The level of water in a dam was decreasing by 20% each day. If the level of water was 1500cm,what was the level after two days?

Answer:

They are not perpendicular because their slopes are not negative reciprocals.

Step-by-step explanation:

Well first we need to find slope.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

Line HJ)

(-4,-2) , (0,4)

y2 is 4 y1 is -2, so 4 - -2 = 6

0 - -4 = 4

6/4 -> 3/2

Due to the point (0,4) having no x value 4 is the y intercept.

Hence, y = 3/2x + 4 is the slope of line HJ

Line FG)

(-4,1) , (0,-2)

y2 is -2 y1 is 1, so -2 - 1 = -3

0- -4 = 4

Because (0,-2) is missing an x value -2 is the y intercept,

Equation: y = -3/4x - 2

They are not perpendicular because their slopes are not negative reciprocals.

The slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

Recall:

Given that lines HJ (blue line) and FG (red line) are on a coordinate plane as shown in the diagram attached below, let's find their slope:

Slope of line HJ:

[tex]Slope (m) = \frac{-2 - 4}{-4 -0} = \frac{-6}{-4} = \frac{3}{2}[/tex]

Slope of line FG:

[tex]Slope (m) = \frac{-2 - 1}{0-(-4)} = \frac{-3}{4} = -\frac{3}{4}[/tex]

Therefore, the slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

Learn more here:

https://brainly.com/question/18975049

Answer:

[tex]AB = 10 units[/tex]

Step-by-step explanation:

The line of segment AB can be calculated using distance formula, [tex] d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} [/tex] , to calculate the distance between point A(6, 2) and point B(0, 10).

A(6, 2) can be (x1, y1),

B(0, 10) can be (x2, y2)

[tex] d = \sqrt{(0 - 6)^2 + (10 - 2)^2} [/tex]

[tex] d = \sqrt{(-6)^2 + (8)^2} [/tex]

[tex] d = \sqrt{36 + 64} [/tex]

[tex] d = \sqrt{100} [/tex]

[tex] d = 10 [/tex]

Answer:

k=5

a= -5

Step-by-step explanation:

if the polynomial x^4-6x^3+16x^2-25x+10 is divided by x^2-2x+k the remainder comes out to be x+a,find k and a

Solution

x^4-6x^3+16x^2-25x+10 / x^2-2x+k = x-a

We have,

(4k-25+16-2k)x+[10-k(8-k)] = x+a

(2k+9)x + (10-8k+k^2)=x+a

2k-9=1

2k=1+9

2k=10

Divide both sides by 2

2k/2=10/2

k=5

And

10-8k+k^2=a

10-8(5)+(5^2)=a

10-40+25=a

-5=a

Therefore, a=-5

x^4-6x^3+16x^2-25x+10 divided by x^2-2x+5 = x-5

Answer:

18

Step-by-step explanation:

j represents Jeffrey's age

j - 5 represents brother

Jeffrey is 23 so j = 23

j-5 = 23-5 =18 = brother

Answer:

J=23

Then J-5= his brother

substitute and u will find j-5=23-5

=18 so his brother age is 18 years old

Step-by-step explanation:

Answer: The probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Jennifer wants to visit 4 different cities A,B,C and D on her vacation.

If she visits in an order , total such orders will be [tex]4![/tex] = 4 x 2 x 3 x 1 =24.

Since probability = [tex]\dfrac{\text{Favourable outcomes}}{\text{total outcomes}}[/tex]

In this case favorable outcomes ( ABCD ,  DCBA)=  2

Total outcomes = 24

Required probability = [tex]\dfrac{2}{24}=\dfrac{1}{12}[/tex]

Hence, the probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Answer:

y = 10

Step-by-step explanation:

y = 2x + 6

Let x  =2

y = 2*2 +6

y = 4+6

y = 10

Answer:

Step-by-step explanation:

[tex]y = 2x + 6 \\ x = 2 \\ y = 2(2) + 6 \\ y = 4 + 6[/tex]

[tex]y = 10[/tex]

Answer:

10

Step-by-step explanation:

let n represent the number

sum means to add

product means multiply

n + 9 < n • 4

if you fill in 10 for your variable n you will get:

19 < 40

10 plus 9 is 19

10 by 4 is 40

and

because 19 is less than 40 that statement is true

Answer:

Option B

Step-by-step explanation:

When we compare the number of shirt with it's cost, we find out that 8 shirts cost $120.

For more understanding, see the attached file.

Answer:

Option (A)

Step-by-step explanation:

By satisfying the equation of a function 'f' by each coordinates given in the options we can get the point which lies on the graph of f(x) = [tex]2\times (5)^x[/tex]

Option (A). (1, 10)

f(1) = [tex]2\times (5)^1[/tex]

10 = 10

True.

Therefore, point (1, 10) lies on the graph.

Option (B). (0, 10)

f(0) = [tex]2\times 5^0[/tex]

10 = 2

Not true.

Therefore, point (0, 10) doesn't lie on the graph.

Option (C). (10, 1)

f(10) = [tex]2\times 5^{10}[/tex]

1 = 19531250

Not true.

Therefore, point (10, 1) doesn't lie on the graph.

Option (D). (0, 0)

f(0) = [tex]2\times 5^0[/tex]

0 = 2

Not True.

Point (0, 0) doesn't lie on the graph.

Option (A) will be the answer.

I believe it is C, as the graphs do look the same.

Answer:

B.

Step-by-step explanation:

Again, to find the equation of the line, we need to find the slope and y-intercept. First, let's find the slope. Let (-1,5) be x₁ and y₁ respectively and (1,3) be x₂ and y₂, respectively. So:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{1--1}=\frac{-2}{2}=-1[/tex]

So the slope is -1.

Now, to find the y-intercept, we can use the point-slope form. I'm going to keep using (-1,5) as the coordinate. Thus:

[tex]y-y_1=m(x-x_1)\\y-5=-1(x-(-1))\\y-5=-(x+1)\\y-5=-x-1\\y=-x+4[/tex]

This is slope-intercept form. We want the answer to be in standard form, where:

[tex]Ax+By=C[/tex]

A, B, and C are integers (and, conventionally, A is positive).

Thus, we need to rearrange the terms:

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

The answer is B.

Answer:

Average speed

= 5 5/6 mph , or

= 5.83 mph (to 2 decimals)

Step-by-step explanation:

Average speed is total distance divided by the total time it takes to cover the given distance.

Since uphill = 5 mph, and downhill = 7 mph, we know the average speed is between 5 and 7 mph.

Let

x = distance uphill, and also distance downhill.

Total distance = 2x miles

Total time = x/5 + x/7 hours  = 12x/35 hours

Average speed

= total distance/total time

= 2x / (12x/35) mph

= 70x / 12x

= 5 5/6 mph

= 5.83 mph (to 2 decimals)

Answer:

[tex]\boxed{\mathrm{False}}[/tex]

Step-by-step explanation:

[tex](p-q)^2[/tex]

[tex](p-q)(p-q)[/tex]

Use FOIL method.

[tex]p^2-pq-pq +q^2[/tex]

[tex]p^2-2pq +q^2[/tex]

Answer:

135.5

hope this helps :)

Answer:

Let x be the original number.  Also, please note that a percentage can be written as a decimal(54%=0.54), and that a percentage increase is the percent +1(A 54% increase is x*1.54), and that a percentage decrease is 1- the percent(A 54% decrease is 0.46)

1)1.8*0.6x= 1.08x (greater than the original)

2).6666*1.5x=0.9999x (same as original)(.999999 is essentially 1, because .3333 is not equal to 1/3)

3)x+25-30 = x-5 (less than original)

4)0.5*2x=x (same as original)

5)1.2*.75x=.9x (less than original)

Hope it helps <3

Greater than the original.

Same as the original.

Less than the original.

Same as the original.

Less than the original.

To check all the scenarios, let's say that the original value is 100.

An 80% increase followed by a 40% decrease:

100 * (1 + 0.8) = 100 * 1.8 = 180.

180 * (1 - 0.4) = 180 * 0.6 = 108.

It is greater than the original.

A 33 1/3% decrease followed by a 50% increase:

100 * (1 - 0.33333333) = 100 * 0.6666666667 = 66.666666667.

66.6666666667 * (1 + 0.5) = 66.666666667 * (3/2) = 100.

It is the same as the original.

A $25 increase followed by a $30 decrease:

100 + 25 = 125.

125 - 30 = 95.

It is less than the original.

A 50% decrease followed by a 100% increase:

100 * (1 - 0.5) = 100 * 0.5 = 50.

50 * (1 + 1) = 50 * 2 = 100.

It is the same as the original.

A 20% increase followed by a 25% decrease:

100 * (1 + 0.2) = 100 * 1.2 = 120.

120 * (1 - 0.25) = 120 * 0.75 = 90.

It is less than the original.

You are correct. The higher the standard deviation is, the more spread out the data set will be. Nice work.

Answer:

Hey there! The correct answer is A. Data set C.

---

Standard deviation is simply defined as the spread of a data set in relation to the mean of the data set. The standard deviation can be calculated with a formula as shown below.

[tex]\displaystyle \sigma = \sqrt{\frac{\Sigma(x_i-\mu)^2}{N}[/tex]

Each variable has a significant meaning for this formula.

With this information, we can find the standard deviation of a data set.

Generally speaking, statisticians want a standard deviation that is on the lower end so that conclusions can be drawn about the data that was observed.

If a standard deviation is large, that means that most of the data is quite far from the mean and the data usually disproves a hypothesis. This is undesirable since the original hypothesis cannot be proven with this experiment.

When the standard deviation is quite low, this points to data that can be relied upon since it fulfills the initial requirement to prove the hypothesis.

Therefore, since the highest standard deviation correlates with the most spread out data, A. Data set C is the answer.

Answer:

2, 3

Step-by-step explanation:

5 lies between 2 perfect squares 4 and 9.

√4 < √5 < √9

√4 = 2

√9 = 3

2 < √5 < 3

Answer:

Ok, a system of equations means that we have a given number of equations with the same solutions.

If we only have tables, this means that we need to have one table for each equation:

For example, if we are working only with two variables, x and y, in those tables we can see the pints (x, y) that belong to each equation.

Now, a point (x, y) will be a solution of the system of equations only if it belongs to the data table for each equation

This would mean that if we graph those data sets, the graphs will intersect at the point (x, y) that belongs to all the tables of data.

Other way may be using the data in the tables to construct the equations, but you said that you only want to use the tables, so this method can be discarded.

Answer:

did you already try A???

Answer:

Probability : [tex]\frac{5}{33}[/tex]

Step-by-step explanation:

The probability of drawing an orange on the first attempt would be 5 / 12, considering that in this first attempt their are 5 oranges present out of a total of 12 fruits. Now after that fruit is chosen their are 4 out of 11 oranges present, such that the probability of drawing an orange on the second attempt would be 4 / 11.

Probability of choosing an orange on the first try : [tex]5 / 12[/tex]

Probability of choosing an orange on the second try : [tex]4 / 11[/tex]

Probability of selecting two oranges in a row ( blindfolded ) : [tex]5 / 12 * 4 / 11[/tex]

[tex]\frac{5}{12}\cdot \frac{4}{11}[/tex] ( cross cancel common factor 4 )

[tex]\frac{5}{3}\cdot \frac{1}{11}[/tex] ( multiply fractions )

[tex]\frac{5\cdot \:1}{3\cdot \:11}[/tex] = [tex]\frac{5}{3\cdot \:11}[/tex] = [tex]\frac{5}{33}[/tex] - the probability of selecting two oranges in a row blindfolded, is [tex]\frac{5}{33}[/tex].

Answer:

Step-by-step explanation:

each term has h^1

each term's coefficient is divisible by 12

12h( 3, h^5, 4h^4)

Answer:

Step-by-step explanation:

The gray shadowed area is below descending function and the line is dashed.

It means coefficient x is m<0 and the sign of inequality is y <  

So the inequality wich  fit it is  y < -1/2x + 2

The blue shadowed area is above ascending function and the line is uninterrupted.

It means coefficient x is m>0 and the sign of inequality is y ≥

So the second inequality of system (y ≥ 3x - 1)  also match.

The system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

The standard equation of a line is expressed as y = mx + b;

For the blue line, the y-intercept is at y = -1. For the slope passing through (0, -1) and (2, 5):

m = 5+1/2-0

m= 6/2

m = 3

The equation of the line is y = 3x - 1

Since the line is dashed and the left part shaded, the inequality expression will be y < 3x - 1

For the black line, the y-intercept is at y = 2. For the slope passing through (0, 2) and (4, 0):

m = 0-2/4-0

m= -2/4

m = -1/2

The equation of the line is y = -1/2x + 2

Since the line is solid and the lower part shaded, the inequality expression will be y ≤ -1/2x + 2

Hence the system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2  and y < 3x - 1​

Learn more on inequality graph here: https://brainly.com/question/9774970

Answer:

Step-by-step explanation:

Hello!

X: content of sugar of a sample of cereal.

Data set:

0.03, 0.24, 0.30, 0.47, 0.43, 0.07, 0.47, 0.13, 0.44, 0.39, 0.48, 0.17, 0.13, 0.09, 0.45, 0.43

n= 16

[tex]\frac{}{X}[/tex]= 0.295g

S= 0.17g

You have to test if the mean sugar content is less than 0.3g

H₀: μ ≥ 0.3

H₁: μ < 0.3

α: 0.05

Assuming that the variable has a normal distribution, you have to conduct a t test:

[tex]t= \frac{\frac{}{X}-Mu }{\frac{S}{\sqrt{n} } } ~~t_{n-1}[/tex]

[tex]t_{H_0}= \frac{0.295-0.30}{\frac{0.17}{\sqrt{16} } } = -0.12[/tex]

p-value: 0.4533

The p-value is greater than α, the decision is to not reject the null hypothesis.

At a 5% significance level the decision is to not reject the null hypothesis. You can conclude that the average sugar content of the cereal is equal or greater than 0.3g of sugar per gram of cereal.

I hope this helps!

ok                                                         its 11 sqrt 6                                    

because if sqrt 6 is x, and 5x +6x=11x

so its 11 sqrt 6              

so first day and so on

7, 10, 13,....

as you can see it's an arithmetic progression

so sum for nth term= n/2 { 2a + (n-1) d}

it's the sum of the 7th term

so

7/2 { 7 ×2 + ( 7-1) 3}

7/2 × 32

7× 16

112 fishes

Answer:

I think the answer is 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

first term = a = 3

common ratio = 2nd term ÷ first term

                       = 12 ÷ 3

                      r = 4

[tex]a_{n} = ar^{n-1}\\\\a_{10}=3*4^{9}\\\\\\ = 3 * 262144\\\\= 786432[/tex]

Answer:

a) 294

b) 180

c) 75

d) 168

e) 105

Step-by-step explanation:

Given the numbers 0, 1, 2, 3, 4, 5 and 6.

Part A)

How many 3 digit numbers can be formed ?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For unit's place, any of the numbers can be used i.e. 7 options.

For ten's place, any of the numbers can be used i.e. 7 options.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Total number of ways = [tex]7 \times 7 \times 6[/tex] = 294

Part B:

How many 3 digit numbers can be formed if repetition not allowed?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Now, one digit used, So For unit's place, any of the numbers can be used i.e. 6 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = [tex]6 \times 6 \times 5[/tex] = 180

Part C)

How many odd numbers if each digit used only once ?

Solution:

For a number to be odd, the last digit must be odd i.e. unit's place can have only one of the digits from 1, 3 and 5.

Number of options for unit's place = 3

Now, one digit used and 0 can not be at hundred's place So For hundred's place, any of the numbers can be used i.e. 5 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = [tex]3 \times 5 \times 5[/tex] = 75

Part d)

How many numbers greater than 330 ?

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 7

Number of options for unit's place = 7

Total number of ways = [tex]3 \times 7 \times 7[/tex] = 147

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 7

Total number of ways = [tex]1 \times 3 \times 7[/tex] = 21

Total number of required ways = 147 + 21 = 168

Part e)

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 6

Number of options for unit's place = 5

Total number of ways = [tex]3 \times 6 \times 5[/tex] = 90

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 5

Total number of ways = [tex]1 \times 3 \times 5[/tex] = 15

Total number of required ways = 90 + 15 = 105

Answer:

17 cans

Step-by-step explanation:

18 cans

7 are taken away

18-7 =11

Then we put 6 back on

11+6 = 17

There are now 17 cans

Answer:

p(x) = (x + 1) (x - 3) (x + 2)

Step-by-step explanation:

x³ - 7x - 6

(x+1) (x² - x - 6) found by doing long division

(x+1) ( x - 3) (x + 2) are the factors

The polynomial p(x) as a product of linear factors is; p(x) = (x + 1) (x - 3) (x + 2)

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

We are given the polynomial as;

x³ - 7x - 6

Then we found by doing long division;

(x+1) (x² - x - 6)

(x+1) ( x - 3) (x + 2)

These are the factors.

Hence, The polynomial p(x) as a product of linear factors is; p(x) = (x + 1) (x - 3) (x + 2)

Learn more about polynomials here:

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Answer:

80 in²

Step-by-step explanation:

8/10 = x/100

x = 80

Answer:

Step-by-step explanation:

what do u see!????????