Expand By using the binomial theorem show all steps(4x-7y)^4

The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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yes, he is right all distance is the same from the origin point to any side of the circle same as radius which is half a line starts at any side of the circle and ends at the origin point.

Mason is correct.

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

A circle centered at the origin with a radius of 4 units can be represented by the equation:

x² + y² = r²

Substituting the coordinates of the point (4, 4), we have:

4² + 4² = r²

16 + 16 = r²

32 = r²

Taking the square root of both sides, we get:

r = 4√2

Therefore,

The circle centered at the origin with a radius of 4 units has an equation of x^2 + y^2 = 32.

Point (4, 4) satisfies this equation since:

4² + 4² = 32

16 + 16 = 32

32 = 32

Thus,

The point with the coordinates (4, 4) lies on the circle centered at the origin with a radius of 4 units.

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Answer:

10

Step-by-step explanation:

25 times .60 then take that answer and subtract it from 25 or half of 25 which it 12.5 then take off another 10%

The conclusion is option A, we cannot reject the null hypothesis.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

The null hypothesis cannot  be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.

Therefore, we can not reject the hypothesis.

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Answer:

the value of the expression 14 1/3 - 6 5/8 is 185/24.

Step-by-step explanation:

To solve this problem, you can convert both mixed numbers to improper fractions, then subtract the fractions and simplify the result. Here are the steps:

1. Convert 14 1/3 to an improper fraction:

14 1/3 = (14 x 3 + 1) / 3 = 43 / 3

2. Convert 6 5/8 to an improper fraction:

6 5/8 = (6 x 8 + 5) / 8 = 53 / 8

3. Subtract the fractions:

43 / 3 - 53 / 8 = (43 x 8 - 53 x 3) / (3 x 8) = (344 - 159) / 24 = 185 / 24

So the value of the expression 14 1/3 - 6 5/8 is 185/24.

Step-by-step explanation:

Answer:

Step-by-step explanation:

t = tackle score

s = sack score

t = s + 10

t + s = 36

s + 10 + s = 36

2s = 26

s = 13 points

t = 13 + 10 = 23 points

Answer:

20%is the increase in the amount

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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a) The angle swept out  since kelsey started skiing: 1.1498 radians

b) The distance Kelsey skied:  3.334 km

In this question, we have been given Kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail.

Consider the following figure for reference.

We need to find the angle θ and the distance kelsey skied (i.e., the arc length)

Here, the horizontal distance x = 1.185 km and the vertical distance y = 2.647 km

a. the tangent of angle θ would be,

tan(θ) = y/x

tan(θ) = 2.647/1.185

tan(θ) = 2.2337

θ = arctan(2.2337)

θ = 65.88°

θ = 1.1498 radians

b. The length of the arc is:

s = rθ

s = 2.9 * 1.1498

s = 3.334 km

Therefore, a) the angle swept out : 1.1498 radians

b) the distance Kelsey skied:  3.334 km

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Answer:

116

Step-by-step explanation:

we do pemdas so start with parenthesis

6+4=10

10 squared =100

then we divide before adding so

10/2 = 5+11= 16

100+16= 116

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

Answer:

true

Step-by-step explanation:

Answer:

a

Use the distance formula to see if at least two sides are congruent.

Step-by-step explanation:

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle

Answer:

Charlotte's mix has a bluer shade of purple

Step-by-step explanation:

Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red

Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red

This can be expressed as the ratio
\(\dfrac{ 2 \;blue}{1\;red} = \dfrac{2}{1} = 2\)

\(-------------------\)

Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red

The ratio of blue to red
= \(\dfrac{3 \;blue}{2\;red} = \dfrac{3}{2} = 1\dfrac{1}{2} \;\; (or\; 1.5)\)

Since
\(2 > 1\dfrac{1}{2} \;\;\;(or\; 2 > 1.5)\)  

Charlotte's mix has a bluer shade of purple

Answer:

1332 i think

Step-by-step explanation:

287+379=666

666*2=1332

x = 100

why?

because,

(76 + 124) ÷ 2 = 200 ÷ 2

= 100

your welcome :)

give me the brainliest please thank you

Answer:

Step-by-step explanation:

. 6

Answer:

2/3 or .6666666666......

Step-by-step explanation:

isolate x  by dividing -1.2 by 1.8

Answer:

Step-by-step explanation:

\(n^{5}= 1254\\n^{5} = 2.3.11.19\)

Therefore it is not possible that n is a perfect power of 5

           it is approximately 4.16

Answer:

n ≈ 4.165

Step-by-step explanation:

To solve this, you need to take the 5th root of both sides:

\(n^5=1,254\)

\(\sf{\sqrt[5]{n^5} =\sqrt[5]{1254}}\)

On the lhs we're only left with n as n^5 and the 5th root cancel each other out.

On the right-hand side we need to calculate:

\(n\approx4.165\)

The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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Answer:

200

Step-by-step explanation:

26% = 0.26

52 divided by 0.26 = 200

200 and to get a decimal just move your decimal place back twice so 2.00 or 200

Answer: 3 or 4

Step-by-step explanation:

f(x)=0.48In(x+2)+27=28  multiply both sides by 100

48In(x+2)+2700=2800  subtract 2700 from both sides

48In(x+2)=100

In(x+2)=\(\frac{25}{12}\)  apply log rule

x+2 = e\(\frac{25}{12}\)

x = e\(\frac{25}{12}\) - 2

x = 3.66

Given:

If Liz is in eighth grade, then she takes Spanish.

Required:

We need negation of the given statement.

Explanation:

There are some rules for then negation statement and one of those rules is

"if A, then B" negation of this is "A and not B"

Final answer:

Liz is in eighth grade and she does not take Spanish.

The solution to the inequality 6x - 6 < -30 is x < -4, and it is graphically represented as a closed circle at -4 and shading to the left of -4 on the number line.

To solve the inequality 6x - 6 < -30, we can follow these steps:

Step 1: Add 6 to both sides of the inequality to isolate the variable:

6x - 6 + 6 < -30 + 6

6x < -24

Step 2: Divide both sides of the inequality by 6 to solve for x:

(6x)/6 < (-24)/6

x < -4

The solution to the inequality is x < -4. This means that any value of x less than -4 will satisfy the inequality.

To graph the solution on the number line, we represent -4 as a closed circle (since it is not included in the solution) and shade the region to the left of -4 to indicate all values less than -4.

On the number line, mark a point at -4 with a closed circle:

<--------●-----------------

Then, shade the region to the left of -4:

<--------●================

The shaded region represents the solution to the inequality x < -4.

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If 7 feet below the surface of a river is written as -7 then 0 would be the surface of the river.

Answer:

Step-by-step explanation:

Recall that the equation of a line is y = mx + b.

Excellent. Let's plug in the values we are given into the general equation for a line. We get 10 = 1/2 * 4 + b.

Simplify to 10 = 2 + b, and we get b = 8.

Our final equation, then, is y = 1/2 x + 8.

Hope this helps!

The measure of three angles of triangular backyard are 28°, 31°  and 121°.

Given that, a home has a triangular backyard.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let the measure of first angle be x.

The second angel of the triangle is 3 more than the first angel = x+3

The third angel is 9 more than four times the first angel = 4x+9

Using angle sum property of a triangle

x+x+3+4x+9 = 180°

⇒ 6x + 12 = 180

⇒ 6x = 168

⇒ x = 28°

So, x+3 = 31° and 4x+9 = 121°

Therefore, the measure of three angles of triangular backyard are 28°, 31°  and 121°.

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