Car Survey in a survey of 3,200 people who owned a certain type of car, 2,240 said they would buy
that type of car again. What percent of the people surveyed were satisfied with the car?

A vessel of 7,560 liters

Step-by-step explanation:

This means finding the Least Common Multiple for;

108 168 180

We begin by finding the multiples of each number;

Multiples of 108:

108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776

Multiples of 168:

168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856, 3024, 3192, 3360, 3528, 3696, 3864, 4032, 4200, 4368, 4536, 4704, 4872, 5040, 5208, 5376, 5544, 5712, 5880, 6048, 6216, 6384, 6552, 6720, 6888, 7056, 7224, 7392, 7560, 7728, 7896

Multiples of 180:

180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920

The Least Common Multiple for the 3 number is;

= 7560

Therefore a vessel of 7,560 liters fills each one of them an exact number of times with no remainder.

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Answer:

7x

Step-by-step explanation:

Assuming your expression is :

[tex]e^{\ln 7x}[/tex]

Then we simplify as follows

[tex]e^{\ln 7x}=e^{\ln x+\ln 7}[/tex] since [tex]\ln A+\ln B=\ln AB[/tex]

[tex]\implies e^{\ln 7x}=e^{\ln x}\times e^{\ln 7}[/tex] since [tex]a^{m+n}=a^m\times a^n[/tex]

[tex]\implies e^{\ln 7x}=x\times7[/tex] since [tex]e^{\ln a}=a[/tex]

[tex]\implies e^{\ln 7x}=7x[/tex]

Answer:

you will need 4cups of flour

Answer:

y-9=5(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-9=5(x-(-3))

y-9=5(x+3)

Answer:

The city’s total budget is [tex]\$54,860,151[/tex]

Step-by-step explanation:

we know that

31.84% of the city's total budget represent $17,467,472

so

using proportion

Find out what is the city’s total budget (100% percentage)

[tex]\frac{\$17,467,472}{31.84\%}=\frac{x}{100\%}\\\\x=\$17,467,472(100)/31.84\\\\x=\$54,860,151[/tex]

Answer:

D) (-2)^2-(-8)+1

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:

This board of 24.5 inches long is not enough to be cut into the four walls of the bird house.

Step-by-step explanation:

Hodi is building a birdhouse. Each of the four walls of the birdhouse needs to be 5.5 inches long.

So, to get four 5.5 inches long walls we need to have (5.5 × 4) = 22 inches ling board from which four equal 5.5 inches board can be made.

Now, Hodi has a piece of a board that is 24.5 inches long.

Therefore, this board is not enough to be cut into the four walls of the birdhouse. (Answer)

Answer:

2

2x + 3 = 5x - 3

Move x to one side:

[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]

Remove the -3:

[tex]3x-3(+3)=(3+3)[/tex]

[tex]3x=6[/tex]

Remove the 6 to get x by itself:

[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]

The number 2 from the number set would solve the equation.

2(2) + 3 = 5(2) - 3

4 + 3 = 10 - 3

7 = 7

The statement is true.

An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be simplified as shown below,

2x + 3 = 5x - 3

Subtract 2x from both sides of the equation,

2x + 3 - 2x = 5x - 3 - 2x

3 = 5x - 3 - 2x

Add 3 on both sides of the equation,

3 + 3 = 5x - 3 - 2x + 3

6 = 3x

3x = 6

Divide both the sides of the equation by 3,

3x/3 = 6/3

x = 2

Hence, the number(s) from the set that will satisfy the given equation is 2.

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Answer:

The Length of side of park is 20 meter.

Step-by-step explanation:

Given:

Shape of a Park is SQUARE

Area of a square park = 400 sqm

To Find:

The length of side of park = side =  ?

Solution:

We know For a SQUARE

All the sides are equal

And Area of a square is given as

[tex]\textrm{Area of Square Park}= (Side)^{2} \\[/tex]

Substituting the given values we get

[tex]400=(side)^{2} \\\\\textrm{Square rooting we get}\\\\side=\sqrt{400} \\\\\therefore side = 20\ meter[/tex]

The Length of side of park is 20 meter.

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points:

[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)[/tex]

We can find the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}[/tex]

Thus, the equation is of the form:

[tex]y = \frac {5} {2} x + b[/tex]

We substitute one of the points and find "b":

[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4[/tex]

Finally, the equation is:

[tex]y = \frac {5} {2} x-4[/tex]

Thus, it is observed that the lines have the same y-intercept

Answer:

Option D

Answer:

Step-by-step explanation:

error in measurement  = 480 - 469 = 11 inches

Percent error = error *100/actual length

= 11 * 100 /480 = 2.9%

Answer:

[tex]\frac{4}{11}[/tex]

Step-by-step explanation:

The total length of KN is 11 units and the length of LM is 4 units. This means that the probability would be [tex]\frac{4}{11}[/tex]

Answer : The probability that p on LM is, [tex]\frac{4}{11}[/tex]

Step-by-step explanation :

Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.

[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}[/tex]

Favorable outcomes on line KN are, 2, 4, 5

Favorable outcomes on line LM is, 4

Number of favorable outcomes = 4

Total number of outcomes = 2 + 4 + 5 = 11

[tex]\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}[/tex]

[tex]\text{Probability}=\frac{4}{11}[/tex]

Therefore, the probability that p on LM is, [tex]\frac{4}{11}[/tex]

Answer:

The female would pay  $322.00 less for a policy of $25,000

Step-by-step explanation:

Since we have given that

Amount for policy = $25000

If she opt for 20 year life insurance at $2.90 per $1000.

so, her amount of premium becomes

[tex]25000\times \frac{2.9}{1000}[/tex]

=$72.50

If she opt for straight life insurance at $15.78 per $1000,

Then, her amount of premium becomes

[tex]25000 \times \frac{15.78}{1000}[/tex]

= $394.50

Difference between them is given by

$394.50-$72.5 = $322.00

Answer:

The answer to this question is $322.

Step-by-step explanation:

From the question, we recall the following

23-year-old female pay for a $25,000 policy less policy of 20 year life insurance.

The first step is to calculate the policy of 20 year life insurance

The number of thousands on 2500 is, 25000/1000=25

25*2.9  = 72.5

The next step is to get the straight life

Thus,

25×15.78  = 394.5

Now,

How much less  would the 23 year old pay

394.5−72.5  = $322

Answer:

1.26 kg.

Step-by-step explanation:

We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.

First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:

[tex]\text{Amount of candy bought in grams}=14\times 90[/tex]

[tex]\text{Amount of candy bought in grams}=1260[/tex]

We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:

[tex]\text{Amount of candy bought in kilograms}=\frac{1260}{1000}[/tex]

[tex]\text{Amount of candy bought in kilograms}=1.26[/tex]

Therefore, Mr. Snow bought 1.26 kilograms of candy.

Answer:

[tex]A=6.33\ cm^2[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

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

we have

[tex]C=\frac{28}{3.14}\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute the values

[tex]\frac{28}{3.14}=2(3.14)r[/tex]

[tex]r=\frac{28}{19.7192}\ cm[/tex]

[tex]r=1.42\ cm[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

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

substitute the values

[tex]A=(3.14)(1.42)^{2}[/tex]

[tex]A=6.33\ cm^2[/tex]

Answer:

3r-5r

Step-by-step explanation:

Answer:

9 should be added to the expression to make it a perfect square

Step-by-step explanation:

Given expression:

[tex]w^2-6w+_-[/tex]

To fill in the missing term such that the expression becomes a perfect square.

Solution:

In order to make the expression a perfect square we will use completing the square method.

We have : [tex]w^2-6w[/tex]

By complete the square method we will add the square of the quotient of the co-efficient of the middle term which is [tex]-6w[/tex] and 2.  

The co-efficient of middle term = -6

Thus the number to be added will be = [tex](\frac{-6}{2})^2=(-3)^2=9[/tex]

Thus, on adding 9 the expression will become:

[tex]w^2-6w+9[/tex] which is a perfect square of the binomial [tex](w-3)[/tex]

This can be shown as:

[tex](w-3)^2=w^2-6w+9[/tex]

Thus, we add 9 to the expression to make it a perfect square.

Answer:

9

Step-by-step explanation:

Given: [tex]w^{2} -6w+[/tex]

Finding the number to make expression a perfect square.

From the expression we can see that coefficient of variable is 1 and -6.

Now, lets take a= 1 and b= -6 and finding c .

∴ c= [tex]\frac{b^{2} }{4a}[/tex]

Subtituting the value of a and b.

⇒ c= [tex]\frac{-6^{2} }{4\times 1} = \frac{36}{4}[/tex] (∵ [tex]-6\times -6= 36[/tex])

∴ c= 9

Next putting the value in the expression.

[tex]w^{2} -6w+9[/tex]

= [tex](w-3)(w-3)[/tex]

= [tex](w-3)^{2}[/tex]

Hence, 9 is a number to make the expression a perfect square.

Answer:

[tex]-5c[/tex]

Step-by-step explanation:

To find: The sum of [tex]6c-5c[/tex] and opposite of [tex]6c[/tex]

Opposite of [tex]6c[/tex] means taking the opposite sign.

[tex]6c[/tex] is positive. So, opposite sign is [tex]-6c[/tex].

Therefore, the addition is given as:

[tex]=6c-5c+(-6c)[/tex]

Opening the parenthesis, we get:

[tex]6c-5c-6c[/tex]

Now, as per PEDMAS rule, we subtract [tex]6c\ and\ 5c[/tex], we get

[tex]6c-5c=(6-5)c=1c[/tex]

Now, we are left with [tex]1c-6c[/tex]

Subtracting a bigger number from a smaller number will give a negative answer.

So, [tex]1c-6c=(1-6)c=-5c[/tex]

Therefore, the final answer is [tex]-5c[/tex]

Answer:

The probabilities are 0.4 and 0.6 respectively.

Step-by-step explanation:

We are given two spinning wheels with numbers on it and we have to find the probability of getting 3.

In the first wheel, there are 5 slots and the numbers are 3, 3, 2, 5 and 4.

So the probability of getting 3 =[tex]\frac{number of 3's}{total number of slots}[/tex]

                                            = [tex]\frac{2}{5}[/tex]

                                            = 0.4

In the second spinner there are three 3's and total of 5 slots.

So probability of getting 3 = [tex]\frac{number of 3's}{total number of slots}[/tex]

                                             = [tex]\frac{3}{5}[/tex]

                                             = 0.6

Hence the probabilities are 0.4 and 0.6 respectively.

Answer:

y+4=7/4(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=7/4(x-3)

y+4=7/4(x-3)

Answer:

The equation representing total food consumption in [tex]x[/tex] days can be given as:

[tex]y=12x[/tex]

where [tex]y[/tex] represents total food taken which is =250 pounds and [tex]x[/tex] represnts the number of days the food will last.

The food will last for [tex]20\frac{5}{6}[/tex] days.

Step-by-step explanation:

Total pounds of food taken at the beginning =  250 pounds

Food consumed per day = 12 pounds

Let the total food at the beginning be = [tex]y[/tex] pounds

Let number of days the food will last be = [tex]x[/tex] days

Using unitary method to find the food consumed in [tex]x[/tex] days.

If in 1 day food consumed = 12 pounds

Then, in [tex]x[/tex] days food consumption = [tex]12\times x = 12x[/tex] pounds

So,the equation representing total food consumption in [tex]x[/tex] days can be given as:

[tex]y=12x[/tex]

Total food taken =250 pounds

Plugging in [tex]y=250[/tex] in the equation:

[tex]250=12x[/tex]

Solving for  [tex]x[/tex]

Dividing both sides by 12.

[tex]\frac{250}{12}=\frac{12x}{12}[/tex]

[tex]\frac{250}{12}=x[/tex]

Simplifying fractions.

[tex]\frac{125}{6}=x[/tex]

Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.

∴ [tex]x=20\frac{5}{6}[/tex] days.

Thus, the food will last for [tex]20\frac{5}{6}[/tex] days.

Answer:

No.

Step-by-step explanation:

Because perpendicular means negative reciprocal of the slope. So 4 and -1/4 are perpendicular.

Answer:

The area of the pool increasing at the rate of 653.12[tex]cm^2/min[/tex]  when the radius is 13 cm

Step-by-step explanation:

Given:

radius of the pool increases at a rate of 8 cm/min

To Find:

How fast is the area of the pool increasing when the radius is 13 cm ?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A =[tex]\pi r^2[/tex]-----------------------------(1)

The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

[tex]\frac{d A}{d t}=\pi \cdot 2 r \cdot \frac{d r}{d t}[/tex]

we have to find  [tex]\frac{d A}{d t}[/tex] with [tex]\frac{d r}{d t}[/tex] = 8 cm/min and  r =  13cm

substituting the values

[tex]\frac{d A}{d t}=\pi \cdot 2 (13) \cdot 8[/tex]

[tex]\frac{d A}{d t}=\pi \cdot 26 \cdot 8[/tex]

[tex]\frac{d A}{d t}=\pi \cdot 208[/tex]

[tex]\frac{d A}{d t}= 208 \pi[/tex]

[tex]\frac{d A}{d t}=653.12[/tex]

Answer:

208pi cm^2/min

Step-by-step explanation:Take the derivative of the formula for Area and substitute the values

Answer:

a = -2  and  b = 7

Step-by-step explanation:

We need to solve for the value of "a" and "b".

We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.

We will use the distributive property shown below to expand the left side and simplify.

Distributive Property:  a(b-c) = ab - ac

Now, simplifying left hand side:

5x - 7(x - 1)

= 5x -7(x) -7(-1)

= 5x -7x +7

= -2x + 7

The right hand side is "ax + b".

If we match left-hand side and right-hand side, we see that:

a = -2

and

b = 7

THese are the only solution.

Answer:

Area of the circle is following:

[tex]a = \pi \: r {}^{2} [/tex]

So there is radius=1

Putting it into formula:

[tex]a = \pi \: 1 {}^{2} \\ a = \pi \\ a = 3.14[/tex]

So the answer is

[tex]3.14 \: units {}^{2} [/tex]

Good luck!

Intelligent Muslim,

From Uzbekistan.

Answer: 7 and 8

Step-by-step explanation:

The square root of 7 is 49 and the square root of 8 is 64

52 is in between the 2 consecutive integers 7 and 8

Answer: b) 7 and 8

Step-by-step explanation:

The formula for calculating the square root of non perfect square is given as :

square root of non perfect square = square root of the nearest lower perfect square + (difference between the number and the perfect square)/ 2x the perfect square.

To find the square root of 52.

The nearest lower perfect square to 52 is 49 , applying the formula , we have:

[tex]\sqrt{52}[/tex] = [tex]\sqrt{49}[/tex] - [tex]\frac{52-49}{2\sqrt{49}}[/tex]

[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{2(7)}[/tex]

[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{14}[/tex]

This shows clearly that [tex]\sqrt{52}[/tex] is between the integer 7 and 8

Answer:

[tex]B=\frac{4}{3}A[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a proportional relationship because the line passes through the origin (0,0)

Find the value of k

[tex]k=\frac{B}{A}[/tex]

take the point (3,4)

A=3,B=4

substitute

[tex]k=\frac{4}{3}[/tex]

The equation of the line is

[tex]B=\frac{4}{3}A[/tex]

Answer: 5 feet tall

Step-by-step explanation:

because he is beside the bird house he is 5 feet tall

The birdhouse's height is 20 feet, calculated using the proportion: [tex]\( \frac{h}{12} = \frac{5}{3} \).[/tex]

We can solve this problem using proportions.

Let [tex]\( h \)[/tex] be the height of the birdhouse.

According to the given information, the ratio of Jin's height to his shadow length is the same as the ratio of the birdhouse's height to its shadow length:

[tex]\[ \frac{h}{12} = \frac{5}{3} \][/tex]

Now, cross-multiply to solve for [tex]\( h \):[/tex]

[tex]\[ 3h = 5 \times 12 \][/tex]

[tex]\[ 3h = 60 \][/tex]

[tex]\[ h = \frac{60}{3} \][/tex]

[tex]\[ h = 20 \][/tex]

So, the height of the birdhouse is 20 feet.

Answer:

Inconsistent

Step-by-step explanation:

Given system of equations.

A) [tex]y-2x=4[/tex]

B) [tex]y+2=2x[/tex]

We will solve the system of equations to check the solutions and tell whether the system is consistent or inconsistent

Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]

Adding both sides by [tex]2x[/tex]

[tex]y-2x+2x=4+2x[/tex]

[tex]y=4+2x[/tex]

Substituting value of [tex]y[/tex] we got from A into equation B.

[tex]4+2x+2=2x[/tex]

Simplifying.

[tex]2x+6=2x[/tex]

Subtracting both sides by [tex]2x[/tex]

[tex]2x-2x+6=2x-2x[/tex]

[tex]6=0[/tex]

This is never true. So, we can say the system of equation has no solutions as the equations of the lines given are parallel.

Any system of equation with no solutions is termed as inconsistent.

Answer:

D) Consistent and Independent

Step-by-step explanation:

I did it on USA test prep.