%

We are given;

Population mean; μ = 52.5 mm

Population standard deviation; σ = 2.5 mm

Formula for z-score is;

z = (x' - μ)/σ

A) For less than 48.9 mm,P(X' < 48.9);

z = (48.9 - 52.5)/2.5

z = -1.44

From online p-value from z-score calculator, we have;

P(X' < 48.9) = 0.075 or 7.5%

B) For x' between 49 and 55, P(49 < X < 55)

At x' = 49;

z = (49 - 52.5)/2.5

z = -1.4

Z-score at x' = 55;

z = (55 - 52.5)/2.5

z = 1

From online p-value from z-score calculator, the p-value between the two z-scores is;

p = 0.7664 or 76.64%

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The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

$131.25

Step-by-step explanation:

Original Price of the TV: $375

Price after markdown:

0.35 x 375

= $131.25

Just multiple the original price by the percentage.

Answer:

x= 3

Step-by-step explanation:

12 ÷ 4 +3

The algebraic expression 4x = 12 represents "four x equals twelve" and the solution of the expression 4x = 12 is the value of variable x is 3.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The given statement is "four x equals twelve"

According to the given question, translate the phrase into an algebraic expression:

⇒ 4x = 12

Thus, the algebraic expression is 4x = 12 represents "four x equals twelve"

Now the above expression solves for variable x,

⇒ 4x = 12

Divided by 4 into both sides of the above equation,

⇒ 4x / 4 = 12 / 4

⇒ x = 3

Therefore, the solution of the expression 4x = 12 is the value of variable x is 3.

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Answer:

2, (x+13)/6, -7

Step-by-step explanation:

The -1 bit means do it backwards, so look the for the output of the function with the value given.

In g, when we put in 2 we get 9 out, so g^-1(9) is 2.

For the second one we need to rearrange it to get x = something.

h(x) + 13 = 6x

x = (h(x) + 13)/6

Then replace the h(x) with x and the x with h^-1(x) to get

h^-1(x) = (x + 13)/6

The last one is a trick. Note that h and h^-1 are opposites. If we do something then do the opposite of it, we haven't done anything at all! So the number stays the same.

If x and y be  i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero.

Yes, x y are x y independent studysoup.

Here  x and y be i.i.d. unif(0, 1)

The i.i.d stands for independent and identically distributed

unif means that the uniformly distributed

Here x and y are i.i.d unif (0,1)

The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable

Here we have to find the covariance of x + y and x - y

According to the properties of covariance

Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0

Because Cov(x, x) = Cov (y, y)

Cov(y, x) = Cov(x, y)

Therefore, the covariance of x+y and x - y is 0.

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The 46th term of the sequence is 324.

We have,

To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.

Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference

of 7.

To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:

a(n) = a(1) + (n - 1) d

where a(1) is the first term, d is the common difference, and n is the term number we want to find.

Using the given information, we have:

a(1) = 9

d = 7

n = 46

Plugging these values into the formula, we get:

a (46) = 9 + (46 - 1)7

a (46) = 9 + 45 (7)

a(46) = 9 + 315

a(46) = 324

Therefore,

The 46th term of the sequence is 324.

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Answer:

40x+24y-56=

8(5x+2y-7)

Step-by-step explanation:

Answer:

.5

Step-by-step explanation:

30 miles a hour divide by 60 so your going half a mile a minute

Your speed in feet per minute is 2640 ft/min.

A unit rate means a rate for one of something.

Given that, Your rate of speed is 30 miles for every 1 hour

We know, 1 mile = 5280 feet

Therefore, 30 miles = 30x5280 = 158400 feet

That means, you are travelling 158400 feet for every hour

In an hour, there are 60 minutes,

Therefore, you are travelling 158400 feet in every 60 minutes.

In 60 minutes = 158400 feet

In 1 minute = 158400/60 = 2640 feet

That means you are travelling 2640 feet in every 1 minute.

Hence, your speed in feet per minute is 2640 ft/min.

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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a) There are 2 students who study both Maths and Physics in the year group of 100 students at School A.

b) School B has more pupils studying both subjects.

Part A:

To solve this problem, we can use the principle of inclusion-exclusion. This states that the total number of students who study either Maths, Physics, or both can be calculated by adding the number of students who study Maths, the number of students who study Physics, and the number of students who study both, and then subtracting the number of students who study both.

In this case, the total number of students who study either Maths, Physics, or both is:

(73 students + 58 students) - (2 students) = 131 students - 2 students = 129 students

To find the number of students who study both Maths and Physics, we can subtract the number of students who study only one subject from the total number of students who study either Maths, Physics, or both:

129 students - (73 students - 2 students) - (58 students - 2 students) = 129 students - 71 students - 56 students = 2 students

Therefore, there are 2 students who study both Maths and Physics in the year group of 100 students at School A.

Part B:

To determine which school has more pupils studying both Maths and Physics, we need to calculate the number of students at each school who study both subjects.

At School A, we know that there are 2 students who study both Maths and Physics.

At School B, we know that 24% of the students study both Maths and Physics. To find the number of students at School B who study both subjects, we can multiply the total number of students by the percentage who study both:

(150 students) * (24%) = 36 students

Since 36 is greater than 2, there are more students at School B who study both Maths and Physics. Therefore, School B has more pupils studying both subjects.

Answer:

In School B there are more pupils stydying both maths and physics

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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TU is parallel to MN.

Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.

Therefore,

Considering the line TU, find the slope = y₂-y₁ / x₂-x₁

= 10-1 / 5-8 = -9/3 = -3

Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.

Hence TU is parallel to MN.

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Answer:

b=–2

Step-by-step explanation:

we've got:

(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243

and we've also got the coefficient of x³ as –720

90b³=–720===> b³=–8===> b=–2

Answer:

60%

Step-by-step explanation:

25-10=15

15÷25=0.6

0.6×100=60

The first step will be subtract 3 from each side of the model.

By subtracting 3 from each side of the model, the 3 in the Right Hand Side will be cancelled, and the model will be:

2x = 5 - 3 = 2

Then the next step will be dividing 2 from each side of the model.

2x + 3 = 5

By subtracting 3 to both the sides, we get

2x + 3 - 3 = 5 - 3

or, 2x = 2

By dividing 2 to both the sides, we get

2x/2 = 2/2

or, x = 1

The value of x is 1.

Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Answer:

0,5

Step-by-step explanation:

Missing number 5 or it can be a 0

This is beacause a number that ends with 0 or 5 is divisible by 5. Divisibilitiy rules state that!

Ex: 5 x 5 = 25

5 x 4 = 20

Answer: I'm not sure if you're trying to find x or y, but y = x/3 and x = 3y

Step-by-step explanation:

Answer:

no se hduxuwvqnx8whfbxywiwbfjci

the answer is 1296 =6^4

Answer: y=29 / (4,29)

Step-by-step explanation:

By graphing \(f(x)=8x-3\) and \(f(4)=0\) on Desmos. You'll be able to find that when x is 4, y is 29.

Similarly, you can plugin 4 into the original equation (\(f(x)=8x-3\)) Which looks like:

\(8(4)-3\\32-3=29\)

Additionally, you can change \(f(x)=\) to \(y=\) as it is the exact same thing. With that in mind, you can do the same with \(f(x)=0\) and just change it to x=4. As you're wanting to know what the y-value is when x=4.

Answer:

4x²-3x+c is our original equation

Step-by-step explanation:

we have an independent number I called this number c

put 4 from x and try to find c

f(4)=4*(4²)-3*(4)+c=0

we have to be careful about f(4) is 0

64-12+c=0 and c is -52 so our original equation is 4x²-3x-52

Answer:

20.68976

Step-by-step explanation:

Convert the percentage into decimal :

58% = 0.58

0.58 × x = 12

Divide both sides by 0.58 :

x = 12÷0.58

x = 20.689655...

x = 20.68976

So the method to these types of question is to make the question into an equation by converting the percentage into a decimal, rearrange to make the unknown number the subject and solve .

Hope you understood and have a good day