what multiples to -64 and adds to -12

Answer:

B.

About 16% of the books have fewer than 150 pages.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 180, standard deviation = 30.

150 pages:

150 is 180 - 30 = 1 standard deviation below the mean.

We have that approximately 68% of measures are within 1 standard deviation of the mean, so 100 - 68 = 32% are more than one standard deviation.

The normal distribution is symmetric, which means that of those 32%, 32/2 = 16% are more than 1 standard deviation below the mean, that is, below 150.

So the correct answer is given by option B.

Answer:

the correct answer is D. (5/2x^3 -3/2x^2 +13x+ 20). Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, the height of the prism is (1/2x-3), the length is (x+5), and the width is (x-4).

Substituting these values into the volume formula, we get:

V = (1/2x-3)(x+5)(x-4)

Expanding this expression using the distributive property, we get:

V = (1/2x^2 - 3x)(x+5)(x-4)

Using the distributive property again, we get:

V = (1/2x^2 - 3x)(x^2 + x - 20)

Using the distributive property once more, we get:

V = 1/2x^3 - 3x^2 - 4x + 20

This expression is equivalent to the expression in answer choice D. Therefore, the correct answer is D. (5/2x^3 -3/2x^2 +13x+ 20)

Answer:

Step-by-step explanation:

f(x) = 3x – 2, g(x) = 7 – x2.

3f(1) - 49(-2)

Substitute the given value into the function and evaluate.

101

The value of 3f(1) - 49(-2) for the given function f(x) = 3x – 2 will be 101.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

Given the function,

f(x) = 3x – 2

Now,

f(1) = 3(1) - 2 = 1

So,

3f(1) - 49(-2) = 3×1 - 49(-2)

⇒ 3 + 98 = 101

Hence "The value of 3f(1) - 49(-2) for the given function f(x) = 3x – 2 will be 101".

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The Product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

To find the product and simplify completely, you need to perform multiplication and simplify the resulting fraction. Here, we are multiplying the following fractions and mixed numbers:1, 5/8, 2, and 3/5.The first step is to convert the mixed numbers into improper fractions.

We do that by multiplying the whole number by the denominator, and then adding the numerator.For 1 5/8, we get:$$1 \frac{5}{8} = \frac{8}{8} \times 1 + \frac{5}{8} = \frac{13}{8}$$For 2, we get:$$2 = \frac{2}{1} = 2 \times \frac{1}{1} = \frac{2}{1}$$For 3/5, we leave it as is since it's already a fraction.

Now that we have all the numbers as fractions, we can multiply them:$$\frac{13}{8} \times \frac{2}{1} \times \frac{3}{5} = \frac{13 \times 2 \times 3}{8 \times 1 \times 5} = \frac{78}{40}$$

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:$$\frac{78}{40} = \frac{2 \times 39}{2 \times 20} = \frac{39}{20}$$

Therefore, the product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

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Answer:

12

Step-by-step explanation:

Answer:

y = -x

Step-by-step explanation:

Let the equation representing the table attached is,

y = mx + b

Here, m = Slope of the line

b = y-intercept

Since, slope of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

From the table attached,

Slope of the line passing through (23, -23) and (33, -33),

m = \(\frac{-33+23}{33-23}\)

m = -1

Equation of the line will be,

y = -x + b

Since, this line passes through another point (43, -43),

-43 = -43 + b

b = 0

Therefore, equation of the line representing the table will be,

y = -x  

Answer:

$800 at 3%, $1,200 at 5%

Step-by-step explanation:

\(.03x - .05(2000 - x) = 84\)

\(100 - .02x = 84\)

\(.02x = 16\)

\(x = 800\)

\(2000 - x = 1200\)

The solution for the inequality -2(8x - 4) < 2x + 5 is x > 1/6.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Let's simplify the inequality -

-2(8x - 4) < 2x + 5

Distribute the -2 -

-16x + 8 < 2x + 5

Subtract 2x from both sides -

-18x + 8 < 5

Subtract 8 from both sides -

-18x < -3

Divide both sides by -18, remembering to reverse the inequality because we're dividing by a negative number -

x > 3/18

Simplifying, we get -

x > 1/6

Therefore, the solution to the inequality is -

x > 1/6

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Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer:

The answer is option A

Slope of the line using points

( 2,0) and (0, 3)

Slope = 3 - 0 / 0 - 2 = -3/2

Hope this helps

Start at the y-intercept of 3 on the coordinate system.

Remember, when choosing points, chose clear

cut points where the line crosses them.

The next put is on the x-intercept and it's 2.

To get from (0,3) to (2,0), we go down 3 units and run 2 units.

Since our slope is going down, it's negative.

So the slope is -3/2.

The measurement of each of the squares will guarantee Mrs. O'Dell has 8 different squares and they are all the same size are 75 centimeters by 100 centimeters.

To begin, let's identify the best way to divide the total area. For this, there are 2 options:

Let's use the first pattern:

Based on this, the dimensions for each section should be 75 centimeters by 100 centimeters.

Note: This question is incomplete; here is the missing section:

Dimensions of the garden: 3 meters x 2 meters

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Answer:

p = 1⅖

Step-by-step explanation:

The least common multiple of 598 and 45 is 26, 910

To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.

This gives:

598 prime factorization :

2 x 13 x 23 = 598

45 prime factorization :

3 x 3 x 5 = 45

The least common multiple is;

= 2 x 13 x 23 x 3 x 3 x 5

= 26, 910

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Answer:

c

Step-by-step explanation:

The probability that their average length is less than 10 inches is; 5.71%

The formula for z-score is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

x' = 10 inches

μ = 9.7 inches

σ = 1.2 inches

n = 40

Thus;

z = (10 - 9.7)/(1.2/√40)

z = 0.3/0.1897367

z = 1.58

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

P(z < 1.58) = 0.0571 or 5.71%

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Answer:

-23 degree

Step-by-step explanation:

=>-14-5-3-1

=>-23

Answer:

-23°

Step-by-step explanation:

= -14 - (5+3+1)

= -14 - 9

= -23°

Option (a) T2 = identity transformation. (b) The kernel of T is the zero matrix. (c) Every matrix is in the range of T. this are true extra properties.

The transformation T that transposes every matrix is indeed linear.

Let's analyze each of the extra properties:

(a) T² = identity transformation: This is true. When you transpose a matrix twice (apply T twice), you get the original

matrix back.

Step 1: Apply T to a matrix M to get its transpose M'.

Step 2: Apply T to the transpose M' to get (M')' which is equal to M.

(b) The kernel of T is the zero matrix: This is true. The kernel of T consists of all matrices M such that T(M) = 0. Since the

transpose of a zero matrix is still a zero matrix, the kernel of T only contains the zero matrix.

(c) Every matrix is in the range of T: This is true. Given any matrix M, there exists another matrix M' such that T(M') = M.

This is because T(M') = M implies M' = T(M), so the transpose of any matrix M can be found by applying T to M.

(d) T(M) = -M is impossible: This is false. It is possible for T(M) = -M in the case of skew-symmetric matrices. A skew

symmetric matrix M satisfies the property that its transpose M' = -M.

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Answer:

the answer shouuld be $1.96

Step-by-step explanation:

24.50x.08= 1.96

Answer:

1.96 in sales tax

Step-by-step explanation:

to get percent of a number just multiply the percent in decimal form by the number for example 8% --> .08

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

5500 ml or 5.5 liters

Step-by-step explanation:

First, we should note that there are 1000 milliliters in 1 liter of liquid.

So, in milliliters, Peter filled three containers with 1500 ml, 750ml, and 2250 ml with 1000ml left over.

To find the total amount, we find the sum of all the milliliters:

1500 + 750 + 2250 + 1000 = 5500 ml

Again, we know that there are 1000 milliliters in 1 liter of liquid, so:

\(\frac{5500}{1000}\) = 5.5 liters

The solution -1 is an extraneous solution

Neither -1 nor -6 is a true solution to the equation.

Option D is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation x + 4 = √(x + 10), we need to isolate the radical term on one side of the equation and then square both sides to eliminate the radical.

Here are the steps:

x + 4 = √(x + 10)

Subtract 4 from both sides:

x = √(x + 10) - 4

Square both sides:

x² = (√(x + 10) - 4)²

Expand the right side using the formula (a - b)^2 = a^2 - 2ab + b^2:

x² = x + 6 - 8√(x + 10)

Move all terms to the left side:

x² - x - 6 + 8√(x + 10) = 0

To solve this equation, we can use a substitution u = √(x + 10):

u = √(x + 10)

Square both sides:

u² = x + 10

Substitute into the original equation:

(u² - 10) + 4 = u

Simplify:

u² - u - 6 = 0

Factor:

(u - 3)(u + 2) = 0

So u = 3 or u = -2.

But u = -2 leads to a negative value under the square root in the substitution u = √(x + 10), which is not allowed.

Therefore, we only consider u = 3, which gives:

√(x + 10) = 3

Square both sides:

x + 10 = 9

Subtract 10 from both sides:

x = -1

So the solution to the original equation is x = -1.

To check if it is extraneous, we need to substitute it back into the original equation:

x + 4 = √(x + 10)

-1 + 4 = √(-1 + 10)

3 = √9

3 = 3

The equation is true, so x = -1 is a valid solution and not extraneous.

Therefore,

Neither -1 nor -6 is a true solution to the equation.

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Answer:

Step-by-step explanation:

“One number is larger than the other by 4 2/3”

x = y + 4⅔

“The difference of the numbers is equal to the smaller number.”

x-y = y

x = 2y

y + 4⅔ = 2y

y = 4⅔

x = 2y = 9⅓

“The sum of the numbers is natural number”

x+y ∈ ℕ

9⅓ + 4⅔ = 14 ∈ ℕ

Answer:

9 1/3 and 4 2/3

Step-by-step explanation:

:)

Answer:

\(sin(0)=opposite/hypotenuse,cos(0)=adjacent/hypotenuse\)

\(sin(60)=\frac{x}{8\sqrt{5} } ,\:\:cos(60)=\frac{y}{8\sqrt{5} }\)

\(\frac{\sqrt{3} }{2} =\frac{x}{8\sqrt{5} } \:\:\:\:\frac{1}{2} =\frac{y}{8\sqrt{15} }\)

\(2x=8\sqrt{5} \times\sqrt{3} \:\;\:\:2y=1\times8\sqrt{15}\)

\(2x=\frac{8\sqrt{15} }{2} \:\:\:\:2y=8\sqrt{15}\)

\(x=8\sqrt{15} /2\:\:\: y=8\sqrt{15} /2\)

\(x=4\sqrt{15}\)    \(y=4\sqrt{15}\)

OAmalOHopeO

Answer:

198 1/3

Step-by-step explanation:

arithmetic sequence formula for the nth term:

aₙ = a₁ + (n-1)d

d = the common difference between each term

a₇ = a₁ + (7-1)d

34 = 5 + 6d

subtract 5 from both sides to isolate d and its coefficient

29 = 6d

divide both sides by 6 to isolate d

d = 29/6

a₄₁ = a₁ + (n-1)d

    = 5 + (41-1)d

    = 5 + 40d

    = 5 + 40(29/6)

    = 198 1/3

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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