Suppose z varies inversely with t and that z = 10 when t = 12. What is the value of z when t = 5?

The a whole number or in simplest form is 2.2.

We are given that;

Right rectangle length=33 and height=11, left triangle length=11 height=5

Now,

The length of the right rectangle is 33 and the length of the left rectangle is 11. To find the scale factor, we divide the length of the right rectangle by the length of the left rectangle:

33 / 11 = 3

This means that the right rectangle is 3 times as long as the left rectangle. The scale factor is 3.

We can check our answer by comparing the heights:

The height of the right rectangle is 11 and the height of the left rectangle is 5. To find the scale factor, we divide the height of the right rectangle by the height of the left rectangle:

11 / 5 = 2.2

Therefore, by fraction the answer will be 2.2.

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The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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The value of the variable x is 51.340 degrees

Note that their are six different trigonometric identities in mathematics.

These identities are;

Also, these identities have their different ratios, they are;

sin θ= opposite/hypotenuse

tan θ = opposite/adjacent

cos θ = adjacent/hypotenuse

From the information given, we have that;

Opposite = 10cm

Adjacent = 8cm

Substitute the values

tan x = 10/8

Divide the value, we have;

tan x = 1.25

Find the tangent inverse, we get;

x = 51. 340 degrees

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The value of the index form is x¹³/11

Index forms are simply described as mathematical forms or expressions that are used to represent numbers or variables that are too large or too small to be written conveniently.

Some rules of index forms are;

From the information given, we have that;

x⁹/11 × x⁴/11

Since they are of the same bases, add the exponent values

x¹³/11

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Answer:

22 m^2

Step-by-step explanation:

multiply the sides

Based on the information, the regular polygon has 35 sides.

In order to determine the number of sides that a regular polygon has if the sum of the interior angles is given, you can use the formula:

sum of interior angles = (n - 2) x 180°

solve for n, you can rearrange the formula as:

n = (sum of interior angles ÷ 180°) + 2

Then, plug in the given sum of interior angles and solve for n.

b. Using the formula above, we can find the number of sides of the regular polygon with a sum of interior angles of 6,300°:

n = (6300° ÷ 180°) + 2

n = 35

The regular polygon has 35 sides.

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The desired outcomes use in finding the probability of blue pens is 7.

Given that a bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.

We need to find desired outcomes for him to use in finding the probability of blue pens,

We know that the desired outcomes or the favorable outcomes are the same thing which is the number of the element of whose probability is to be find,

Here we are to find the probability of getting a blue pen and the number of blues pen is 7.

Hence the desired outcomes use in finding the probability of blue pens is 7.

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Answer:

Let's start by using the formula for the perimeter of a rectangle, which is:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width.

We're given that the perimeter is 78 meters, so we can write:

78 = 2L + 2W

Simplifying this equation, we get:

39 = L + W

We're also given that the length is 6 meters less than four times the width, so we can write:

L = 4W - 6

Now we can substitute this expression for L into the equation we got earlier:

39 = (4W - 6) + W

Simplifying this equation, we get:

39 = 5W - 6

Adding 6 to both sides, we get:

45 = 5W

Dividing both sides by 5, we get:

W = 9

So the width of the rectangle is 9 meters. We can use this value to find the length:

L = 4W - 6 = 4(9) - 6 = 30

So the length of the rectangle is 30 meters.

The type of graph would have the title, "Monthly Company Profit for the Year?" is line graph (option a).

Using a line graph to display monthly company profits allows for the visualization of the overall trend and any fluctuations or changes in the profits over the year. It also allows for easy comparison of the profits from one month to another, as well as identifying which months were particularly profitable or unprofitable.

In mathematical terms, a line graph can be defined as a graph in which the data points are plotted as individual points, and a line is drawn to connect the points.

The line represents a mathematical function that can be used to model the relationship between the variables being plotted. In the case of the monthly company profits, the function would model the relationship between time and profit.

Hence the correct option (a).

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The statement that is true for the Cartesian coordinate system is A. the values below the X-axis are negative values of x.

The Cartesian coordinate system, also called rectangular coordinate system, helps plot coordinates in a two-dimensional plane. This model contains two axes -- the x-axis (horizontal) and y-axis (vertical) -- that meet at the origin. The values beneath the x-axis represent negative y-values, not x-values as some assume.

Likewise, above the x-axis represents positive y-values, not x-values. Meanwhile, points along the x-axis aren't considered either positive or negative but rather labeled based on their distance away from the origin as per this structure's guidelines.

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The solution is : the value of y is 7.

Here, we have,

The perimeter of a rectangle is found by

P = 2 (l+w)

P = 2( 3y+3+2y)

Combine like terms

P = 2(5y+3)

We know the perimeter is 76

76 = 2(5y+3)

Divide each side by 2

76/2 = 2/2(5y+3)

38 = 5y+3

Subtract 3 from each side

38-3 = 5y+3-3

35 = 5y

Divide each side by 5

35/5 = 5y/5

7 =y

We want the length of AD = BC = 2y

AD = 2y=2*y = 14

Hence, The solution is : the value of y is 7.

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Answer:

Step-by-step explanation:

Given expression is 7 1/3t-(10 2/3t-6)

Now, convert the proper fraction present in the question to improper fractions.

proper fractions are 7 1/3 and 10 2/3

so, 7 1/3 =(7*3+1)/3 = 22/3

     10 2/3 = (10*3+2)/3=32/3

= >22t/3 - (32t/3 -6)

= >22t/3 - 32t/3 +6

= >6 - 10t/3

This is the final solution.

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The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

We can derive an inequality from the problem statement which is:

8X + 12Y ≥ 1000

This inequality represents the amount of money the basketball team needs to raise by selling donuts.

X is the number of half dozen boxes sold

Y is the number of full dozen boxes sold.

To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:

If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:

8(50) + 12(50) = $400 + $600 = $1000

So this is a valid solution that meets the fundraising goal.

If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:

8(100) + 12(0) = $800

This is not enough to meet the fundraising goal, so it is not a valid solution.

If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:

8(0) + 12(100) = $1200

This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.

Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

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David is studying Giraffe.

The correct option is (d)

Here, The table of the given information is:

Animal                      speed               Type                Habitat

Elephant                   25 mph            Mammal           Grassland

Sailfish                      68 mph            Fish                   Oceans

Giraffe                       32 mph            Mammal           Grassland

Dolphin                     30 mph            Mammal           Oceans

And, The options are given :

David is studying a mammal, but Ping is not.

Therefore, Ping is studying Sailfish.

The animal that Mandy is studying can be found in the ocean.

Therefore, Mandy is studying Dolphin.

The animal that Alan is studying is slower than the animal that David is studying,

Therefore, Alan is studying Elephant which is slower than Giraffe.

Finally David is studying Giraffe.

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I think it is C.

C. 2 tons = 64, 000 ounces

Answer:

0.75

Step-by-step explanation:

P(A) = 9+9 = 18

P(B) = 9+9 = 18

P(A and B) = 9

P ( A or B) = 18+18-9 = 27

Probability = ans / total = 27/36 = 0.75

The probability that either event will occur is given as follows:

P(A or B) = 0.75.

We have,

The figure about the possible outcomes are shown in image.

Now, The formula used to calculate the probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

The total number of events from the Venn's diagram is given as follows:

4 x 9 = 36.

Hence the probability of each outcome is given as follows:

P(A) = (9 + 9)/36 = 0.5.

P(B) = (9 + 9)/36 = 0.5.

P(A and B) = 9/36 = 0.25.

Hence the or probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

P(A or B) = 0.5 + 0.5 - 0.25

P(A or B) = 0.75.

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Answer:

line RQ

Step-by-step explanation:

The points on a line can be flipped when naming. For example, line AB is the same as line BA.

As we have shown that matrix multiplication is associative.

Let us start by computing the products (AB) and (BC) separately. To multiply matrix A by matrix B, we need to take the dot product of each row of A with each column of B.

Simplifying the above expression, we get:

A*B = [11 -10 39] *  [21 28 13]

Similarly, to multiply matrix B by matrix C, we need to take the dot product of each row of B with each column of C. Thus, the resulting matrix (B*C) will have the same number of rows as B and the same number of columns as C. Using the given matrices B and C, we have:

B*C = [1 -2 5] * [1    -2      10]

Simplifying the above expression, we get:

B*C = [39 18]

Thus, the resulting matrix (A(BC)) will have the same number of rows as A and the same number of columns as (BC). Using the given matrices A, B, and C, we have:

A*(B*C) = [7 1] * [39  18]

Simplifying the above expression, we get:

A*(B*C) = [327 489]

Now, let us compute the product ((AB)C) by multiplying the matrix (AB) with matrix C. To do this, we need to take the dot product of each row of (AB) with the only column of C. Thus, the resulting matrix ((A*B)C) will have the same number of rows as (AB) and the same number of columns as C. Using the given matrices A, B, and C, we have:

(A*B)*C = [11 -10 39] * [1      -2       10]

Simplifying the above expression, we get:

(A*B)*C = [327     489]

As we can see from the above calculations, both the products (A*(BC)) and ((AB)*C) have the same result, which is [327 489]. Therefore, we can conclude that matrix multiplication is associative.

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Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer: 2.1468 times 10^15

Step-by-step explanation: you times them together

The given point (8, -15) is located in the third quadrant of the coordinate plane.

In this quadrant, the x-coordinate is negative and the y-coordinate is also negative.

Let us consider some common functions to determine which of them are positive in the third quadrant:

A linear function is of the form f(x) = mx + b,

where m is the slope and b is the y-intercept. In the third quadrant, both the slope and y-intercept are negative.

Therefore, if m > 0, then f(x) is negative for all x-values in the third quadrant.

If m < 0, then f(x) is positive for all x-values in the third quadrant.

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The solution is : equation for the perpendicular bisector of the line segment is:  7x -2y = 6

Here, we have,

The perpendicular bisector has a slope that is the opposite of the reciprocal of the slope of the segment between the two points. It must go through the midpoint of the segment.

The latter can be found by averaging the coordinates of the end points:

 ((-5, 6) +(9, 2))/2 = ((-5+9)/2, (6+2)/2) = (2, 4)

The difference in endpoint coordinates is ...

 (Δx, Δy) = (9-(-5), 2-6) = (14, -4)

For our purpose, we're only interested in the ratio of these values, so we can divide both by the common factor of 2:

 (Δx, Δy) = (7, -2)

A line perpendicular to this segment through the point (h, k) can be written as ...

 Δx·x +Δy·y = Δx·h +Δy·k

 7x -2y = 7(2) -2(4)

 7x -2y = 6 . . . . . . . standard form equation for the perpendicular bisector

Hence, The solution is : equation for the perpendicular bisector of the line segment is:  7x -2y = 6

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There are 6 whole weeks will it take her to save $160.

We have to given that;

Amy is going on a road trip with her friends and needs to save $160.

And, she starts saving 18% of her weekly earnings at the pool,

Now, Let number of weeks it take her to save $160 is, x

Hence, We get;

160 = 160 x 0.18 x t

t = 1/0.18

t = 5.55 weeks

Thus, There are 6 whole weeks will it take her to save $160.

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The inequality that can be used to find the number of sales she needs to make is D. 100 + 15x ≥ 500.

In this scenario, Aaliyah wants to earn at least $500. The fixed amount she earns is $100, and she earns $15 for each sale.

Therefore, the total amount she earns can be represented as 100 + 15x, where x is the number of sales she makes. To ensure that she earns at least $500, we can set up the inequality 100 + 15 x ≥ 500.

With this inequality, we can see that the sum of the $ 100 base salary and the $ 15 per sale would add up to a sum that is either $ 500 or above.

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Answer:

The volume is 200.7 cm^3

Step-by-step explanation:

The volume of a cylinder is:

Vol = pi•r^2•h

The radius and height were given, so fill them in.

V = pi • (4.4)^2 • 3.3

V = 200.710071

This is the answer you get if you use the pi key on the calculator.

Round to the nearest tenth.

V = 200.7

The volume is 200.7cm^3.

***(If your teacher/class/text/program says to use 3.14 for pi, the answer will come out as 200.6)

The required surface area of the given rectangular prism is 202 square yd.

Here, we have,

Given that,

the surface area of a rectangular prism with a base length of 9 yd, a base width of 5 yd, and a height of 4 yd is to be determined.

We have,

Surface area is defined as the measure of a region or surface is called as surface area.

Here,

The surface area of the rectangular prism is given as,

S = 2(lw + lh + wh)

S = 2 [9×5 + 5×4 + 4×9]

S = 202 square yd.

Thus, the required surface area of the given rectangular prism is 202 square yd.

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As we have proved that if p ≡ 1 (mod 4), then -r is also a primitive root of p.

Since r is a primitive root of p, we know that every non-zero integer modulo p can be written as a power of r. That is, for any integer a with gcd(a, p) = 1, there exists an integer k such that a ≡ rˣ (mod p). This follows from the fact that the order of the element r modulo p is φ(p) = p-1, where φ denotes the Euler totient function.

Now, let us consider the case where p ≡ 1 (mod 4). This means that there exists an integer x such that p = 4x + 1. We want to show that -r is also a primitive root of p.

To do this, we first observe that (-1)² ≡ 1 (mod p) since p is an odd prime. Therefore, (-1)^(4x) ≡ 1 (mod p), which implies that (-1)²ˣ ≡ 1 (mod p).

Now, if we can show that (-1)ˣ = -1, then we will have (-1)²ˣ = (-1)ˣ*(-1)ˣ = (-1)*(-1) = 1 (mod p), which will allow us to prove that -r is also a primitive root of p.

To see that (-1)ˣ = -1, we use the fact that p ≡ 1 (mod 4) and the properties of quadratic residues. Specifically, we know that -1 is a quadratic non-residue modulo p, since if -1 ≡ a² (mod p) for some integer a, then we would have

=> [tex](-1)^{((p-1)/2) }[/tex] ≡ [tex]a^{(p-1) }[/tex]≡ 1 (mod p),

which contradicts the fact that

=> [tex](-1)^{((p-1)/2) }[/tex]= -1.

Therefore, there exists an integer b such that b² ≡ -1 (mod p).

Now, consider the product brˣ. We claim that brˣ is a primitive root of p. To see this, note that for any integer a with gcd(a, p) = 1, we can write a ≡ rˣ (mod p) for some integer k. Then, we have:

(a*brˣ)² = a² * b² * r²ˣ ≡ r²ˣ * (-1) ≡ -r²ˣ (mod p)

Since r is a primitive root of p, we know that rˣ and r²ˣ cover all the non-zero residue classes modulo p. Therefore, we can choose k such that r²ˣ ≡ -1 (mod p), which implies that (a*brˣ)² ≡ -1 (mod p).

Since a was arbitrary, this shows that brˣ is a quadratic non-residue modulo p, and therefore a primitive root of p.

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