a box without a top is made from a rectangular piece of cardboard, with dimensions 6 feet by 8 ft, by cutting out square corners with side length x. which expression can be used to determine the greatest possible volume of the cardboard box?

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Final answer:

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. In this case, the recursive formula for the arithmetic sequence is A1 = 5 and An = An-1 - 4.

Explanation:

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. In this case, the recursive formula for the arithmetic sequence is A1 = 5 and An = An-1 - 4. Let's find some terms in this sequence:

A1 = 5

A2 = A1 - 4 = 5 - 4 = 1

A3 = A2 - 4 = 1 - 4 = -3

A4 = A3 - 4 = -3 - 4 = -7

...

So the first few terms in this arithmetic sequence are 5, 1, -3, -7, ...

Answer:

Step-by-step explanation:

The formula of an area of a parallelogram:

[tex]A=bh[/tex]

b - base

h - height

We have

[tex]b_1=36,\ h_1=24\\\\b_2=27,\ h_2=h[/tex]

Calculate the area:

[tex]A=(36)(24)=864[/tex]

[tex](27)(h)=864[/tex]           divide both sides by 27

[tex]h=32[/tex]

This is because that’s the smallest number in the multiple of both numbers.

The Lowest common multiple of 5 and 6 is 30

This is the lowest factor that can divide all other values without remainder.

In order to find the LCM of 5 and 6, we will Simply multiply thevalues together as shown:

LCM = 5 * 6

LCM = 30

Hence the Lowest common multiple of 5 and 6 is 30

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Answer:

IV: Color of containers

DV: Temp of water

3 Constants: How much water, container size, container material

Hypothesis: The water in the red container will heat up the quickest

Hope this helps!

Red, black, white containers

Dependent variable: how much heat a container absorbed from the Sun.

Independent variable: temperature measured in the container

3 Constant: heat given by Sun, 300ML water, thermometer reading accuracy

Hypothesis: the black container will absorb the most heat from the Sun and will transfer the heat to the water first, the red will be second and white third.

Answer:

Point-slope equation of this line:

[tex]\displaystyle y - 1 = \frac{1}{2}(x-5)[/tex].

Step-by-step explanation:

The equation for a line in a cartesian plane can take multiple forms. This question gives

The point-slope form will the most appropriate.

What is the point-slope form equation of a line [tex]l[/tex]?

In general,

[tex]l:\; y - y_0 = m (x - x_0)[/tex],

where

In other words, [tex](x_0,\; y_0)[/tex]the point on the line.

For this line,

Thus the equation for this line:

[tex]\displaystyle y - 1 = \frac{1}{2} (x - 5)[/tex].

Answer:

3.73 in expanded form

3 + 0.7+ 0.03

Final answer:

The number 3.73 in expanded form is written as 3 + 0.7 + 0.03, showing the value of each digit according to its place value.

Explanation:

The question is asking to write the number 3.73 in expanded form which is a way of writing numbers to show the value of each digit. When a number is written in expanded form, we break apart the number by each digit's place value, isolating each digit to represent the total sum of each part.

So, for the number 3.73, we can expand it as follows:

Now, combining these values together, we can write 3.73 in expanded form as:

3 + 0.7 + 0.03

The range of the function [tex]y=5^x[/tex] is all real numbers greater than 0, represented as (0, ∞).

The range of the function defined as [tex]y=5^x[/tex] refers to the set of all possible output values the function can produce. We know that exponentiation with a positive base other than 1 results in positive numbers regardless of the exponent's value. The function [tex]y=5^x[/tex] can take any real number x and will output a positive value since raising 5 to any power results in a positive number. Therefore, the range of [tex]y=5^x[/tex]  is all real numbers greater than 0, which can be expressed mathematically as (0, ∞).

Answer:

After 3 hours, both the airplanes are at a distance of 938.9 meters from each other.

Step-by-step explanation:

Speed of plane A = 275 mph

Speed of plane B = 375 mph

Angle between their flight path = Ф = 55°

Let their paths after 3 hours make a triangle.

Path of plane A is side 'a' = 275*3 = 825

Path of plane B is side 'b' = 375*3 = 1125

Distance between both planes after 3 hours = side 'c'

Here, we have two sides and one angle of the triangle.

We can find the third side using the law of cosines which is given as:

c² = a² + b² - 2ab*cosФ

c² = 825² + 1125² - 2(825)(1125)(cos(55°))

c² = 680625 + 1265625 - 1064745             where cos(55°) = 0.5736

c² = 881,505

c = √881,505

c = 938.9

c = 938.9 meters

I honestly think that the answer is a

Option: a is the correct answer.

                (a)  1

              Now, it is given that:

Feynman, produces output, that is 5 times its input followed by an increase of 2.

i.e. the equation that will be formed using this information is:

                  [tex]f=5i+2------------(1)[/tex]

The output of Feynman feeds into Maxwell.

Let the output of Maxwell be denoted by m and it's input is f.

Maxwell, produces output, that is 5 times its input followed by a decrease of 2.

This means that the equation that will be formed using this information is:

             [tex]m=5f-2----------------(2)[/tex]

Now, we put the value of f from equation (1) into equation (2)

i.e.

[tex]m=5(5i+2)-2\\\\i.e.\\\\m=25i+10-2\\\\i.e.\\\\m=25i+8[/tex]

If the output of Maxwell is: 33

i.e.

[tex]m=33[/tex]

Then

[tex]33=25i+8\\\\i.e.\\\\25i=33-8\\\\i.e.\\\\25i=25\\\\i.e.\\\\i=\dfrac{25}{25}\\\\i.e.\\\\i=1[/tex]

Hence, the input of Feynman is: 1

ANSWER

C)7cb^2

EXPLANATION

We want find the term among the given options that can be added to

[tex]8 {b}^{2} c[/tex]

That term must be similar to the given term.

It means that,it must be a

[tex] {b}^{2} c[/tex]

term.

From the alternatives provided, the only term, that is similar to the given term is

[tex]7c {b}^{2} [/tex]

Therefore, the correct answer is C

Answer:

C)  [tex]7cb^2[/tex]

Step-by-step explanation:

Given expression is [tex]8b^2c[/tex].

Now we need to find about which of the following terms can be added to the given expression  [tex]8b^2c[/tex].

A)   [tex]8b^2c^2[/tex]

B)  [tex]8bc[/tex]

C)  [tex]7cb^2[/tex]

D)  [tex]10c^2b[/tex]

We know that we are allowed to add only like terms. So

[tex]8b^2c[/tex] can be added with that term only which contains  [tex]b^2c[/tex].

Choice C)  [tex]7cb^2[/tex] contains [tex]b^2c[/tex].

Hence correct answer is C)  [tex]7cb^2[/tex].

Kyra sold a car that cost $26,500

1325 = 0.05x

1) 0.05x = 1325

2) Divide both sides by 0.05 -—> 0.05x/0.05 = 1325/0.05

3) x = 26,500

Final answer:

Kyra's commission of $1,325, which is 5% of the car's cost, leads us to calculate the cost of the car by dividing the commission by the commission rate, resulting in a car cost of $26,500.

Explanation:

Kyra receives a 5% commission on every car she sells. We are given that her commission on the last car she sold was $1,325. To find the cost of the car, we use the formula:

Commission = (Commission Rate) × (Cost of the Car)

Therefore,

Cost of the Car = Commission ÷ Commission Rate

Cost of the Car = $1,325 ÷ 0.05

Cost of the Car = $26,500

So, the car that Kyra sold was worth $26,500.

The highest peak is in the middle and both sides of it are fairly similar, so this would be a bell shaped distribution.

Answer:

Greatest Common Factor of 36 and 60. Greatest common factor (GCF) of 36 and 60 is 12. We will now calculate the prime factors of 36 and 60, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36 and 60.

Step-by-step explanation:

The greatest common factor of 36 and 60 can be found to be B. 12.

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest number that divides exactly into two or more numbers.

Let's find the GCF of 36 and 60.

36 = 2 x 2 x 3 x 3

60 = 2 x 2 x 3 x 5

The GCF is found by multiplying the common prime factors. In this case, the common prime factors are two 2s and one 3.

So, the GCF of 36 and 60 is:

= 2 x 2 x 3 = 12

In conclusion, option B is correct.

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Answer:

Step-by-step explanation:

Type in "sqrt .... "   or   click on the "omega" icon below for a list of built-in math characters, including  "√"

For this case we must find the values of "a" and "b" that make the expressions equivalent:

We have:

[tex]\sqrt {\frac {126xy ^ 5} {32x ^ 3}} =[/tex]

We take common factor "2" from the numerator and denominator:

[tex]\sqrt {\frac {2 * (63xy ^ 5)} {2 * (16x ^ 3)}} =[/tex]

Eliminating common factors of numerator and denominator:

[tex]\sqrt {\frac {63y ^ 5} {16x ^ 2}} =[/tex]

So, we have that the values of a and b are:

[tex]a = 16\\b = 2[/tex]

Answer:

[tex]a = 16\\b = 2[/tex]

Note: To write square root on pc we use sqrt

Answer:

The probability is 0.0015

Step-by-step explanation:

We know that the mean [tex]\mu[/tex] is:

[tex]\mu=6:30\ p.m[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=0:15\ minutes[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(x>7:15\ p.m.)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{7:15-6:30}{0:15}[/tex]

[tex]Z=\frac{0:45}{0:15}[/tex]

[tex]Z=3[/tex]

The score of Z = 3 means that 7:15 p.m. is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

[tex]P(x>7:15\ p.m.)=P(Z>3)=0.0015[/tex]

ANSWER

P(x)=2(f+g)(x)

EXPLANATION

The perimeter of a rectangle is calculated using the formula:

P=2(l+w)

From the table

The length is f(x)=x+3

The width is g(x)=x+2

This implies that the perimeter is

P(x)=2(f(x)+g(x))

This is the same as

P(x)=2(f+g)(x)

Answer: If you take the $8 service fee away from 38 you get 30. Then do 30/.12 and you get 250. To check it just do 250 x .12 and you'll get 30.

The answer is 250 minutes

Step-by-step explanation:

To find the number of minutes the customer used the phone, solve the equation c = 0.12m + 8 where c is the total cost for one month and m is the number of minutes used. Given that the customer's bill for the month is $38.00, substitute this value and solve for m. The customer used the phone for 250 minutes.

To find the number of minutes the customer used the phone, we can solve the equation

c = 0.12m + 8

where c is the total cost for one month and m is the number of minutes used.

Given that the customer's bill for the month is $38.00, we can substitute this value for c in the equation:

$38.00 = 0.12m + 8

Next, we can subtract 8 from both sides of the equation and then divide by 0.12 to isolate the variable m:

$38.00 - 8 = 0.12m

$30.00 = 0.12m

m = $30.00 / 0.12

m = 250 minutes

So, the customer used the phone for 250 minutes.

A picture of graph of g(x) = (1/5x)^2 .

Answer: [tex]x[/tex]≈[tex]0.732[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x" you need to apply the following property of logarithms:

[tex]log(m)^n=nlog(m)[/tex]

Apply logarithm on both sides of the equation:

[tex]90^x=27\\\\log(90)^x=log(27)[/tex]

Now, applying the property mentioned before, you can rewrite the equation in this form:

[tex]xlog(90)=log(27)[/tex]

Finally, you can apply the Division property of equality, which states that:  

 [tex]If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Therefore, you need to divide both sides of the equation by [tex]log(90)[/tex]. Finally, you get:

[tex]\frac{xlog(90)}{log(90)}=\frac{log(27)}{log(90)}\\\\x=\frac{log(27)}{log(90)}[/tex]

[tex]x[/tex]≈[tex]0.732[/tex]

Answer:

A

Step-by-step explanation:

Given 2 similar figures with sides in the ratio a : b

Then the ratio of their areas is a² : b²

Hence

ratio of sides = 2 : 9, then

ratio of areas = 2² : 9² = 4 : 81 → A

The answer is A.

Hope this helps!

Answer:

(g+f)(x)=(2^x+x-3)^(1/2)

Step-by-step explanation:

Given  

f(x)= 2^(x/2)

And

g(x)= √(x-3)

We have to find (g+f)(x)

In order to find (g+f)(x), both the functions are added and simplified.

So,

(g+f)(x)= √(x-3)+2^(x/2)  

The power x/2 can be written as a product of x*(1/2)

(g+f)(x)= √(x-3)+(2)^(1/2*x)

We also know that square root dissolves into power ½

(g+f)(x)=(x-3)^(1/2)+(2)^(1/2*x)

We can see that power ½ is common in both functions so taking it out

(g+f)(x)=(x-3+2^x)^(1/2)

Arranging the terms

(g+f)(x)=(2^x+x-3)^(1/2)  ..

Answer:

The correct answer option is B. 7/12.

Step-by-step explanation:

We are given that a baseball player gets to base 7 times and strikes out 5 times during a tournament.

We are to find the experimental probability of the player getting on base.

Assuming that there are only two outcomes,

number of times player gets on base = 7

number of times player strikes out = 5

total number of both outcomes = 12

Experimental probability of getting on base = 7/12

The answer above is right

Answer:

Option A.) 88 inches

Step-by-step explanation:

step 1

Find the circumference of the wheel

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

we have

[tex]D=28\ in[/tex]

[tex]\pi =\frac{22}{7}[/tex]

substitute

[tex]C=(\frac{22}{7})(28)=88\ in[/tex]

The distance a bicycle moves forward each time the wheel goes around is equivalent to the circumference of the wheel, which can be calculated using the formula C=πd. For a wheel with a diameter of 28 inches, the circumference is 88 inches.

The distance a bicycle wheel travels in one full rotation (which is also the perimeter of the wheel) can be calculated using the formula for the circumference of a circle, which is C=πd where π is a mathematical constant (about 22/7 or 3.14) and d is the diameter of the circle.

The diameter of this bicycle tire is given as 28 inches. Therefore, substituting 28 inches for the diameter (d) in the formula gives us C=22/7*28, which simplifies to 88 inches. So the bicycle moves forward approximately 88 inches each time the wheel goes around. Therefore, "the correct answer is A.) 88 inches".

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Answer:

B is the right choice

Hope This Helps!  Have A Nice Day!!

Answer:

B. 650 Roast Beef, 490 Tuna, 900 Turkey

Step-by-step explanation:

As this chart displays the order that occured in one week, in order to find the estimate for the month is to multiply the values on the chart by how many weeks there are in a month.

As there are 4 weeks in a months, we can multiply each value by this ratio

Roast Beef: [tex]4*152=608[/tex]

Tuna: [tex]4*114=456[/tex]

Turkey: [tex]4*209=836[/tex]

As this is an estimate, we are looking for the option that is the closest to these estimated values.

Option B is the closest to these values.

Answer:4w+5

Step-by-step explanation: take 3w away from 7w and get 4w

I only know number 9

9:0.70

8. 960 / 40 = 24

9. 7/10 = 0.7

10.   36.90

         7.35

Once added its sum is 44.25.

Answer:

The time a student learns mathematics is important for their score

Step-by-step explanation:

Observe the boxes diagrams. Where the horizontal axis represents the score obtained by the students in the test.

The vertical lines that divide the boxes in two represent the value of the median.

The median is the value that divides 50% of the data.

For the class of the morning the value of the median is 50 points, with a maximum value of 80 and a minimum value of 10.

For the afternoon class, the median value is 65 points with a minimum value of 30 and a maximum value of 100.

This indicates that in general, the highest number of high scores were obtained in the afternoon class.

Therefore it can be said that the time a student learns mathematics is important for their  score

Answer Sorry if this is too late but the answer is yes because the median test score of the afternoon class is 15 points above the morning class other wise the first option

Step-by-step explanation:

Answer:

Part 5) ∠x=122°

Part 6) Option D. ∠x=114°

Part 7) Option B.300π cm^3

Part 8) The volume of the cone is [tex]V=602.88\ in^{3}[/tex]

Part 9) The value of x is 12 cm

Part 10) BC=21 units

Part 11) Option D.reflection across the y-axis

Part 14)  [tex]x=15.6\ cm[/tex]

Part 15) B. 5, 12, 13

Step-by-step explanation:

Part 5)  What is the value of x?

we know that

∠x+58°=180°------> by supplementary angles

solve for x

∠x=180°-58°=122°

Part 6)  What is the value of x?

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

The measure of the third interior angle of the triangle is equal to

180°-61°-53°=66°

so

66°+∠x=180° -----> by supplementary angles

solve for x

∠x=180°-66°=114°

Part 7) A cylinder has a radius of 5 cm and a height of 12 cm. What is the volume of the cylinder?

we know that

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=5\ cm[/tex]

[tex]h=12\ cm[/tex]

substitute

[tex]V=\pi (5)^{2} (12)[/tex]

[tex]V=300\pi\ cm^{3}[/tex]

Part 8) A cone has a diameter of 12 in. and a height of 16 in. What is the volume of the cone?

we know that

The volume of the cone is equal to

[tex]V=(1/3)\pi r^{2} h[/tex]

we have

[tex]r=12/2=6\ in[/tex] ------> the radius is half the diameter

[tex]h=16\ in[/tex]

substitute

[tex]V=(1/3)(3.14)(6)^{2} (16)[/tex]

[tex]V=602.88\ in^{3}[/tex]

Part 9) Rectangle ABCD is similar to rectangle FGHI. What is the value of x?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

AB/FG=BC/GH

substitute the values

8/6=x/9

x=9*8/6

x=12 cm

Part 10) Given quadrilateral ABCD ~ quadrilateral JKLM and AD = 14, JM = 6, and KL = 9, what is BC?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

AD/JM/BC/KL

substitute the values

14/6/BC/9

BC=14*9/6

BC=21 units

Part 11) What transformation was performed on triangle ABC to create triangle A'B'C' ?

we know that

The rule for a reflection over the y -axis is (x,y)→(−x,y)

so

When reflecting across the y- axis the x-values will be multiplied by negative one, but the y-values will not change

This problem is a reflection across the y-axis

Part 14) What is the value of x? Round to the nearest tenth    

we know that

Applying the Pythagoras Theorem

[tex]x^{2}=10^{2}+12^{2}\\ \\x^{2}=244\\ \\x=15.6\ cm[/tex]

Part 15) Which set of side lengths defines a right triangle?

we know that

If the set of side lengths defines a right triangle, then must satisfy the Pythagoras Theorem

Verify each case

case A. 6, 8, 11

[tex]11^{2}=6^{2}+8^{2}\\ \\121=100[/tex]

Is not true

therefore

Is not a right triangle

case B. 5, 12, 13

[tex]13^{2}=5^{2}+12^{2}\\ \\169=169[/tex]

Is true

therefore

Is a right triangle

case C. 7, 9, 13

[tex]13^{2}=7^{2}+9^{2}\\ \\169=130[/tex]

Is not true

therefore

Is not a right triangle

case D. 6, 9, 11

[tex]11^{2}=6^{2}+9^{2}\\ \\121=117[/tex]

Is not true

therefore

Is not a right triangle