Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial:

0.01b^2+ ∗ +100c^2

The probability of picking a 7 and then picking a 7 is 8.33%.

Since we are not replacing the first card before drawing the second one, the probability of drawing a 7 on the first card is 1/4. After drawing the first card, there are three remaining cards, and only one of them is a 7. Therefore, the probability of drawing a 7 on the second card given that the first card was a 7 is 1/3.

Using the multiplication rule of probability, the probability of drawing a 7 on the first card and then drawing a 7 on the second card without replacement is

P(7 on the first card) x P(7 on the second card | 7 on the first card) = (1/4) x (1/3) = 1/12

P(7 on the first card and then a 7 on the second card) = 1/12 x 100% = 8.33%

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The average change in field position on each run was a loss of 7/4 yards.

A mixed number in mathematics is a number that combines a whole number and a fraction. The entire number and the fraction are often separated by a space or a plus sign when writing mixed numbers. As an illustration, the mixed number 2 1/3 stands for the sum of 2 and 1/3. By dividing the entire number by the fraction's denominator and adding the numerator, mixed numbers can be transformed into improper fractions. For instance, we would multiply 2 by 3 and add 1 to get 7, which is an incorrect fraction of 2 1/3. In order to obtain 7/3, we would then write the fraction using the same denominator as the original fraction.

The total change in position for a total loss of 15/3/4 yards is:

Total change in field position = - (15 + 3/4) yards

Given the, number of runs = 9

Thus:

Average change in field position = Total change in field position / Number of runs

Average change in field position = (- 15 - 3/4) yards / 9

Average change in field position = (- 63/4) yards / 9

Average change in field position = - 7/4 yards

Hence, the average change in field position on each run was a loss of 7/4 yards.

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Thus, the one notebook' price n = $6 and the price of one pencil is p = $2.4.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. Once an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

Let cost of a notebook to be 'n' dollars

Let the cost of a pencil to be 'p' dollars,

Then, the system of equations are-

3n + 5p = 30   ..eq 1

n + 10p = 30  ....eq2

multiply eq 2 with 3

3n + 30p = 90 ...eq 3

Subtract eq 3 from eq 1

3n + 5p - 3n - 30p = 30 - 90

25p = 60

p = 2.4

n + 10(2.4) = 30

n = 30 - 24

n = 6

Thus, the price of one notebook n = $6 and the price of one pencil is p = $2.4.

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The probability of being in the first or second position in a heat with 10 cars can be calculated by finding the total number of ways that the cars can be arranged in the heat and then dividing by the number of ways that result in being in the first or second position.

There are 10 cars in the heat, so there are 10 possible positions for the first car, and once that car has been assigned a position, there are 9 possible positions remaining for the second car, and so on. Therefore, the total number of ways that the cars can be arranged is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This is equivalent to 10! (read as "10 factorial"), which is the product of all the positive integers from 1 to 10.

To be in the first or second position, there are 2 possible positions out of the 10 total positions in the heat. So, the number of ways to be in the first or second position is:

2 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

which is equivalent to 2 x 9!, since we only need to consider the arrangements of the remaining 9 cars after we have assigned ourselves to one of the first two positions.

Therefore, the probability of being in the first or second position is:

(2 x 9!) / 10!

Simplifying this expression, we get:

(2 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

which simplifies further to:

2 / 10

or:

1 / 5

So, the probability of being in the first or second position is 1/5 or 0.2, which means that there is a 20% chance of being in one of those positions in any given heat.

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations can be used to model a wide range of real-world situations, and they are an essential tool in many fields of study, including physics, engineering, and economics.

To solve for y, we need to isolate y on one side of the equation. We can do this by first distributing the 3 on the right-hand side:

24 = 3y + 18

Next, we can isolate 3y by subtracting 18 from both sides:

24 - 18 = 3y

6 = 3y

Finally, we can solve for y by dividing both sides by 3:

y = 2

Therefore, the solution to the equation 24 = 3(y + 6) is y = 2.

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Thus, the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².

A rectangular prism is one of the more usual shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. An other faces also were rectangles because the bases are rectangles. These are a rectangular prism's characteristics:

Given dimensions for the rectangular prism :

Then ,

surface area of the prism S = 2(lw + wh + hl)

Put the values:

S = 2(11.75*5.75 + 5.75*4 + 4*11.75)

S = 2*137.5625

S = 275.125

S = 275 ¹/₈ cm²

Thus, the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².

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Answer:

x=4

Step-by-step explanation:

We can solve for x by using the definition of logarithms.

log₃(x+5) = 2 can be rewritten in exponential form as 3² = x + 5.

Simplifying 3² gives 9, so we have:

x + 5 = 9

Subtracting 5 from both sides, we get:

x = 4

Therefore, the equivalent equation is x = 4.

Answer:20

Step-by-step explanation:

Answer:

[tex]-x^{5} -5x+6[/tex]

Step-by-step explanation:

Answer:

117in

Step-by-step explanation: 9in x 13in=117in

So, Edward needs to use a round cast iron pan with a radius of 177 inches to have the same area as the rectangular pan. correct answer is (d).

To find the area of a circle, you need to know its radius (the distance from the center of the circle to any point on its perimeter). Once you know the radius, you can use the following formula:

[tex]Area = \pi * radius^2[/tex]

where π (pi) is a mathematical constant approximately equal to 3.14159.

So, to find the area of a circle, follow these steps:

Measure the radius of the circle.

Square the radius (multiply it by itself).

Multiply the squared radius by π.

Round your answer to the desired number of decimal places (usually 1 or 2).

The area of a 9-in. by 13-in. rectangular pan is:

Area = length x width = 9 in. x 13 in. = 117 in.²

So, the area of the rectangular pan is 117 in.².

To use a round cast iron pan with the same area, Edward needs to find the radius of the circle with an area of 117 in.²:

Area of a circle = πr²

[tex]= \pi r^2[/tex]

[tex]= 117 in.^2 /[/tex]

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the complete question: Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise.

her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.

Edward would like to use a round cast iron pan like his grandmother does.

What is the area of a 9-in. by 13-in. pan?

[tex](a) 22in^{2} \\(b)44in^{2} \\(c)108in^{2} \\(d)117in^{2}[/tex]

The  five different math vocabulary that can be used to describe each given expression 6(t+2)-8

Expression: A combination of numbers, variables, and operators that can be evaluated or simplified.

Coefficient: A number that is multiplied by a variable.

Distributive Property: The property that allows you to multiply a factor by each term inside a set of parentheses.

Simplify: To reduce an expression to its simplest form.

Linear: An expression that has no exponents or other operations besides addition, subtraction, and multiplication by a constant.

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Answer:

[tex]x = 1 \frac{49}{57} [/tex]

Step-by-step explanation:

[tex]6.75x + \frac{3}{8} x = 13 \frac{1}{4} [/tex]

Multiply the whole equation by 8, to eliminate the fractions:

[tex]54x + 3x = 106[/tex]

[tex]57x = 106[/tex]

Divide both parts of the equation by 57:

[tex]x = \frac{106}{57} = 1 \frac{49}{57} [/tex]

1. The two triangles are congruent, ASA criteria. angle H ≅ angle M, HY ≅ MN and EY ≅ AN using CPCT. 2. The two triangles are congruent, ASA criteria. AT ≅ AP, by CPCT. Angle T ≅ angle P. CT ≅ RP, by CPCT.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

1. For the given triangle HEY and triangle MAN we see that,

angle E ≅ angle A

angle Y ≅ angle N

and HE ≅ AM

Thus, the two triangles are congruent using the ASA criteria.

Also angle H ≅ angle M (CPCT)

HY ≅ MN

EY ≅ AN using CPCT.

2. For triangle CAT and PAR we have:

angle A ≅ angle A (vertically opposite angles)

Angle C ≅ angle R

AC ≅ AR

Thus, the two triangles are congruent using the ASA criteria.

Also, AT ≅ AP, by CPCT

Angle T ≅ angle P, by CPCT

CT ≅ RP, by CPCT.

3. For the triangles ACL and triangle ARS:

AC ≅ AR and angle 1 ≅ angle 2 (Given)

Also, angle A = angle A (Vertically opposite angle)

Thus, the two triangles are congruent using ASA criteria.

Now, angle 3 ≅ angle 4 using CPCT.

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For given Sample Space, the probability that both responses are correct is 12.5%.

A sample space is the collection of all potential results of an experiment or random process in probability theory. It is a key idea that allows us to define and assess event probability.

Consider the following experiment: rolling a six-sided die. This experiment's sample space is the set of all potential results of rolling the dice, which are 1, 2, 3, 4, 5, 6. Each member of the sample space indicates a possible experiment outcome.

Now,

The probability of answering the true/false question correctly by random guess is 1/2, since there are two possible choices.

The probability of answering the multiple-choice question correctly by random guess is 1/4, since there are four possible choices.

The probability of both events happening together = product of individual probabilities:

P(correct on both) = P(true/false correct) × P(multiple-choice correct)

= (1/2) × (1/4)

= 1/8

= 0.125

Therefore, the probability that both responses are correct is 0.125 or 12.5%.

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Answer: While I cannot give an exact answer without additional context, the answer should have a slope of 12, and should look like the image below.

Answer:

12

Step-by-step explanation:

Answer:

B?

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 15 out of 50 students are twelve years old, we can estimate the proportion of twelve-year-olds in the whole school as follows:

Proportion of twelve-year-olds = 15/50

Simplifying this fraction by dividing both numerator and denominator by 5, we get:

Proportion of twelve-year-olds = 3/10

Similarly, if 20 out of 50 students are thirteen years old, we can estimate the proportion of thirteen-year-olds in the whole school as:

Proportion of thirteen-year-olds = 20/50

Simplifying this fraction by dividing both numerator and denominator by 10, we get:

Proportion of thirteen-year-olds = 2/5

Finally, if 15 out of 50 students are fourteen years old, we can estimate the proportion of fourteen-year-olds in the whole school as:

Proportion of fourteen-year-olds = 15/50

Simplifying this fraction by dividing both numerator and denominator by 5, we get:

Proportion of fourteen-year-olds = 3/10

Therefore, the best estimate of the proportion of students who are twelve, thirteen, and fourteen years old in the school, respectively, is:

3/10 are twelve years old

2/5 are thirteen years old

3/10 are fourteen years old

Answer:

(G) -1

Step-by-step explanation:

Let the integer be [tex]x[/tex].

Then, it folloes that [tex]-x=x^2[/tex].

Because [tex]x \neq 0[/tex], dividing both sides by [tex]x>/tex] yields [tex]x=-1[/tex].

Answer:
x > 53

30 + x > 83

Subtract 30 from both sides:

x > 53

Therefore, the solution is:

x > 53

Answer:

y = 3 cot (1x)?

Step-by-step explanation:

Triangle ABC's longest side is found as 4 units. Thus, Triangle DEF has a 100-times larger area than triangle ABC.

A ratio is a tool being used compare the sizes of two or more quantities with relation to one another in mathematics. By making amounts easier to understand, ratios enable us to evaluate and express quantities.

Given that both triangles remain similar, triangle DEF is 10 times larger than triangle ABC according to the ratio 1:10.

Thus, Triangle DEF has a 100-times larger area than triangle ABC.

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Answer:

The factor by which the amount of drug in the body is multiplied by each passing hour can be found using the formula:

b = 1/2^(t/h)

where:

t = time elapsed (in hours)

h = half-life of the drug

In this case, the half-life of the drug is 5 hours, so we have:

h = 5 hours

For each passing hour, the time elapsed increases by 1 hour, so we can calculate the factor b after 1 hour as:

b = 1/2^1/5

b = 0.63

This means that after 1 hour, the amount of drug in the body is multiplied by 0.63. After 2 hours, it is multiplied by 0.63 again, and so on.

Step-by-step explanation:On a coordinate plane you move 9 to the right and 2 up

1. The diagonal of the base of the box is shorter than the length of the wind chime. 2. The interior diagonal of the box shorter than the length of the wind chime. 3.  The wind chime will not fit in the box.

A diagonal is a line segment that connects two polygonal corners (vertexes), although it is not an edge (side). In other words, it connects any two polygonal vertices that are not neighboring. So, when we directly link any two vertices that are not connected by any sides, we may draw the diagonals in a polygon. A diagonal is a line that runs straight across the vertices of a polygon and joins its opposing corners. In other terms, a line segment connecting any two non-adjacent corners is a polygon's diagonal. Depending on how many sides a polygon has, distinct polygons may have a variable number of diagonals.

Given that the length of the wind chime is 16 inches thus,

1.  diagonal of base of the box = √10²+8² = √164 = 12.8

Hence, the diagonal of the base of the box is shorter than the length of the wind chime.

2.  interior diagonal of the box = √6²+8²+10² = √200 = 14.14

The interior diagonal of the box shorter than the length of the wind chime

3.  The wind chime will not fit in the box

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8 possible sequences in total. Thus, A tree with 8 outcomes, option 1 is correct.

A diagram with a structure of branching connecting lines, representing different processes and relationships.

Here is a tree diagram showing all the possible outcomes of Sandra tossing a coin three times:

In the diagram, each branch represents the outcome of one toss of the coin. The letters "H" and "T" represent "heads" and "tails," respectively. Each path from the top of the tree to a bottom node represents a possible sequence of coin tosses, and there are 2³ = 8 possible sequences in total.

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Complete question:

Sandra tossed a coin 3 times. Which tree diagram shows al the possible outcomes of the coin landing heads up or tails up.

A tree with 8 outcomes

A tree with 12 outcomes

A tree with 9 outcomes

A tree with 6 outcomes

Part (a)

Answers:

A' = (0, 2)

B' = (-1, -2)

C' = (-3, -2)

D' = (-4, -1)

Explanation:

Multiply each coordinate by 1/3.

For instance,

[tex]B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)[/tex]

====================================================

Part (b)

Answers:

A' = (-5, 5)

B' = (-8, -7)

C' = (-14, -7)

D' = (-17, -4)

Explanation:

Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.

I'll show an example using point C.

[tex](\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\[/tex]

Therefore, C(-9,-6) moves to C ' (-14,-7)

Answer 6

Step-by-step explanation:  A = 1/2 bh, 6 x 2 is 12 and 1/2 of 12 is 6

The leading coefficient of the polynomial is 4.

The leading coefficient of a polynomial, we first need to understand what the leading term of the polynomial is.

The leading term is the term with the highest degree in the polynomial.

For example, in the polynomial [tex]3x^4 + 2x^3 - 5x^2 + 4x - 1[tex], the leading term is 3x^4.
To determine the leading coefficient of a polynomial, we simply look at the coefficient of the leading term. For example, in the polynomial [tex]3x^4 + 2x^3 - 5x^2 + 4x - 1[/tex], the leading coefficient is 3.
Now, let's apply this concept to the polynomial graphed below. From the graph, we can see that the polynomial has a degree of 2, meaning that the highest power of x in the polynomial is 2.

Therefore, the leading term of the polynomial is [tex]ax^2[/tex], where a is the leading coefficient.
The vertex is the point on the graph where the polynomial reaches its maximum or minimum value. In this case, the vertex is located at [tex](-2, 4)[/tex]
Since the vertex is the highest point on the graph, we know that the coefficient of x^2 must be positive.

In this case, the value of y at the vertex is 4.

Therefore, the leading coefficient of the polynomial is 4.

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It asserts that if the sky is clear, then it is not possible for the plane to be on time.

In general, a hypothesis is a proposed explanation or tentative answer to a research question or problem. It is a statement that can be tested through investigation and analysis of data.

The statement "q -> ~p" can be interpreted as "If the sky is clear, then the plane is not on time."

This is a conditional statement, where q represents the hypothesis or condition ("the sky is clear") and ~p represents the conclusion or result ("the plane is not on time").

It asserts that if the sky is clear, then it is not possible for the plane to be on time.

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Answer:   To find the time at which the temperature is maximum, we need to find the vertex of the quadratic function T(x) = -0.07x^2. Recall that the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c is given by -b/2a. In this case, a = -0.07 and b = 0 (since there is no linear term), so the x-coordinate of the vertex is x = -b/2a = -0/(-0.14) = 0.

Since x is the number of hours after 6 a.m., the time corresponding to x = 0 is 6 a.m. Therefore, the temperature is a maximum at 6 a.m.

To find the maximum temperature, we evaluate T(0) = -0.07(0)^2 = 0. Therefore, the maximum temperature is 0 degrees Fahrenheit. Note that this result makes sense, since the quadratic function T(x) = -0.07x^2 is a downward-facing parabola, which means that the temperature decreases as the number of hours after 6 a.m. increases.

Step-by-step explanation:

First, we need to find the cross-sectional area of each figure:

Since the cross-sectional areas are equal at every level, we can set up the following equation:

5x = 9π

Solving for x, we get:

x = 9π/5

Now, we can find the volume of the rectangular prism:

V = 5x * 8 = 72π cubic meters

And the volume of the cylinder:

V = π(3^2) * 8 = 72π cubic meters

Since the volumes are equal, we can set up the following equation:

72π = 72π

Simplifying, we get:

9πx = 40π

Solving for x, we get:

x = 40/9

Rounding to the nearest tenth, we get:

x ≈ 4.4 meters

Therefore, the width of the rectangular prism is approximately 4.4 meters.