use the fundamental theorem to evaluate the definite integral exactly. 16 1 3/pi of x dx enter the exact answer. g

Tally won the dirt throwing game and his score was 1.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information, The score of Tally is,

= 3×2 - 3×3 + 4×1.

= 6 - 9 + 4.

= 1.

The score of Awasin is,

= 4×2 - 4×3 + 2×1.

= 8 - 12 + 2.

= - 2.

So, Tally won the game and his score is 1.

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Answer:

The probability is   \(G  =  85% \)

Step-by-step explanation:

From the question we are told that

   The percentage of parents that have one child under 18 in their homes is  k = 15%

  The percentage of parents that have two children is  T = 65%

    The percentage of parents that have three or more children is  Y = 20%

Generally the probability that any given family who is selected have two or more children at home is mathematically evaluated as

     \(G  =  T  +  Y\)

=>  \(G  =  65% +  20% \)

=>  \(G  =  85% \)

Answer:

The answer is

\( \huge y + 1 = 15(x - 3) \\ \)

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question we have the final answer as

\(y + 1 = 15(x - 3)\)

Hope this helps you

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Answer:

Restaurant A and C: 23 grams of fat

Restaurant B: 31 grams of fat

Answer:

Restaurant A's chicken salad has  7.7 grams of fat.

Restaurant​ B's chicken salad has  61.6 grams of fat.

Restaurant​ C's chicken salad has  7.7 grams of fat.

Step-by-step explanation:

Restaurant A = C

Restaurant B = 8 × Restaurant A

Total Grams of Salad = 77

Let Reataurat A and C be x

and Reataurant B be 8x

so

A + B + C = 77

x + 8x + x = 77

2x + 8x = 77

10x = 77

x = 77 ÷ 10

x = 7.7

Restaurant A's chicken salad has  7.7 grams of fat.

Restaurant​ B's chicken salad has  61.6 grams of fat.

Restaurant​ C's chicken salad has  7.7 grams of fat.

If u want to crass check so

7.7 + 61.6 + 7.7 =

69.3 + 7.7 =

= 77

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Answer:x > 15

Step-by-step explanation:

simplify both sides of the inequality

2x + 9 > 39

subtract 9 from both sides

2x + 9 - 9 > 39 -9

2x > 30

divide both sides by 2

2x/2 > 30/2

x > 15

Brainliest please

Answer:

\( |T- 98.6| \geq 3\)

And in order to solve this we have two possibilities:

Solution 1

\( T -98.6 \leq -3\)

And solving for T we got:

\( T \leq 98.6- 3\)

\( T\leq 95.6\)

Solution 2

And the other options would be:

\( T -98.6 \geq 3\)

\( T \geq 101.6\)

Step-by-step explanation:

For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:

\( |T- 98.6| \geq 3\)

And in order to solve this we have two possibilities:

Solution 1

\( T -98.6 \leq -3\)

And solving for T we got:

\( T \leq 98.6- 3\)

\( T\leq 95.6\)

Solution 2

And the other options would be:

\( T -98.6 \geq 3\)

\( T \geq 101.6\)

Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .

In the question ,

a rectangle is given

the vertex of the rectangle ABCD is given as

A(-10,-6) , B(-10,-2) , C(-6,-2) , D(-6,-6) .

On applying the translation 6 units to right and 3 units up ,

the rule is (x,y)→(x+6,y+3)

by applying the rule for the translation

we get image as

A'(-4,-3) ,B'(-4,+1) , C'(0,1) , D'(0,-3)

The image is plotted below .

Therefore , The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .

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After answering the given query, we can state that  the parabola equation expands upwards, and the apex is (4, 4.5).

Using the equals sign (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical formulas through a mathematical assertion. The equal symbol, for example, puts a space between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two lines that are printed on opposite sides of a letter. Most of the time, the emblem and the particular program match. e.g., 2x - 4 = 2 is an example.

P equals 1/2, meaning that the distance between the apex and the focus is equal to the distance between the directrix and the focus.

As a result, the parabola's equation is:

\((x - 4)^2 = 4(1/2)(y - 1.5)\\(x - 4)^2 = 2(y - 1.5)\)

The left half of the equation is expanded as follows: x2 - 8x + 16 = 2(y - \(1.5) x2 - 8x + 13 = 2y\\y = (1/2)x^2 - 4x + 13/2\)

The problem can also be expressed in vertex form by filling in the cube as follows:

\((x - 4)^2 = 2(y - 1.5)\\(x - 4)^2 = 2(y - 1.5) + 6\\(x - 4)^2 = 2(y - 4.5)\\(x - 4)^2/8 = (y - 4.5)\\\)

Therefore, the parabola expands upwards, and the apex is (4, 4.5).

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For given functions, The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

What is the definition of a function?

A function is a mathematical rule that gives each input value a distinct output value. A function is officially defined as a collection of ordered pairs (x, y) in which each input value x is coupled with exactly one output value y. The domain of the function refers to the input values, while the range refers to the output values. A graph, table, equation, or verbal explanation can all be used to depict a function. When the input value is x, the notation f(x) is commonly used to express the output value of a function f.

Now,

From given function f(x) and g(x)

For f(x) when x=0 then y=1 or y-intercept=1

for g(x), the y-intercept is 1 from equation y=4x+1

and slope of g(x)=4

and slope of f(x)=(11-1)/(2-0)

=10/5

=2

Hence,

           The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

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\(\large{\green{\underline{\underline{\bf{\orange{ANSWER:-}}}}}}\)

The question and data provided in the information is that (<J ≈ <K) are congruent to each other. Then (<J + <L = 180°) here supplementary means that there sum tends to 180°. And we have also provided the value of <K = 71°.

Now as per question we can write that,

\(\longrightarrow\bf{ \angle j + \angle l = 180}\)

\(\longrightarrow\bf{ \angle k + \angle l = 180 \: .... \: ( \angle j = \angle k)}\)

Now substituting values,

\(\longrightarrow\bf{71 + \angle l = 180}\)

\(\longrightarrow\bf{ \angle l = 180 - 71}\)

\(\longrightarrow\bf{ \angle l = 109}\)

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:11

Step-by-step explanation:x+12=23

                                            x=23-12

                                              x=11

The required money saved is $9,256 after 6% sales tax.

Given that,
Ben bought a house for $102,850 and received a rebate of 15% off. He paid 6% in sales tax, how much did he save is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
rebate amount = 105850 × 0.15 = $15,877
sale tax = 105850 × 0.06 = $6171
Money saved = 15, 877 - 6171 = $9,256

Thus, the required money saved is $9,256 after 6% sales tax.

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Answer:

They will need 160 cans to make 5 lbs

32 cans for 1 lbs

Step-by-step explanation:

We can use ratios to solve

8 cans             x cans

--------------- = ---------------

1/4 lbs             5 lbs

Using cross products

8 * 5 = 1/4x

40 = 1/4 x

Multiply each side by 4

4 * 40 = 1/4 x * 4

160 =x

They will need 160 cans to make 5 lbs

8 cans             x cans

--------------- = ---------------

1/4 lbs             1 lbs

Using cross products

8 * 1 = 1/4x

Multiply each side by 4

8*4 = x

32 cans for 1 lbs

Answer:

32 cans per pound of aluminum

160 cans per 5 pounds of aluminum

Step-by-step explanation:

will make it short and simple.

8 empty cans can make 1/4 pound of aluminum.

therefore... 8 x 4 = 32 cans per pound of aluminum.

Number of cans to make 5 pounds of aluminum = 32 x 5

= 160 cans per 5 pounds of aluminum

Answer:

Step-by-step explanation:

Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D

Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.

Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.

Therefore, the correct answer is D. parallelogram.

It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.

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Answer:

No,

Step-by-step explanation:

All you have to do is use the triangle inequality therorum. if two side lengths of a triangle is always greater than the third side. you will have a triangle.

d = 8

Divide both sides of the equation by the same term

Answer:

d = 8

Step-by-step explanation:

Step 1: Divide both sides by 12.

Therefore, the solution is 8.

Answer:

\(log_2(10)\)

Simplify the equation using logarithms.

\(2^3x=10\)

\(log_1_0(2^3x)=log_1_0(10)\)

log rule ⇩

\(log_a(x^y)=y*log_a(x)\)

move exponent out of log.

\(x*log_1_0(2)=log_1_0(10)\)

isolate variable further

\(x*log_1_0(2)=log_1_0(10)\)

\(x=\frac{log_{10}(10)}{log_{10}(2)}\)

formula for combining logs. ⇩

\(\frac {log_b(x)}{log_b(a)}=log_a(x)\)

the result ⇩

\(x=log_2(10)\)

Answer:

yo answer woud be b √5/4

Step-by-step explanation:

Sqrt(5 / 16)

Let's take the sqrt of both terms individually.

Sqrt(5) / sqrt(16) = sqrt(5) / 4

It would be B)no.

Hope This Helps!

Answer:

y = 2x

the formula for linear equations are y = mx+c,

where m is the gradient,

and c is the y-intercept

to find m (the gradient):

1. pick to points on the graph (eg. -2,-4 and 2,4)

2 substitute the values into the formula for gradient y2-y1/x2-x1.

m = y2-y1/x1-x2

= -4 -4/-2-2

= -8/-4

= 2

to find c (y-intercept):

- the y-intercept is where the graph cuts the y axis

- in this graph, the y-intercept is 0

hence,

c = 0

substitute m = 2 and c = 0 to y = mx+c,

y = 2x + 0

y = 2x

hence, the equation that best represents the relationship shown in the graph is y = 2x.

Answer:

Step-by-step explanation:

As,

\( {(ax)}^{2} = a \times a \times x \times x\)

Hence,

\( {(2x)}^{2} \)

= 2×2×x×x

\( = 4 {x}^{2} (ans)(without \: brackets)\)

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Answer:

We conclude that the length of LM if L(3,4) and M(1,-2) will be:

\(d = 6.3\)

Hence, option D is correct.

Step-by-step explanation:

Given

Determining the length of LM

The length of the distance between (x₁, y₁)  and (x₂, y₂)  can be determined using the formula

\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)

substituting (x₁, y₁) = (3, 4) and (x₂, y₂) = (1, -2)

   \(=\sqrt{\left(1-3\right)^2+\left(-2-4\right)^2}\)

   \(=\sqrt{2^2+6^2}\)

   \(=\sqrt{4+36}\)

   \(=\sqrt{40}\)

   \(=\sqrt{4\times 10}\)

   \(=\sqrt{2^2\times \:10}\)

   \(=2\sqrt{10}\)

   \(=6.3\)

Therefore, we conclude that the length of LM if L(3,4) and M(1,-2) will be:

\(d = 6.3\)

Hence, option D is correct.

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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