-16 + m = -6 SOLVE M.

Answer:

(y^3-2)(x^2-2)

Step-by-step explanation:

x^2y^3-2y^3 can be factored. This will be equal to y^3(x^2-2). Then for the other half it will be equal to -2(x^2-2). Because the insides are the same, the equation is the outside two number y^3 and -2 added together time the inside number x^2-2. This will make the expression (y^3-2)(x^2-2).

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47% of ice cream sold yesterday was marshmallow ice cream

Here, we want to get the percentage of the ice cream sold was marshmallow

From the question, 235 scoops were marshmallow, while 265 was all others combined

The total number of scoops sold is thus;

So, to find the percentage that was marsjmallow, we simply divide the number of marshmallow by the total and multiply by 100%

Mathematically, we have this as;

The value that is not reasonable for the true mean weight of the residents of the town is 193 pounds

Given that the mean weight is 187 pounds with a margin of error of 3 pounds, we can construct the interval as follows:

Mean weight - Margin of error = 187 - 3 = 184 pounds

Mean weight + Margin of error = 187 + 3 = 190 pounds

So, the reasonable range for the true mean weight of the residents of the town is between 184 and 190 pounds.

Now, let's evaluate the options to identify the value that falls outside this reasonable range:

A. 170 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.

B. 188 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.

C. 193 pounds - This value falls above the upper limit of the reasonable range (190 pounds). Therefore, it is not a reasonable value for the true mean weight.

D. 186 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.

E. 182 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.

From the options provided, the value that is not reasonable for the true mean weight of the residents of the town is 193 pounds.

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Answer:

C

Step-by-step explanation:

The slope of the lined graph is 5 / 3

The formula for determining the slope of a line is expressed as;

Slope = y2 - y1/ x2 - x1

From the graph shown;

Now, let's substitute the values

Slope, m = 4 - (-1) / 3 - 0

Find the differences

Slope, m = 4 + 1/ 3

Slope, m = 5 / 3

Thus, the slope of the lined graph is 5 / 3

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Answer:

65

Step-by-step explanation:

multiply 1/2 and 10 to get 10/2

10/2(9.4+3.6)

divide 10 by 2 to get 5

add 9.4 and 3.6 to get 13

5 X 13

multiply to get 65

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=5/2

Decimal Form:

x=2.5

Mixed Number Form:

x=2 1/2

Step-by-step explanation:

The first number is 8.33 percent more than the second number.

Let m be the first number, n be the second number and p be the third number.

Two numbers are respectively twenty percent and ten percent more than a third number.

m = (100 + 20)% of p

m = 120 percent of p

m = 120 % of p

m = (120 / 100) × p

m = 1.2 p

And the second number would be,

n = (100 + 10)% of p

n = 110 percent of p

n = (110 / 100) × p

n = 1.1 p

We need to find by how much number the first number more than the second.

Consider the difference,

1.2 p - 1.1p = 0.1 p

So the required percentage noting but the difference is what percent of the first number.

(0.1 p / 1.2 p) × 100 = 8.33%

Therefore, the first number is 8.33 percent more than the second number.

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The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

So, remember that:

cos(x) > 0   for  -pi/2 < x < pi/2

cos(x) < 0 for  pi/2 < x < (3/2)*pi

and

sin(x) > 0 for 0 < x < pi

sin(x) < 0 for -pi < x <0  or  pi < x < 2pi

Also, we have the periodicty of the sine and cocine equations, such that:

sin(x) = sin(x + 2pi)

cos(x) = cos(x + 2pi)

Now let's solve the problem:

\(sin(\frac{13*\pi}{36} )\)

here we have:

x = (13/36)π

This is larger than zero and smaller than π:

0 < (13/36)π < π

then:

\(sin(\frac{13*\pi}{36} )\)

Is positive.

The next one is:

\(cos(\frac{7*\pi}{12} )\)

Here we have x = (7/12)*pi

notice that:

7/12 > 1/2

Then:

(7/12)*π > (1/2)*π

Then:

\(cos(\frac{7*\pi}{12} )\)

is negative.

next one:

\(sin(\frac{47*\pi}{36} )\)

here:

x = (47/36)*π

here we have (47/36) > 1

then:

(47/36)*π > π

then:

\(sin(\frac{47*\pi}{36} )\)

is negative.

the next one is:

\(cos(\frac{17*\pi}{10} )\)

Here we have x = (17/10)*π

if we subtract 2*π (because of the periodicity) we get:

(17/10)*π - 2*π

(17/10)*π - (20/10)*π

(-3/10)*π

this is in the range where the cosine function is positive, thus:

\(cos(\frac{17*\pi}{10} )\)

is positive.

the next one is:

\(tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}\)

here we have:

x = (41/36)*π

Notice that both functions, sine and cosine are negatives for that value, then we have the quotient of two negative values, so:

\(tan(\frac{41*\pi}{36} ) = \frac{sin(\frac{41*\pi}{36} )}{cos(\frac{41*\pi}{36} )}\)

is positive.

The final one is:

\(tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}\)

Here:

x = (5/9)*π

The sin function is positive with this x value, while the cosine function is negative, thus:

\(tan(\frac{5*\pi}{9} ) = \frac{sin(\frac{5*\pi}{9} )}{cos(\frac{5*\pi}{9} )}\)

Is negative.

Answer:

(a) 0.89

(b) 0.8823

(c) 0.1176

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Total number of parts = 18

Total number of suitable parts = 16

(a). Probability for the first part is suitable are as follows,

Here, favourable outcomes = 16

So, P1 = favourable outcomes ÷ Total number of parts

= 16 ÷ 18

= 0.89

(b). Probability for the second part is suitable are as follows,

Here, favourable outcomes = 16 - 1 = 15

total number of parts = 18 - 1 = 17

So, P2 = favourable outcomes ÷ Total number of parts

= 15 ÷ 17

= 0.8823

(c). Probability for the second part is not suitable are as follows,

Here, favourable outcomes = 17 - 15 = 2

Total number of parts = 17

So, P2 = favourable outcomes ÷ Total number of parts

= 2 ÷ 17

= 0.1176

Answer:  1,000 millimeters

The prefix "milli" means "thousandth". One thousandth of a meter is a millimeter (mm). So it takes 1000 mm to form a full meter.

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Answer:

y=-4x+1

Step-by-step explanation:

You want to find the equation for a line that passes through the point (-1,5) and has a slope of -4.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -4. So you can right away fill in the equation for a line somewhat to read:

y=-4x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-1,5). When x of the line is -1, y of the line must be 5.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-1,5).

So, why not plug in for x the number -1 and for y the number 5? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-1,5). y=mx+b or 5=-4 × -1+b, or solving for b: b=5-(-4)(-1). b=1.

The equation of line passes through the point (-1, 5) will be;

⇒ y = - 4x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (-1, 5).

And, The slope of line is,

⇒ m = - 4

Now,

Since, The equation of line passes through the point (- 1, 5).

And, Slope of the line is,

m = - 4

Thus, The equation of line with slope - 4 is,

⇒ y - 5 = - 4 (x - (-1))

⇒ y - 2 = - 4 (x + 1)

⇒ y - 2 = - 4x - 4

⇒ y = - 4x - 4 + 2

⇒ y = - 4x - 2

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Answer:

4.84

Step-by-step explanation:

Do 100 divided by 22% that's gonna give you 0.002 so then you drop the two zeros after the decimal and you gonna have 0.22 then do 0.22 times 22 and you gonna get your answer 4.84.

Answer:

1

Step-by-step explanation:

Anything to the exponent of 0 is 1.

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Answer:

Adult-. $4

Student-. $2.50

Step-by-step explanation:

equation

1a + 3s = $11.50

3a + 2s = $17.00

$4+$2.50(3)=$11.50

$12+$2.50(2)=$17.00

or

1($4)+3($2.50)=$11.50

3($4)+2($2.50)=$17.00

sorry if this is a little confusing, this is a simpler equation-

$4.00+($2.50x3)=$11.50

($4.00x3)+($2.50x2)=$17.00

Answer:

It should be 42.4

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Answer:

\(X^2-2x+1\)

Step-by-step explanation:

Traditional pattern for a perfect square:

\(x^{2} +2ax+a^{2}\)

Which factors into: \((x+a)^2\)

We know becuase a is "missing" from the original equation that it must equal 1; therefore:

\(x^2+2x+1\)

Which we know is correct because it factors into: \((x+1)^2\)

Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)

\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)

\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)

\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

The solutions to the equation 8x^3 - 1 = 0 are x = 1/2, x = (-2 + 2√2i)/8, and x = (-2 - 2√2i)/8.None of the given Values is NOT a solution of the equation.

The solution(s) of the equation 8x^3 - 1 = 0, we need to determine the values of x that satisfy the equation. We can solve this equation by setting it equal to zero and factoring:

8x^3 - 1 = 0

(2x)^3 - 1^3 = 0

(2x - 1)(4x^2 + 2x + 1) = 0

Now we can find the values of x that make each factor equal to zero:

2x - 1 = 0

x = 1/2

4x^2 + 2x + 1 = 0

Using the quadratic formula, we can solve for x and find two additional solutions:

x = (-2 ± √(-8))/8

x = (-2 ± 2√2i)/8

Therefore, the solutions to the equation 8x^3 - 1 = 0 are x = 1/2, x = (-2 + 2√2i)/8, and x = (-2 - 2√2i)/8.None of the given values is NOT a solution of the equation.

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Answer:

3[x + 3(4x – 5)] = (39x-15)

Step-by-step explanation:

The given expression is : 3[x + 3(4x – 5)]

We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,

\(3[x + 3(4x -5)]=3[x+12x-15]\)

Again open the brackets,

\(3[x+12x-15]=3x+36x-45\)

Now adding numbers having variables together. So,

\(3[x + 3(4x - 5)]=39x-15\)

So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).

The equivalent expressions are B: 2(12m-6p+36) and (c): 12(2m-p+6)

From the question, we have the following parameters that can be used in our computation:

24m-12p+72

Factor out 2 from the expression

So, we have

2(12m-6p+36)

This represents the option (b)

Factor out 12 from the expression

So, we have

12(2m-p+6)

This represents the option (c)

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Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

So

\(\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485\)

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

So

\(\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314\)

Distribution of the difference:

Mean:

\(\mu = \mu_A - \mu_B = 36 - 42 = -6\)

Standard error:

\(s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142\)

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = zs = 1.96*1.4142 = 2.77\)

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step