9) Which inequality represents the solution to the given inequality? State the letter of the correct answer.

-13t≤78

A. t<-6
B. t≤6
C. t>6
D. t>-6

10) For the solution to the inequality in the previous problem, list all integers from -10 through 10 that will make
the inequality a true statement when substituted for "t"? (The integers for -10 through 10 are shown below.)
(-10,-9,-8,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

Father:28

Son: 4

filler since

i need 20 characters

When the  expression [tex]log_b{32} - log_b{7}[/tex], b > 1, is written in the form [tex]log_b{a}[/tex], the value of a is 25

We know that a logarithm of a number is nothing but the power to which a number must be raised to get some other values.

We know that the rules for the addition or subtraction (basic algebraic operations)

When the base od logarithms are same, then only we can add or subtract logarithms.

Consider logartithemic numbers : log₂7 , log₃8 and log₂5

Her we can observe that the base of  logartithemic numbers  log₂7 , log₃8  is different.

Here, the expression [tex]log_b{32} - log_b{7}[/tex]

The base of logartithemic numbers  [tex]log_b{32} , log_b{7}[/tex] is equal.

so, we can perform algebraic operation.

[tex]log_b{32} - log_b{7}\\\\=log_b{32-7}\\\\=log_b{25}[/tex]

Comparing above expression with [tex]log_b{a}[/tex] we have,

a = 25

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A:  The z-score is -0.9375; B:  a z-score of 1.25 corresponds to a score of 750; C: a score of 550 is one standard deviation below the mean.

a) To find the standardized z-score for a student scoring 595 on their GMAT, we use the formula:

z = (x - mu) / sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

z = (595 - 630) / 80 = -0.9375

Therefore, the z-score is -0.9375.

b) To find the number of standard deviations a student scoring 670 is from the mean, we use the formula:

z = (x - mu) / sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

z = (670 - 630) / 80 = 0.75

Therefore, the student scoring 670 is 0.75 standard deviations from the mean.

c) To find the score that corresponds to a z-score of 1.25, we use the formula:

x = mu + z * sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

x = 630 + 1.25 * 80 = 750

Therefore, a z-score of 1.25 corresponds to a score of 750.

d) To find the score that is one standard deviation below the mean, we use the formula:

x = mu - sigma

where x is the student's score, mu is the mean, and sigma is the standard deviation. In this case, mu = 630 and sigma = 80, so we have:

x = 630 - 80 = 550

Therefore, a score of 550 is one standard deviation below the mean.

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The quantity supplied is determined by production costs, and the quantity demanded is determined by the desire for the product

The quantity demanded is a term that is used in economics to describe the total amount of a good or service that consumers demand over a given interval of time

When the production increase, fewer people could afford to put up the capital to do it, which reduce the quantity supplied to the market.

When the desire for a product increased, the amount of demand for a product will be the same since there is a larger amount of consumers who might be willing to obtain the product even at a higher price.

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The significance of the intercept and the coefficient of performance rating is defined below.

The significance level is used to determine the strength of evidence for the relationship between the variables.

A significance level of .01 means that there is only a 1% chance that the relationship between the variables is due to chance. A significance level of .05 means that there is a 5% chance that the relationship is due to chance, and a significance level of .10 means that there is a 10% chance that the relationship is due to chance.

If the significance level is .01, the relationship between the variables is considered to be strictly significant, meaning that there is a very low probability that the relationship is due to chance.

If the significance level is .05, the relationship is considered to be regularly significant, meaning that there is a moderate probability that the relationship is due to chance.

If the significance level is .10, the relationship is considered to be weakly significant, meaning that there is a relatively high probability that the relationship is due to chance.

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The variance of the difference of two independent random variables is equal to the sum of the variances, not the difference.

False. So, var(x - z) = var(x) + var(z).

False. If x ~ n(0,0°), then z = 2x ~ n(0,2°), not n(0,4°). This is because the variance of the difference of two variables is the sum of the variance of the individual variables plus twice the covariance between the two variables. Since x and z are independent, the covariance between them is 0, and so the variance of x - z is equal to the sum of the variances of x and z.

If x ~ n(0,0°), then z = 2x ~ n(0,2°). This is because the mean of a random variable multiplied by a constant is equal to the original mean multiplied by the same constant, and the variance of a random variable multiplied by a constant is equal to the square of the constant multiplied by the original variance. So, if x has mean 0 and variance 0°, then z has mean 0 and variance 2°.

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Yes, the quadratic function f(x) and the linear function g(x) will intersect. The x-coordinate of the point of intersection could be positive, negative or zero, depending on the specific functions.

From the data given, it's not possible to determine the x-coordinate of the point of intersection.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

Linear functions are usually written as y = mx + b and graphed as straight lines.

Begin with the y-intercept or b value, then use the slope to identify a second point on the graph. Quadratic functions are graphed as curved parabolas and have the formula y = ax2 + bx + c.

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Answer:y = -2x + 5

Step-by-step explanation: Slope intercept form is given by the equation y = mx+b where m is the slope and b is the y intercept

1. The slope or m would be -2 because the slope of the live given is -2. We can tell since we can do rise/run or Δy/Δx.  We can take two points on the line and use Δy/Δx

Lets use:

(0,4) and (2,0)

Then plug it in so:

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{4-0}{0-2}[/tex]

m = -2

Now we just need b which is fortunatly given to us since b is when x is equal to 0 and it saids in the question "passes through the point (0,5)" so since its (x,y) and x is 0, b is 5.

Finally, after substitution, we get:

y = -2x + 5

Based on the information, it can be inferred that Kayla would spend $51 buying a pair of jeans and a skirt.

To find the final value that Kayla paid we must carry out the following procedure:

We must find the equivalent of 25% of the total value of your purchase. Then we must add the value of both products and find the discount.

Based on the above, Kayla would pay $51 for both products and the discount would be $17.

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According to the quadratic equation the solution of k is 48 ± 8√26.

In math the term called quadratic equation is known as the polynomial equation whose highest degree is two

As we all know that the value of the quadratic equation is written as,

=> (k - 4)x² - 3kx - 4(k -2) = 0.

Now we have identified that the given equation is in the form of ax² + bx + c = 0.

Here we have also identified the value of a = k - 4, b = -3k and c = 4(k-2)

And then we have to use the quadratic formula to identify the value of k,

Here it can be written as.

=> (-3k)² - (4 x (k - 4) x 4(k-2))

When we expand the term then we get,

=> 9k² - (16k² - 32k - 64k + 128)

When we simplify this one then  we get

=> -5k² + 96k - 128 = 0

Here we have to factorize the expression then we get the value of k as 48 ± 8√26.

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Answer: 10 units

Step-by-step explanation:

    We can use the following formula to determine the diameter of this cone. V is equal to volume, r is equal to radius (half of the diameter), and h is equal to height.

          [tex]\displaystyle \boxed{r=\sqrt{3\frac{V}{\pi h}} }[/tex]

Given:

[tex]\displaystyle r=\sqrt{3\frac{V}{\pi h}}[/tex]

Substitute known values:

[tex]\displaystyle r=\sqrt{3\frac{100\pi}{\pi (12)}}[/tex]

Divide:

➜ [tex]\frac{\pi}{\pi}=1[/tex], so we are left with 100 divided by 12

[tex]\displaystyle r=\sqrt{3(\frac{25}{3} )}}[/tex]

Multiply:

➜ When multiplying, we can think of it as [tex]\frac{3}{1} *\frac{25}{3}[/tex].   [tex]\frac{3}{3} =1[/tex], so we are left with 25.

[tex]\displaystyle r=\sqrt{25}[/tex]

Square root:

r = 5, r = -5

   Since it's a measure of a shape, it cannot be negative. This means the radius is equal to 5. Now, we will find the diameter.

5 units * 2 = 10 units

Answer: Thus the mass of copper in solid form is m = 9860 kg / m^3.

Step-by-step explanation: solve it step by step

It will take 8.8 years for the initial deposit to reach $7,500.

The formula to calculate the number of years it takes for an initial deposit to reach a certain amount with compounding interest is A = P(1+r/n)^nt, where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this example, P = $6,000, r = 3, n = 12 (monthly compounding of interest) and A = $7,500. We can solve for t, the number of years, by rearranging the equation to t = log(A/P)/log(1+r/n). When we plug in the numbers, we find that it will take 8.8 years for the initial deposit to reach $7,500.

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Answer:

x = 3.  y = 11

Step-by-step explanation:

The two equations are two simultaneous equations, which can be solved by substitution, elimination or graphical method.

Elimination method:

The coefficients of 'x’ or ‘y’ need to be the same with opposite signs. The coefficients of ‘y’ will be focused:

                  (17x - y = 40) Multiplied by 4

                  (2x + 4y = 50) Multiplied by 1

                  68x - 4y = 160

                   2x + 4y = 50

In the net total, the ‘y’ terms will cancel each other out:

                 70x = 210

                     x = [tex]\frac{210}{70}[/tex]

                     x = 3

The calculated value of x is substituted in any of the equations to determine the value of y:

                 17(3) - y = 40

                    51  - y = 40

                   51 - y - 40 = 0

                   51 - 40 - y = 0

                   11 - y = 0

                   y = 11

The answer of the  given question based on cryptarithm the answer is ,

958870 - 214803 = 744067, so the solution is correct.

Alphametics, also known as verbal arithmetic or cryptarithm, is a type of mathematical puzzle where letters or symbols are used to represent digits or numbers, and the puzzle solver must determine the correct digit or number to replace each letter or symbol in order to solve the puzzle.

The objective of an alphametic puzzle is to find a unique solution, where each letter or symbol represents a different digit or number, and the arithmetic equation is correct. In some alphametic puzzles, there may be additional constraints, such as leading zeros not being allowed, or certain digits being constrained to specific values.

One possible solution to this cryptarithm is:

 9 5 8 8 7 0

- 2 1 4 8 0 3

_________

7 4 4 0 6 7

In this solution, P=9, E=5, R=8, S=7, A=0, L=4, and Y=6.

To check:

PEPPER = 958870

SALT = 214803

YUMMY = 744067

And 958870 - 214803 = 744067, so the solution is correct.

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The number of round beads in the glitz jewelry kit are 25

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Let x be the number of round beads in the glitz jewelry kit. Then the equation is written as,

6x + 100 = 250

Simplify the equation, then the value of 'x' is given as,

6x + 100 = 250

6x  = 250 - 100

6x = 150

x = 150/6

x = 25

The number of round beads there in each color will be 25.

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The statement A is correct option.

The vertex of a quadratic equation is the minimum or maximum point of the equation.

Given that, the quadratic function f(x) has a vertex at (1, 6) and opens downward and g(x) = (x - 7)² + 1,

The vertex of f(x) is at (1, 6), we know that a vertical line passing through the vertex is called the axis of symmetry for the parabola.

That mean, axis of symmetry will pass through (1, 6)

Therefore, the axis of symmetry for f(x) is x = 1

And, g(x) = (x - 7)² + 1

= x²+49-14x+1

= x²-14x+50

Vertex = -b / 2a

here, b = -14 and a = 1

Vertex (h, k) = 14 / 2 = 7

To find k, put x = 7 in the equation,

(7-7)²+1 = 1

Therefore, point of the vertex = (7, 1)

That mean axis of the symmetry will pass through (7, 1)

Therefore, axis of the symmetry for g(x) = 7

Hence, the statement A is correct option.

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The value of x in the continued proportion is 6

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

3,x,12 are in continued proportion

This means that

x/3 = 12/x

So, we have

x^2 = 36

Take the square roots

x = 6

Hence, the solution is 6

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Answer: I believe it means that there is no solution

Step-by-step explanation: I believe this because we are given: 5 = 0. In linear graphs when lines are equal to 0 there is no equation or solution

The slope, y-intercept, and equation of each of the lines are:

a. m = 2, b = -1.

y = 2x - 1

b. m = -1; b = 2.

y = -x + 2

c. m = -2/3; b = 1

y = -2/3x + 1

d. m = 1/2; b = -2.

y = 1/2x - 2

The slope-intercept form is y = mx + b, where b equals the y-intercept and m is the slope.

a. Slope (m) = change in y/change in x = (3 -(-1))/(2 - 0) = 4/2 = 2

y-intercept (b) = -1.

The equation is: y = 2x - 1

b. Slope (m) = change in y/change in x = (2 -(-2))/(0 - 4) = 4/-4 = -1

y-intercept (b) = 2.

The equation is: y = -x + 2

c. Slope (m) = change in y/change in x = (3 -(-1))/(-3 - 3) = 4/-6 = -2/3

Substitute m = -2/3 and (x, y) = (3, -1) into y = mx + b to find the y-intercept (b):

-1 = -2/3(3) + b

-1 = -2 + b

-1 + 2 = b

1 = b

b = 1

The equation is: y = -2/3x + 1

d. Slope (m) = change in y/change in x = (0 -(-1))/(4 - 2) = 1/2 = 1/2

y-intercept (b) = -2.

The equation is: y = 1/2x - 2

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The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists [tex]$\frac{3}{6}=\frac{1}{2}$[/tex]

The probability that this happens with both dice exists [tex]$\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$[/tex]

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

[tex]$\frac{9}{36}=\frac{1}{4}$$[/tex]

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This statement is true. If a system of linear equations has two different solutions, it must have infinitely many solutions.

Linear equations are equations that involve only linear functions, or functions of the form f(x) = mx + b. These equations can be used to describe a variety of real-world phenomena, such as the motion of a particle along a straight line. Linear equations are generally solved by using the linear equation solving methods, such as substitution, elimination, and graphing. The solutions to a linear equation are the values of the variables that make the equation true.

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Answer:

The number of those line segments which have endpoints of different colors is 47.

By providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship, we have

(i) [tex]3^{n/2}[/tex] = O(2^n)

(ii) [tex]8^{\log n}[/tex] = θ([tex]n^2(\log n)^4[/tex] ≤ 3n^3)

(iii) √n + (log n)^5 = O([tex](2)^{1/2\times\log n}[/tex])

We have to compare the following function pairs by providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship

i) The first function is [tex]3^{n/2}[/tex] vs. 2^n

We can write  [tex]3^{n/2}[/tex] as

[tex]3^{n/2}[/tex] = [tex](\sqrt{3})^n[/tex]

[tex]3^{n/2}[/tex] = (1.732)^n

Clearly, we get for c = 1 and n ≥ 0, then

0 ≤ 1.732n ≤ 2n

Hence, [tex]3^{n/2}[/tex] = O(2^n)

ii) The second function is [tex]8^{\log n}[/tex] vs. n^2(log n)^4 + 2n^3

We can write it as

[tex]8^{\log n}[/tex] = [tex]n^{\log 8}[/tex]

[tex]8^{\log n}[/tex] = [tex]n^{\log 2^3}[/tex]

[tex]8^{\log n}[/tex] = n^3

For n ≥ 0, c(1) = 1 and c(2) = 3, we have

0 ≤ n^3 ≤ [tex]n^2(\log n)^4[/tex] ≤ 3n^3

Hence, [tex]8^{\log n}[/tex] = θ([tex]n^2(\log n)^4[/tex] ≤ 3n^3)

iii) The third function is  [tex](\sqrt{2})^{\log n}[/tex] vs. √n + (log n)^5

We can write [tex](\sqrt{2})^{\log n}[/tex] as

[tex](\sqrt{2})^{\log n}[/tex] =  [tex](2)^{1/2\times\log n}[/tex]

For c = 2 and n ≥ 2, we have

0 ≤ √n + (log n)^5 ≤ [tex](2)^{1/2\times\log n}[/tex]

Hence, √n + (log n)^5 = O([tex](2)^{1/2\times\log n}[/tex])

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The complete question is:

Show your complete work when comparing the following function pairs. provide the c and k values in the formal definition when asserting a big O, Ω or θ relationship(e.g. f(n) is O(g(n)) if there exists C>0 and k≥0 such that f(n)≤Cg(n) for all n≥k).

(i) [tex]3^{n/2}[/tex] vs. 2^n

(ii) [tex]8^{\log n}[/tex] vs. n^2(log n)^4 + 2n^3

(iii) [tex](\sqrt{2})^{\log n}[/tex] vs. √n + (log n)^5

Answer: h= -4

Step-by-step explanation:

To solve the equation 2(h+3.5)=-1, we can use the following steps:

Distribute the 2 on the left side of the equation: 2h + 7 = -1

Subtract 7 from both sides of the equation: 2h = -8

Divide both sides of the equation by 2: h = -4

Therefore, the solution to the equation is h = -4

Point U would be (1, 1)

The x- intercept of  y = x²-4x-2 is 4.44949 and −0.44949.

The line's point of intersection with the coordinate axes is known as an intercept. The y coordinate of the intersection point is zero if the line contacts the X axis, and the intercept is known as the x intercept.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given:

To find the x-intercepts of the function, y = x²-4x-2, we need to make the y-value of the function equal to zero,

So, x²-4x-2 = 0

Now, solving the above Quadratic Equation

x²-4x-2 = 0

D = √(-4)² - 4(1)(-2)

D = √16 + 8

D = √24

D = 2√6

So, x= 4 ±  2√6/ 2

x = 4 +  2√6/2  or x = 4-  2√6/2

x = 2 + √6 or x = 2- √6

x = 4.44949 or x = −0.44949

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Answer:

54 square feet

Step-by-step explanation:

First get the area of both rectangles.

The bigger one is 8 by 9

8 times 9 is 72

the smaller one is 3 times 6 which is 18

Now you subtract both of them

72-18 = 54

Answer:

9

Step-by-step explanation:

g(h(2))= 2(x3-x2)+1 = 2(2^3-2^2)+1 = 2(8-4)+1

=2*4+1 = 9