A car stuck in traffic travels 75 feet in one minute. In each subsequent minute, the car travels three-fourths the distance it traveled in the previous minute. How far does this car travel in 6 minutes?

1st answer: 7j = 91

2nd answer: 13

First, write the statement as an equation.

7j= 91

Now, divide both sides of the equation by 7.

j = 13

Answer:

7 + j = 91

J = 84

Answer:

the volume of the sphere will be 4 times the volume of the cone;

Step-by-step explanation:

The question is on volume comparison

Volume of a sphere=4/3 [tex]\pi[/tex]×r³

Volume of a cone= [tex]\pi[/tex]/3×r²h

where r is the radius and h is the height

Apply the condition

If r=h=1 unit

Then volume of sphere will be= 4/3 × [tex]\pi[/tex]×1³ = 4/3[tex]\pi[/tex]

And volume of the cone will be= [tex]\pi[/tex]/3 ×1²×1 =[tex]\pi[/tex]/3

We can see the volume of the sphere will be 4 times the volume of the cone;

4/3[tex]\pi[/tex] = 4×[tex]\pi[/tex]/3

The volume of the sphere is exactly twice the volume of the cone.

To establish the relationship between the volumes of a cone and a sphere when they have the same radius and height, we need to use the formulas for the volumes of these shapes.

Let's denote the radius of both the cone and the sphere as r  and the height of the cone (which is also the diameter of the sphere) as h .

The volume V  of a sphere is given by the formula:

[tex]\[ V_{\text{sphere}} = \frac{4}{3}\pi r^3 \][/tex]

The volume V  of a cone is given by the formula:

[tex]\[ V_{\text{cone}} = \frac{1}{3}\pi r^2 h \][/tex]

Since the height of the cone is the same as the diameter of the sphere, we have [tex]\( h = 2r \).[/tex]Substituting this into the volume formula for the cone gives us:

[tex]\[ V_{\text{cone}} = \frac{1}{3}\pi r^2 (2r) = \frac{2}{3}\pi r^3 \][/tex]

Now, we can compare the volumes of the two shapes:

[tex]\[ V_{\text{sphere}} = \frac{4}{3}\pi r^3 \] \[ V_{\text{cone}} = \frac{2}{3}\pi r^3 \][/tex]

Dividing the volume of the sphere by the volume of the cone, we get:

[tex]\[ \frac{V_{\text{sphere}}}{V_{\text{cone}}} = \frac{\frac{4}{3}\pi r^3}{\frac{2}{3}\pi r^3} = \frac{4}{2} = 2 \][/tex]

Therefore, the volume of the sphere is exactly twice the volume of the cone when they have the same radius and height.

Answer: Option C)

[tex]a_n = 2.5 + 2.5n[/tex]

Step-by-step explanation:

Note that the sequence increases by a factor of 2.5, that is, each term is the sum of the previous term plus 2.5.

[tex]7.5 - 5 = 2.5\\\\10 -7.5 = 2.5\\\\12.5 -10 = 2.5[/tex]

therefore this is an arithmetic sequence with an increase factor d = 2.5

The linear formula for the sequence [tex]a_n[/tex] is:

[tex]a_n = a_1 + d(n-1)[/tex]

Where

[tex]d = 2.5\\\\a_1 = 5[/tex]

[tex]a_1[/tex] is the first term of the sequence

So

[tex]a_n = 5 + 2.5(n-1)[/tex]

[tex]a_n = 2.5 + 2.5n[/tex]

The answer is the option C)

ANSWER

C)

[tex]a_n=2.5+2.5n[/tex]

EXPLANATION

The given sequence is:

5, 7.5, 10, 12.5, 15,...

where

[tex]a_1=5[/tex]

The constant difference is:

[tex]d = 7.5 - 5 = 2.5[/tex]

The closed linear form is given by;

[tex]a_n=a_1+d(n-1)[/tex]

We substitute the values into the formula to get:

[tex]a_n=5+2.5(n-1)[/tex]

Expand to get;

[tex]a_n=5+2.5n - 2.5[/tex]

[tex]a_n=2.5+2.5n[/tex]

Answer:

1, 2, 4, 5

Step-by-step explanation:

e2020 (edgen)

The information about houses that can affect housing prices are:

If a house is located in a prime location, its values would be higher than that of houses not located in prime areas. The bigger a house is, the higher its value. If a house is fitted with modern facilities, its value would be higher than that of other houses.

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You have to get y by itself and to do that you need to do the opposite of order of operations.

So the opposite of subtraction is addition so you would add 37 to both sides.

It would cancel out itself then leave y by itself while the other side of the equation is 55

Answer: y = 55

Step-by-step explanation: You want to get the variable or y by itself, so you cancel out what number is next to it which is 37, so you add  -37 + 37 and that   cancels it out.The reason you add  them together is because of opposite operations since it was minus you want to add, and what ever you do to one side you have to do to the other, so 18 + 37 is 55 so y is 55

Answer:

The quotient is: x-7

and remainder is : -300

Step-by-step explanation:

We need to divide [tex]X^3+43-49x-7x^2[/tex] by [tex]x^2-49[/tex]

First arrange the term  [tex]X^3+43-49x-7x^2[/tex] in terms of ascending order of x.

Arranging we get:

[tex]x^3 - 7x^2 -49x + 43[/tex] \  [tex]x^2-49[/tex]

The division steps are shown in figure attached.

The quotient is: x-7

and remainder is : -300

Answer: X - 7 R -300

(The person above me said it all and definitely deserves the brainliest)

Answer:

P(green) = ⇒ 5/14

P(red) = ⇒ 2/14

P(green and red) = ⇒ 5/98

The probabilities are P(green) = [tex]\frac{5}{14}[/tex], P(red) = [tex]\frac{1}{7}[/tex] and P(green and red) = [tex]\frac{5}{98}[/tex].

The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes.

In this case, Deepak is choosing two marbles one after the other with replacement, which means after drawing the first marble, he puts it back into the bag before drawing the second one.

Since these are independent events (drawing the first marble does not affect the probability of drawing the second), the probability of both events happening is the product of their individual probabilities.

So, the probability that Deepak will choose one green marble and then one red marble is [tex]\frac{5}{14} *\frac{1}{7} =\frac{5}{98}[/tex].

Complete Question:

A bag contains fourteen marbles. There are 4 purple marbles, 3 blue marbles, 5 green marbles, and 2 red marbles. Deepak randomly chooses two marbles from the bag, one at a time, and replaces the marble after each choice. What is the probability he will choose one green marble and then one red marble? Express the probabilities in fraction form.

Answer:

Option D.

Step-by-step explanation:

we know that

Angle -135° is equal to

360°-135°=225°

The angle belong to the III quadrant

225°-180°=45°

sin(45°)=d/1=d  

therefore

sin(-135°)=-sin(45°)=d  ---> the value is negative

Answer:

13 +5e

Step-by-step explanation:

11-2e+2+7e

Combine like terms

11+2 -2e+7e

13 +5e

Answer:

6

Step-by-step explanation:

Answer: C) 6

Step-by-step explanation:

Given : The cost in dollars, C, of renting a carpet cleaner is given by the linear equation  [tex]C = 20 + 25x[/tex], where x is the number of days.

To find the number of days it can be used for $170, we put C= 175 in the equation, we get

[tex]175 = 20 + 25x\\\\\Rightarrow\ 25x=170-20\\\\\Rightarrow\ 25x=150\\\\\Rightarrow\ x=\dfrac{150}{25}=6[/tex]

Hence, the required number of days = 6.

A.)> 161 is the answer

Answer:

375 units

Step-by-step explanation:

"What will its maximum height be?"

The given equation, h(x) = -3x^2 + 30x + 300, is a quadratic with coefficients a = -3, b = 30 and c = 300.

The axis of symmetry of this parabola will go thru the max ht.  The equation of the axis of symmetry is

x = -b / (2a)

In this particular case, the axis of symm. is x = -(30) / (2·[-3]), or x = 5 time units.

The max height is thus h(5) = -3(5)^2 + 30(5) + 300 = 375 units.

The answer is:

The maximum height reached by the projectile is 375 units.

To know what's the maximum height that the projectile reaches, we need to use the information about the given quadratic equation (parabola) to calculate the y-coordinate of the vertex.

The vertex of a parabola is located at the lowest or highest point depending on if the parabola opens upwards or downwards.

We can calculate the vertex of a parabola using the following equation:

[tex]x_{vertex}=\frac{-b}{2a}[/tex]

Then, after calculating the x-coordinate of the vertex, we need to substitute the x-coordinate value into the equation of the parabola to find the y-coordinate value or the highest point of the parabola.

We are given the parabola:

[tex]h(x)=y=-3x^{2}+30x+300[/tex]

Where,

[tex]a=-3\\b=30\\c=300\\[/tex]

Now, calculating the vertex we have:

[tex]x_{vertex}=\frac{-b}{2a}[/tex]

[tex]x_{vertex}=\frac{-30}{2*(-3)}=5[/tex]

Then, calculating the y-coordinate value, we have:

[tex]y_{vertex}=-3x^{2}+30x+300[/tex]

[tex]y_{vertex}=-3*(5)^{2}+30*(5)+300[/tex]

[tex]y_{vertex}=-3*25+150+300[/tex]

[tex]y_{vertex}=-75+150+300[/tex]

[tex]y=-75+150+300[/tex]

[tex]y_{vertex}=375[/tex]

Hence, the y-coordinate value of the vertex is equal to 375, meaning that the maximum height reached by the projectile is 375 units.

Have a nice day!

The percentage that the store has taken off would be 30%.

The price of the sofa was reduced by 30%.

To calculate the percentage reduction in price:

Find the difference between the original price and the reduced price: $800 - $560 = $240.

Calculate the percentage decrease: ($240 / $800) x 100% = 30%.

Therefore, the price of the sofa was reduced by 30%.

Answer:

3/5

Step-by-step explanation:

Make it a fractiona and simplify. Add 8+12=20 knowing theres twelve girls it would be 12/20. then simplify

Answer:

(1, -10)

Step-by-step explanation:

Only the y can be on the left hand side. The square has been completed so all you need do is transfer the 10 to the right and read the x,y values for the vertex.

I have provided a graph to show you that the vertex and my answer are the same (hopefully).

y + 10 = 4(x - 1)^2          Subtract 10 from both sides.

y + 10-10=4(x -1)^2 -10  Combine

y = 4(x - 1)^2 - 10

Now we need to make the square term = 0

x - 1  = 0                        Add 1 to both sides

x - 1 + 1 = 0 +1               Combine

x = 1                              When x = 1 the square term will equal 0.

The vertex should be (1, - 10)

I think the answer might be C

Answer: A

Step-by-step explanation:

Answer:

the answer is 1.16 shirts

Step-by-step explanation:

the mean absolute deviation is found by finding the average of the difference between each data point and the mean of the data.

1st...find the mean of the data by adding all the numbers according to the data plotted and dividing the by the numbers listed; which in this case is 10

1 +2+ 2+ 3+ 3+ 3+ 4+ 4+ 5+ 6 = 3.3

mean is 3.3

then find the difference between the mean and each data point

Data Point =                       1      2     2      3     3       3      4      4     5      6

Difference from mean = 2.3    1.3   1.3  0.3  0.3   0.3   0.7    0.7   1.7   2.7

Find the average of these differences by adding the (differences from Mean) by 10

2.3  + 1.3  + 1.3  + 0.3  + 0.3  + 0.3  + 0.7  + 0.7 +  1.7 + 2.7

                                             10

the mean absolute deviations is 1.16 shirts

mode: 3

median: 3

___________________________

mean:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 2 = 8

5 x 1 = 5

6 x 1 = 6

1 + 4 + 9 + 8 + 5 + 6 = 33 ÷ 10 = 3.3

_____________________________

mean: 3.3

____________________________

Interquartile Range: 4 - 2 = 2

___________________________

Range: 6 - 1 = 5

____________________________

Mean Absolute Deviation:

3.3 - 1 = 2.3

3.3 - 2 = 1.3

3.3 - 2 = 1.3

3.3 - 3 = 0.3

3.3 - 3 = 0.3

3.3 - 3 = 0.3

3.3 - 4 = 0.7

3.3 - 4 = 0.7

3.3 - 5 = 1.7

3.3 - 6 = 2.7

____________________________

1.3 · 2 = 2.6

0.3 · 3 = 0.9

0.7 · 2 = 1.4

____________________________

2.3 + 2.6 + 0.9 + 1.4 + 1.7 + 2.7 = 11.6/10 = 1.16

____________________________________

So your mean absolute deviation would be 1.16 :)!

Answer: 1.5 kilometers.

Step-by-step explanation:

You need to make the conversion from 500 meters to kilometers.

It is important to remember that:

[tex]1\ kilometer=1,000\ meters[/tex]

Then, 500 m to km is:

[tex](500\ m)(\frac{1\ km}{1,000\ m})=0.5\ km[/tex]

Now you know that he ran 0.5 kilometers in each of his last three track meets.

To calculate the total amount of kilometers ran in those three meets, you need to multiply 0.5 kilometers by 3. Then:

[tex]Total=(0.5\ km)(3)\\Total=1.5\ km[/tex]

Answer:

5 degrees

Step-by-step explanation:

measure of angle 1=1/2(20-10)

because the secants intersect outside of the circle.

measure of angle 1=1/2(10)

measuer of angle 1=5 degrees

Answer:

2/11 = 0.181818...

D. is your repeating decimal.

the LCD is 20

[tex] \frac{3}{4} \times \frac{5}{5} = \frac{15}{20} \\ \\ \frac{7}{10} \times \frac{2}{2} = \frac{14}{20} [/tex]

Final answer:

The expression 5x (36+9) simplifies to 225 by first adding the numbers in the parentheses (36+9) to get 45, and then multiplying 5 by 45.

Explanation:

The expression 5x (36+9) represents the phrase 'five times the sum of thirty-six and nine.' To evaluate this expression, you first perform the operation inside the parentheses. In this case, you add 36 and 9, which equals 45. After simplifying the parentheses, the expression becomes 5x45. As the final step, you multiply 5 by 45, which equals 225. Therefore, the expression 5x (36+9) equals 225.

Answer:

$7.50

Step-by-step explanation:

Sara buys a sweater that costs $30

The store is having a 25% off sale.

To figure out what 25% is you do 25/100, which will give you 0.25,

Multiply 0.25 by $30

You should get $7.50.

The answer is $22.50.

Hope this helps!

6%.

365.70-345=20.7

345*.06=20.7

The percentage of the sales tax Chan pay if Chan bought a $345 smartphone, but his total was $365.70 is 6%.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

The cost of smartphone = $345

The total amount = $365.7

Calculate the percentage as shown below,

Percentage of tax = The total amount - The cost of smartphone / The cost of smartphone × 100

Percentage of tax = (365.7 - 345) / 345 × 100

Percentage of tax = 20.7 / 345 × 100

Percentage of tax = 0.06 × 100

Percentage of tax = 6 %

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Answer:

A. 20

Step-by-step explanation:

Since they both reflect each other, you would set (3x)° equal to (x + 40)°. Then move -x to the other side of the equivalence symbol to get 40 = 2x. This is how x is defined. You immediately divide by 20 to get your result above.

I am joyous to assist you anytime.

Yes an equilateral triangle is a type or acute triangle.

Answer: yes

Step-by-step explanation: An acute triangle means that all of the angles of the triangle are less than 90 degrees.

Since a triangle has three angles which always add to 180 degrees

and an equilateral triangle must have all of the same angles, it's impossible

to have an equilateral triangle that measures anything other than 60°.

Answer:

B. They sold the least lemonade with the recipe that used 7 lemons

Step-by-step explanation:

Answer:

B. They sold the least lemonade with the recipe that used 7 lemons

Step-by-step explanation:

As can be seen from the graph the points are

(3, 37)

This means that when they used 3 lemons then they sold around 37 cups

(4, 32)

This means that when they used 4 lemons then they sold around 32 cups

(5, 40)

This means that when they used 5 lemons then they sold around 40 cups

(6, 35)

This means that when they used 6 lemons then they sold around 40 cups

(7, 26)

This means that when they used 7 lemons then they sold around 26 cups

It can be seen that the last case is when they sold the least number of cups.

To solve this problem, we find the side length of the square pool, find the inner perimeter of the sidewalk, and then calculate the difference between the outer and inner perimeters. The width of the sidewalk is 5 feet.

This is a Mathematics problem that involves some knowledge of geometry. Firstly, let's inspect the given information: The square swimming pool’s area is 225 square feet. Since the pool is square, the side length of the pool can be found by taking the square root of the area: √225 = 15 feet. So, the inside perimeter of the sidewalk is 60 feet (4*15).

However, the outside perimeter of the sidewalk is 80 feet. The difference between the outside and the inside perimeter (80 – 60) is 20. That value is twice the width of the sidewalk because the sidewalk extends around all four sides. Therefore, each side of the sidewalk must cover extra 5 feet (20 / 4). So, the width of the sidewalk is 5 feet.

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Answer: B

Step-by-step explanation:

the sum of any two sides is bigger than the third side... so 5+9= 14, bigger than 6. 5+6=11, greater than 9. 9+6=15, bigger than 5.

Answer:

B

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

So, let's test each of the points:

A) We have the points: 4, 8, 2. If we sum 4 and 2, the result is 6. Which is not greater than the third side which is 8. So it does not qualify for a triangle.

B) We have the points 5, 9, 6. If we sum 5+6 = 11 which is greater than 9. The sum of any two sides from this set is greater than the third side. It could create a triangle.

C) We have the points 6, 8, 16. If we sum  6+8 = 14 which is not greater than the third side 16. So it could not create a triangle.

D) we have the points 10, 4, 3. If we sum 4+3 = 7 which is not greater than 10. For that reason, it could not create a triangle.

Answer:

c. [tex]\:<\:1,-4,-4\:>\:,\sqrt{33[/tex]

Step-by-step explanation:

Given T(2,5,4) and M(3,1,0);

[tex]^{\to}_{TM}=^{\to}_{OM}-^{\to}_{OT}[/tex]

[tex]^{\to}_{TM}=\:<\:3,1,0\:>\:-\:<\:2,5,4\:>\:[/tex]

[tex]^{\to}_{TM}=\:<\:3-2,1-5,0-4\:>\:[/tex]

[tex]^{\to}_{TM}=\:<\:1,-4,-4\:>\:[/tex]

The magnitude of this vector is :

[tex]|^{\to}_{TM}|=\sqrt{1^2+(-4)^2+(-4)^2[/tex]

[tex]|^{\to}_{TM}|=\sqrt{1+16+16[/tex]

[tex]|^{\to}_{TM}|=\sqrt{33[/tex]

Answer:

C

Step-by-step explanation:

Edge 2020 :)