Brian pays £475.29 a year on his car insurance. The insurance company reduces the price by 2.1%. How much does the insurance cost now? Give your answer rounded to 2 DP.

Answer:

The height of the pyramid is 11 cm.

Step-by-step explanation:

We are given the following in the question:

Volume of triangular pyramid = 110 cubic cm

Base of trianle,b = 10 cm

Height of triangle,h = 6 cm

Area of triangular base =

[tex]A = \dfrac{1}{2}\times b\times h\\\\A = \dfrac{1}{2}\times 10\times 6\\\\A = 30\text{ square cm}[/tex]

Volume of triangular pyramid =

[tex]V = \dfrac{1}{3}AH[/tex]

where H is the height of the pyramid, A is the area of triangular base.

Putting values, we get,

[tex]110 = \dfrac{1}{3}\times 30\times H\\\\H = \dfrac{3\times 110}{30}\\\\H = 11\text{ cm}[/tex]

Thus, height of the pyramid is 11 cm.

Answer: The probability is 0.06

Step-by-step explanation:

Urn A contains 1 red ball and 4 blue balls.

Urn B contains 2 red balls and 3 blue balls.

The probability of "selecting" a ball of a given colour is equal to the number of balls of that colour in the urn divided by the total number of balls in the urn.

Now, the probability of drawing two balls of the same color in the fourth selection needs to:

1 selection: red ball from A and one blue ball from B, the probability is:

Pa = 1/5, Pb = 3/5, P = 1/5*3/5 = 3/25

second selection: a blue ball from A and one red ball from B, the probability is (remember that now we have one ball less in each urn):

Pa = 4/4, Pb = 2/4, P = 1*2/4 = 1/2

for the third selection we have that we again need to take a blue ball from A and a red ball from B, here the probability is:

Pa = 3/3, Pb = 1/3, P = 1*1/3 = 1/3

the total probability will be the product of the 3 selections

Pt = (1/3)*(1/2)*(3/25) = 0.02

but we have 3 possible permutations of those selections, in one we took the red ball from A in the first selection, other were we took it in the second, and others where we took it in the third.

So the actual probability is 3*Pt = 3*0.02 = 0.06

From what we know about percentages and unit rates, the correct options are:

1) 100

2) 1

Suppose we have an amount A, this would be the 100%.

If we want to know how much a quantity B represents, compared to A, we have:

A = 100%

B = x

where x is a percentage, to find the value of x we compute:

x = (B/A)*100%

While there is a dependence on A, we actually are comparing the term with 100 (because A represents a 100%), so the correct option is A: 100.

We define the unit rate as the rate for a unit of something.

for example, if we know that

2 apples cost $3

The unit rate per apple is:

U = $3/2 = $1.5

Meaning that each apple costs $1.5

So to get the unit rate, we need to compare the first term with 1 (a unit). So the correct option is D.

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Answer:

c. Survey a random sample of persons within each geographic region of the city.

Step-by-step explanation:

Since the government intends to conduct the survey on a sample of the city residents. The sample must be random and a true representation of those who live in the city. It is therefore important that the survey is carried out on a random sample of persons within each geographic region of the city.

All other options are not true representation of the city's population.

The most appropriate procedure for obtaining a sample of a city's residents that will support the new Middle School is to survey a random sample of persons within each geographic region of the city.

The government of a large city needs to determine whether the city's residents will support the building of a new Middle School. When deciding on the most appropriate procedure for obtaining a sample of the city's residents, the goal is to ensure that the sample is both random and representative of the entire population. Out of the given options:

Survey a random sample of the employees and inmates at the old jail would not be representative of the entire city.

Survey every fifth person who walks into City Hall on a given day could have selection bias and might not be a random sample.

Survey a random sample of persons within each geographic region of the city would likely be the most appropriate method, as it ensures that all areas of the city are represented.

Survey the first 200 people listed in the city’s telephone directory could result in a sample that is not random, as it excludes those not listed in the directory or those with unlisted numbers.

Therefore, the best option among those presented is to survey a random sample of persons within each geographic region of the city. This would provide a more accurate reflection of the city's residents' opinions regarding the new Middle School.

Answer:

$4375

Step-by-step explanation:

What you do first is multiple $5,000 by 3.5% to get $175 after that you would then multiple $175 by 25 for each year you are getting $175 when you do all that you get $4375 in interest  

Answer:

Slope and y intercept.

Step-by-step explanation:

This is necassary to write the equation of a line in y=mx+b

m is where the slope goes, and b is the y intercept.

Alternatively, you could also write the equation for a line with a point on the line and the slope.

You would then write it in point slope formula:

y-y1=m(x-x1)

This can later be converted into slope intercept form.

Answer:

more likely

Step-by-step explanation:

the probability of 0.05 suggests there is a chance of that event happening. A probability of 0 says that such event would never happen. so despite being small the 0.05 chance is higher than the probability of 0

Answer:

More likely

Step-by-step explanation:

.05 > 0 that means no matter how small it's still going to be more likely if bigger than zero

Let x represent time taken by 20 members to paint 9000 square foot wall.

We have been given that all members of our painting team paint at the same rate. 20 members can paint a 6000 square foot wall in 24 minutes. We are asked to find the time taken by 20 members to paint 9000 square foot wall.

We will use proportions to solve our given problem.

[tex]\frac{\text{Time taken}}{\text{Area of wall painted}}=\frac{24\text{ min}}{6000\text{ ft}^2}[/tex]

[tex]\frac{x}{9000\text{ ft}^2}=\frac{24\text{ min}}{6000\text{ ft}^2}[/tex]

[tex]\frac{x}{9000\text{ ft}^2}\times 9000\text{ ft}^2=\frac{24\text{ min}}{6000\text{ ft}^2}\times 9000\text{ ft}^2[/tex]

[tex]x=\frac{24\text{ min}}{6}\times 9[/tex]

[tex]x=4\text{ min}\times 9[/tex]

[tex]x=36\text{ min}[/tex]

Therefore, it will take 36 minutes for 20 members to paint 9000 square foot wall.

Answer:

36 minutes

Step-by-step explanation:

The amount of time needed and the amount of wall to paint are directly proportional. So, when we multiply the amount of wall to paint by 4/3 (going from 6000 square feet to 9000 square feet), we multiply the time needed by 9000/6000 = 3/2. Therefore, the 20 members need 24 * 3/2 = 36 minutes to paint the 9000 square foot wall.

Answer:

62 feet

Step-by-step explanation:

Hi there,

Let's start the problem by figuing out the width of the rectangle.

let w = the width of the rectangle.

The formula for the area of a rectangle is A = l*w, so let's plug in what we know.

228 = 12w

Now, let's solve for w, the width, by dividing both sides by 12

w = 19; The width is 19 feet.

Now, we have our length, 12 feet, and our width 19 feet.

So, we should now use the formula for perimiter to find the perimiter of this rectangle. The formula is P = W + W + L + L

Let's plug in the numbers

P = 12 + 12 + 19 + 19

P = 62 feet

Hope this helps! Stay safe!

- Emily

Answer:

Step-by-step explanation:

We would determine the mean an standard deviation first

Mean = (107 + 92 + 97 + 95 + 105 + 101 + 91 + 99 + 95 + 104)/10 = 98.6

Standard deviation = √(summation(x - mean)/n

n = 10

Summation(x - mean) = (107 - 98.6)^2 + (92 - 98.6)^2 + (97 - 96.6)^2 + (95 - 98.6)^2 + (105 - 98.6)^2 + (101 - 98.6)^2 + (91 - 98.6)^2 + (99 - 98.6)^2 + (95 - 98.6)^2 + (104 - 98.6)^2 = 274

Standard deviation = √(274/10) = 5.23

The confidence interval is used to determine the range of values that could possibly contain a population parameter (population mean)

Confidence interval is written in the form,

(Point estimate - margin of error, Point estimate + margin of error)

The sample mean, x is the point estimate for the population mean.

We will use the t distribution because the sample size is small and the population standard deviation is not given.

Degree of freedom, df = 10 - 1 = 9

α = 1 - 0.99 = 0.01

z α/2 = 0.01/2 = 0.005

The area to the right of z 0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995. Using the t distribution table,

z = 3.25

Margin of error = z × s/√n

Where

s = sample standard Deviation = 5.23

Margin of error = 3.25 × 5.23/√10 = 5.38

Confidence interval = sample mean(point estimate) ± z × σ/√n

The lower boundary of the confidence interval is

98.6 - 5.38 = 93.22

The upper boundary of the confidence interval is

98.6 + 5.38 = 103.98

We estimate with 99% confidence that the mean weekly child care cost of their employees is between $93.22 and $103.98

Also,

99% of the confidence intervals constructed in this way would contain the true value for the population mean of mean weekly child care cost of their employees.

The 99% confidence interval for the average weekly childcare cost based on this sample data is [$94.6, $102.6], which means we're 99% certain the true average cost falls within this range.

When we are talking about a confidence interval for the population mean, we're trying to determine a range within which we're confident the true average child care cost falls, given the data we have from a sample of employees. To do this, we first have to calculate the mean (or average) child care cost and the standard deviation of our sample.

The mean weekly child care cost would be ($107 + $92 + $97 + $95 + $105 + $101 + $91 + $99 + $95 + $104) / 10 = $98.6. To calculate the standard deviation, you would subtract each data point from the mean, square the results, find the average of these squared differences, and finally take the square root. In this case, the standard deviation equates to ~5.27. Now we can use these values to calculate the confidence interval. For a 99% confidence interval with a sample size of 10, the appropriate t-value from the t-distribution table is 3.25. The confidence interval would therefore be Mean +/- t-value*(standard deviation/sqrt(n)). So the interval would be 98.6 +/- 3.25*(5.27/sqrt(10)). This calculates to an interval of [94.6, 102.6]. That means we're 99% confident the true average weekly child care cost falls between $94.6 and $102.6.

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Answer:Demography is the statistical study of the size, structure, and distribution of a population. This includes studying the number of births and deaths a population has as well as how that population changes over time.

Step-by-step explanation:

Answer:

Paul has negative worth of $2,900

His statement is invalid as he did not consider all assets and debts in aggregate.

Step-by-step explanation:

The net worth of Paul is the total asset owned by him less the total of debts owed by him.

Paul's total assets can computed thus:

Stock portfolio                 $21,000

Home worth                     $365,000

Car worth                          $19,000

Total assets                       $405,000

Paul's total debts can be computed as follows:

Mortgage loan                     $362,000

Car loan                                $16,250

credit card debt                     $11,750

Student loan                          $17,900

Total debts                             $407,900

The amount of debts owed by Paul is $2,900($405,000-$407,900) more than his asset worth,which implies that Paul is indebted to the tune of $2,900,hence has negative worth.

Paul's statement is false; he has a negative net worth.

Paul's statement is true, he has a positive net worth.

To calculate Paul's net worth, we subtract his debts from the total value of his assets:

By adding up all his equities, we get $3,000 + $2,750 + (-$8,650) = -$2,900. Therefore, Paul has a negative net worth and his statement is false.

Answer:

the answer is 22 units,hope it helps

The length of line segment AD is 22 units.

ABCD is a kite.

Kite A B C D is shown.

Sides A B and B C are congruent.

The length of A B is 14.

Sides C D and A D are congruent.

The length of C D is 22.

We have to determine the length of line segment AD.

A line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Therefore we can say that,

AD=DC

Therefore the length of line segment AD is 22 units.

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Answer:

24 ÷ 4

Step-by-step explanation:

Putting something into fourths is putting into 4 parts. If you divide 24 by 4 you get 6. 6 equals 1/4 of 24. To check your work add 6 together 4 times.

Answer:

[tex]y-1=\frac{1}{12} (x-7)[/tex]

Step-by-step explanation:

Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex] , where (x_1, y_1) is the point given and m is the slope.

The problem gives us two points, actually: (7, 1) and (-5, 0); the second one is the x-intercept because x-intercepts always have a y-coordinates of 0. We can use these two points to find the slope, which is just change in y over change in x: [tex]\frac{1-0}{7-(-5)}=\frac{1}{12}[/tex]. So, the slope = m = 1/12.

Now, we have our point (7, 1) and the slope 1/12, so just plug these into the above format: [tex]y-1=\frac{1}{12} (x-7)[/tex]

Hope this helps!

Answer:

y - 1 = (1/12)(x - 7)

y = (1/12)(x + 5)

You can use either of these

Step-by-step explanation:

Slope using (-5,0) and (7,1)

m = (0-1)/(-5-7) = -1/-12

m = 1/12

y - 1 = (1/12)(x - 7)

Or,

y - 0 = (1/12)(x - -5)

y = (1/12)(x + 5)

Answer:

Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles below are similar, compare their corresponding sides

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Use Law of Sines.

Find third angle, which is 26 degrees.

x/sin28=8.2/sin26

cross multiply, which becomes

xsin26=8.2sin28

then divide sin26 both sides

x=8.78

Answer:

B) 98

Step-by-step explanation:

98+5=103

103+5=108

108+5=113

113+5=118

Answer:

Minimum number of pennies = 10

Step-by-step explanation:

Given:

Maximum number of coins Hannah have = 25

Total number of of nickels (coins) she has = 11

Total value of the combined coins = $ 0.65

We have to find the minimum number of pennies.

Let the number of pennies be "p"  and no. of nickels be "n".

Note:

Value of 1 penny = $ 0.01

Value of 1 nickel = $ 0.05

Arranging the above situation in terms of equations:

According to their quantities.

⇒ [tex]n+p\leq 25[/tex]  and [tex]11+p\leq 25[/tex] so [tex]p\leq 14[/tex]

According to their values.

⇒ [tex]0.05(n)+0.01(p)\leq \$\ 0.65[/tex]

⇒ [tex]0.05(11)+0.01(p)\leq \$\ 0.65[/tex]

⇒ [tex]\$\ 0.55+0.01(p)\leq \$\ 0.65[/tex]

⇒ [tex]0.01(p)\leq \$\ 0.65-\$\ 0.55[/tex]

⇒ [tex]0.01(p)\leq \$\ 0.10[/tex]

⇒ [tex](p)\leq\frac{ \$\ 0.10}{0.01}[/tex]

⇒ [tex](p)\leq 10[/tex]

Minimum number of pennies :

⇒ [tex](p)\leq 10[/tex] which also satisfies [tex]p\leq 14[/tex]

Therefore :

⇒ [tex]p=10[/tex]

Plugging p= 10 we can verify the values.

⇒ [tex]0.05(11)+0.01(10)\leq \$\ 0.65[/tex]

⇒ [tex]0.55+0.10\leq \$\ 0.65[/tex]

⇒ [tex]\$\ 0.65\leq \$\ 0.65[/tex]

So,

Minimum number of pennies Hannah have = 10

Final answer:

Hannah can have a minimum of 10 pennies along with her 11 nickels to make at least $0.65, while having a maximum of 25 coins in total.

Explanation:

Hannah has a maximum of 25 coins and among them, she has 11 nickels. Since she has a minimum combined worth of $0.65, we can calculate the minimum number of pennies she could have. One nickel is worth $0.05, so 11 nickels have a combined worth of $0.55 (11 times $0.05). To reach at least $0.65, we need at least $0.10 more.

A penny is worth $0.01, so to make up the additional $0.10, Hannah would need a minimum of 10 pennies. Therefore, with 11 nickels already accounted for, and the rest being pennies to reach $0.65, Hannah could have a minimum of 10 pennies. She cannot have more than 25 coins in total, so the number of pennies must also not exceed the limit of 25 total coins when added to the number of nickels she has. Since 11+10=21, this is less than the maximum of 25 coins, and thus, it is possible for Hannah to have a minimum of 10 pennies.

Answer:

$342.7

Step-by-step explanation:

Let the sale price be x.

So,

x - 30% of x = $239.89

x - 30/100*x = 239.89

(100x-30x)/100 = 239.89

70x = 239.89 *100

x = 23989/70

x = $342.7

sale price = $342.7

Answer:

342.70

Step-by-step explanation:

Since 100%-30%=70% our equation will be:

0.70x=239.89

x=original price

0.70x=239.89

/0.70   /0.70

Divide both sides by 0.70

x=342.7

$342.70

Step-by-step explanation:

5/7 < 9/11

Square both to get

(25/49) < (81/121)

----------------------

Least common multiple of the fraction denominators is 81*121 because they

share no factors.

---------------------

Rewrite the fractions as

((25*121)/(49/121)) < (81*49)/(81*49))

Simplify to get:

3025/5929 < 3969/5929

-------------

pick some numbers between 3025 and 3969

like 3127, 3255, 3659

------------------------

Form the fractions: 3127/5929, 3255/5929, 3659/5929

----------------------

Take the square root of each:

sqrt[3127/5929], sqrt[3255/5929], sqrt[3659/5929]

------------------------

Each of these will be irrational numbers between 5/7 and 9/11

Answer:

Step-by-step explanation:

hello :

5/7 ≅ 0.71                     9/11≅0.82

3 irrational number 5/7 between 9/11​ are :

72/100  ,   73/100  , 74/100

Answer:

x>1

Step-by-step explanation:

2x+3≥7 OR 2x+9>11

Solve each one separately

2x+3≥7

Subtract 3 from each side

2x+3-3≥7-3

2x ≥ 4

Divide each side by 2

2x/2≥ 4/2

x≥ 2

2x+9>11

Subtract 9 from each side

2x+9-9>11-9

2x > 2

Divide by 2

2x/2>2/2

x>1

Put them back together

x>1  or x≥ 2

Since the x>1 is less restrictive and we are using or, we use that as our answer

Answer:

A

Step-by-step explanation:

the explanation is in the picture

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Answer:

[tex]A' = (1.707,-5.121)[/tex]

The new point belongs to the fourth quadrant.

Step-by-step explanation:

The relative vector is:

[tex]\vec r = (2-1,-1+3)[/tex]

[tex]\vec r = (1, 2)[/tex]

The length of the vector is:

[tex]\|\vec r\| = \sqrt{1^{2}+2^{2}}[/tex]

[tex]\|\vec r\| = \sqrt{5}[/tex]

The angle with respect to the horizontal (+x direction) is:

[tex]\theta = \tan^{-1} \frac{2}{1}[/tex]

[tex]\theta \approx 63.435^{\textdegree}[/tex]

The new angle with respect to the horizontal (+x direction) is:

[tex]\theta' = 63.435^{\textdegree}-135^{\textdegree}[/tex]

[tex]\theta' = -71.565^{\textdegree}[/tex]

The new point is:

[tex]A' = (1 + \sqrt{5}\cdot \cos (-71.565^{\textdegree}),-3 + \sqrt{5}\cdot \sin(-71.565^{\textdegree}))[/tex]

[tex]A' = (1.707,-5.121)[/tex]

The new point belongs to the fourth quadrant.

Answer:

The new point A location is (1.69, -51267)

The quadrant is 4th quadrant

Step-by-step explanation:

Here we have a point rotating about another point, therefore we have;

Let point (1, -3) be = P

Therefore the length of line AP is given by the following relation;

[tex]AP =\sqrt{(2-1)^2+(-1-(-3))^2} = \sqrt{5}[/tex]

With angle

[tex]Actan (\frac{-1 -(-3)}{2-1}) = Actan( 2) = 63^{\circ} \ due \ North \ of \ East[/tex]

Rotating through 135° clockwise gives;

63° - 135° = 72° Due south of east from P

The coordinates is then given as follows;

y coordinates = -3 - sin 72×√5 = -5.1267

The x coordinates will be 1 + cos 72×√5 = 1.69

The coordinate of the new point A location = (1.69, -51267)

Therefore the quadrant remains the 4th quadrant.

Answer:

a = -1 and a = 4

Step-by-step explanation:

∛a³ + 4a² -3 = a + 1    

a³ + 4a² - 3 = (a + 1)³

a³ + 4a² -3 = a³ + 3a² + 3a + 1

a² - 3a -4

(a + 1) (a - 4)

a + 1 = 0

a = -1

a -4 = 0

a = 4

Answer:

a = -1, a=4

Step-by-step explanation:

( a^3 +4a^2 -3) ^1/3 = a+1

We need to cube each side to get rid of the radical

( a^3 +4a^2 -3) ^1/3 ^3 = (a+1)^3

( a^3 +4a^2 -3)  = (a+1)^3

Using the formula  (x+y)^3=x^3+3x^2y+3xy^2+y^3

we can expand (a+1)^3 to a^3+3a^2+3a+1

( a^3 +4a^2 -3)  =a^3+3a^2+3a+1

Moving all the terms to the left hand side

( a^3 +4a^2 -3) -(a^3+3a^2+3a+1)   =a^3+3a^2+3a+1-(a^3+3a^2+3a+1)

Distribute the minus sign

( a^3 +4a^2 -3) -a^3-3a^2-3a-1   =0

Combine like terms

a^2 -3a-4 =0

Factor

(a-4) (a+1) =0

Using the zero product property

a-4 =0   a+1=0

a=4  a=-1

Check since we cubed each side for extraneous solutions

( a^3 +4a^2 -3) ^1/3 = a+1

a=4

( 4^3 +4 *4^2 -3) ^1/3 = 4+1

(64 +64 -3) ^1/3 =5

125 ^1/3 =5

5=5  True

a=-1

( (-1)^3 +4 *(-1)^2 -3) ^1/3 = -1+1

(-1 +4 -3) ^1/3 =0

0 ^1/3 =0

0=0  True

Answer:

2 distinct real number zeros

Step-by-step explanation:

The discriminant b^2 - 4ac

= (-17)^2 - 4*4*3

= 241

So it has 2 distinct roots.

The gradient of the line that is perpendicular to the line 2y = 3 + 5x is found to be -0.4, after converting the given equation to slope-intercept form and determining the negative reciprocal of the original slope.

To find the gradient of a line that is perpendicular to the given line 2y = 3 + 5x, we first need to put the given equation in slope-intercept form (y = mx + b). By dividing everything by 2, we get y = 2.5x + 1.5, where the gradient (or slope) of this line is 2.5. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line perpendicular to the given one is -1/2.5, which simplifies to -0.4. Therefore, the gradient of the line that is perpendicular to the line 2y = 3 + 5x is -0.4.

Answer:

10

Step-by-step explanation:

Based on the concept of measurement and the information given in the question, the liters that made 1 dekaliter is 10 liters.

Measurement is a term that is used to describe the process of associating numbers with physical quantities and phenomena.

Generally, the process of measurement includes the unit conversion, thereby making the same property as a different unit of measurement. For instance, liters can be expressed in dekaliters.

In this case, 10 liters is equivalent to 1 dekaliter

Hence, in this case, it is concluded he correct answer is option B. 10 liters.

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Answer:

He is not correct

Step-by-step explanation:

70%=70/100= 0.7

70% of 30 =0.7x 30= 21 not 24