Dan paid $34.30 for a sweater the price included a 40% markup what is the cost of the sweater before the markup

Answer:

∠6 > ∠3 is TRUE.

Step-by-step explanation:

We know that acute angle is less than 90 degree while obtuse angle is more than 90 degree. By looking at the given angles, we can easily determine which angle is obtuse or acute. then we can decide which angle is bigger to find the answer.

∠10 > ∠7

FALSE;

Because∠10 is acute while ∠7 is obtuse.

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

∠6 > ∠3

TRUE;

Because∠3 is acute while ∠6 is obtuse.

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

∠9 > ∠11

FALSE;

Because∠9 is acute while ∠11 is obtuse.

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

∠8 > ∠11

FALSE;

Because∠8 is acute while ∠11 is obtuse.

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

Answer:

Step-by-step explanation:

If ΔABC and ΔDEF are similar, then

AB is proportional to DE

BC is proportional to EF

CA is proportional to FD

and

angles A and D are congruent

angles B and E are congruent

angles C and F are congruent

Answer:

B.)Segment BC is proportional to segment EF, and angles A and D are congruent.

Step-by-step explanation:

Answer:

1.  P ( tails) = 1/2

2.P (number greater than 4)   = 1/3

3.  P (2 die sum to 8) = 5/36

Step-by-step explanation:

A coin only has 2 possibilities, head or tails, and they are equally likely

So the probability of getting a tails is 1/2

P ( tails) = 1/2

A die has the numbers 1,2,3,4,5,6 .  There are 2 numbers greater than 4.  They are 5 and 6.  So there are 2 of the 6 choices that work.

P (number greater than 4)  = 2/6  = 1/3

See the dice chart

There are 36 possibilities when you roll the die.

There are 5 that sum to 8

P (2 die sum to 8) = 5/36

Answer:

Guy above is correct

Step-by-step explanation:

Answer:

32 houses will have a pool

Step-by-step explanation:

40% of 80 is 32

Answer:

D

Step-by-step explanation:

An inequality is an expression which means more than one number is a solution. We graph the solutions on a number line to show all possible values. We graph using circles and arrows.

This is a filled in circle on -2 so this is [tex]\leq or \geq[/tex]. This means only answers C and D are options.

Answer D points to the right.

Answer:

The answer is D

Step-by-step explanation:

MrsStrong was correct!!!! Thank you

Answer:

150 feet

Step-by-step explanation:

in order to find the solution we have to take the L.C.M of 25 and 30

L.C.M of 25 and 30 is 150

so after 150 feet , they will both fall down

Answer: They will both fall down after 150 feet.

Step-by-step explanation:

Hi, to answer this question we have to find the least common multiple (LCM)

of 30 and 25:

To obtain the multiple of a number we have to multiply that number by another number (not zero) in the multiplication table order (by 1,by 2,by 3,etc)

30,60,90,120,150

25,50,75,100,125,150

The LCM is a number that appears on both lists, and is the smallest.

They will both fall down after 150 feet.

Feel free to ask for more if needed or if you did not understand something.

Answer:

The answer is A. 1 1/2

Step-by-step explanation:

You have 3 5/12  - 2 1/3

1/3 of 12 is 4.

So change 2 1/3 to 2 4/12

3 5/12 - 2 4/12 = 1 1/2

I hope this helps!

Cheers, July.

Answer:

25

Step-by-step explanation:

There are 100 capsules and she can only buy 1/4

Multiply 100 * 1/4

100 * 1/4 =

100/4

25

We can check  by  calculating how many she leaves at the store

100 * 3/4 =

300 /4 = 75

The ones she bought , plus the ones she left behind should be 100 capsules

25+ 75 = 100

100 = 100

Check

Answer:

HELLO :

f(4) = -1/2(4)+5 = -2+5=3

Answer:

a. -2, even mult. and 1, odd mult.

b.[tex](x+2)^2(x-1)[/tex]

c. Odd degree of 3 or higher, likely higher due to the turns in the graph.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -2,1

We can write them in intercept or factored form as (x-1) and (x+2).  

Because the graph never crosses the x-axis at x=-2 the zero has an even multiplicity of at least 2.  The opposite is true for x=1 because it crosses. Therefore it has an odd multiplicity of at least 1.

The graph is a sideways s shape and ends up so is positive.  

This means the function has a degree of 3 or higher with the degree being odd.

Answer:

10.82 is the answer

Step-by-step explanation:

The x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.

To find the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4, we can use the slope formula:

slope = (change in y) / (change in x)

Given that the slope is -4 and the two points are (x, -9) and (0, 1), we can plug the values into the slope formula:

-4 = (-9 - 1) / (x - 0)

Now, simplify the equation:

-4 = -10 / x

Now, cross-multiply:

-4x = -10

Now, solve for x by dividing both sides by -4:

x = -10 / -4

x = 5/2

So, the x-value that makes the line through the points (x, -9) and (0, 1) have a slope of -4 is x = 5/2 or 2.5.

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Answer:

m∡1 + m∡2 = 180

Step-by-step explanation:

m∡1 + m∡2 = 180

This is because supplementary means they add up to 180°.

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right by h units, then

 the new function g(x) = f(x - h)  

- If the function f(x) translated horizontally to the left by h units, then

 the new function g(x) = f(x + h)  

- If the function f(x) translated vertically up by k units, then the new

 function g(x) = f(x) + k  

- If the function f(x) translated vertically down by k units, then the

 new function g(x) = f(x) – k  

- A vertical stretching is the stretching of the graph away from the

 x-axis  

- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically  

 stretched by multiplying each of its y-coordinates by k.  

- A vertical compression is the squeezing of the graph toward  

 the x-axis.  

- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)

 vertically compressed by multiplying each of its y-coordinates by k.  

* Lets solve the problem

∵ f(x) = sin(x)

∵ f(x) is stretching vertically by a factor of 4

∴ f(x) multiplied by 4

∵ f(x) is shifting 3 units to the right

∴ We will change x to (x - 3)

∵ The new function is g(x)

∴ g(x) = 4 sin(x - 3)

- The attached graph for more understand

f(x) is the red graph

g(x) is the blue graph

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

The given function is:

f(x) = sin(x)

Stretching by a factor of 4:

A vertical stretch or compression of f(x) can be expressed as:

cf(x), where c is any constant

if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.

Since, given function is being stretched by a factor of 4, the transformed function will become:

4f(x)

Shifting by 3 units right:

A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:

f(x - 3)

Applying both the transformations to f(x), we get g(x) as:

g(x) = 4 f(x - 3)

g(x) = 4 sin(x - 3)

Answer:

n = 9 is the value in the replacement set is a solution to the equation [tex]3(n+7)=48[/tex]

Step-by-step explanation:

Given an equation: [tex]3(n+7)=48[/tex]                      .....[1]

Replacement set: {8, 9, 10}

For n = 8

Substitute in equation [1], we get;

[tex]3(8+7)=48[/tex]  

[tex]3(15)=48[/tex]

[tex]45=48[/tex]           False.

Similarly, For n = 9

Substitute in equation [1], we get;

[tex]3(9+7)=48[/tex]  

[tex]3(16)=48[/tex]

[tex]48=48[/tex]           True.

for n = 10

Substitute in equation [1], we get;

[tex]3(10+7)=48[/tex]  

[tex]3(17)=48[/tex]

[tex]51=48[/tex]           False.

Therefore, the value in the replacement set is a solution to this equation [tex]3(n+7)=48[/tex] is, 9

Answer:

9

Step-by-step explanation:

Answer:

-1< x< 3  x is an integer

Step-by-step explanation:

There are the dots on the number line.  Three points are represented

x= 0,1,2

We want an inequality

-1< x< 3  x is an integer

Answer: 173

Step-by-step explanation: 173 x 3 = 519. 520-173 = 347

Let S = spoon

Let K = knife

1 knife is thee times the cost of a spoon, so it would be 3S

Now you have 9S + 12K = 82.80

We can replace the K with 3S:

9S +12(3S) = 82.80

Simplify the left side:

9S + 36S = 82.80

Add:

45S = 82.80

Divide both sides by 45"

S = 82.80 / 45

S = 1.84

One spoon cost $1.84

We know one knife cost 3 times as much, so multiply the cost of a spoon by 3:

Knife = 1.84 x 3 = $5.52

Answer:

1.84 x 3 = $5.52

Answer:

Total = 686000 meters for 10 weeks 7 days a week.

Step-by-step explanation:

Let's solve this by doing the increase on just 1 training day per week. Then we can find the grand total for 7 days a week by multiplying by 7

a = 8000

n = 10

d = 400

Sum = (a + L)*n/2

Sum = (8000 + 11600)*10/2

Sum = 19600 * 10/2

Sum = 98000 meters.

This total represents 1 training day a week.

The total amount is 7 times this figure.

Total = 7 * 98000 = 686 000 meters.

Answer:

45/63

Step-by-step explanation:

6 3/10=63/10,    4  1/2=45/10,

(45/10)/(63/10)=45/63

Answer: 5, 3, [tex]\dfrac{1}{6}[/tex], D

Step-by-step explanation:

-5 < 0 so f(-5) = | -5 | = 5

-3 < 0 so f(-3) = | -3 | = 3

6 > 0 so f(6) = [tex]\dfrac{1}{6}[/tex]

graph D (since x can equal zero)

Answer:

64.5A

Step-by-step explanation:

[tex]f(x)=x^3+3x^2-10x-24\\\\y-intercept\ for\ x=0:\\\\f(0)=0^3+3(0)^2-10(0)-24=-24[/tex]

Answer:

The attached image shows he graph for given function.

Step-by-step explanation:

We are given the following expression in the question:

[tex]f(x) = x^3 + 3x^2-10x-24[/tex]

The zeroes of the given function can be calculated as:

[tex]x^3 + 3x^2-10x-24 = 0\\x = -4, x = -2, x=3[/tex]

Thus,the graph for the given function passes through the x-axis on the points (-4,0), (-2,0) and (3,0).

The function crosses the y-axis at the point (0,24)

The attached image shows the graph for given function.

Thus, the second option is the correct graph for given function.

QUESTION 34

We want to find the variance of [tex]82,44,67,52,120[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]

[tex]\bar X =\frac{365}{5}[/tex]

[tex]\Rightarrow \bar X =73[/tex]

This means that,

[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]

This gives us,

[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]

[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]

[tex]\sigma^2=\frac{3608}{5}[/tex]

[tex]\sigma^2=721.6[/tex]

QUESTION 35

We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]

[tex]\bar X =\frac{148}{10}[/tex]

[tex]\fRightarrow \bar X =14.8[/tex]

This means that,

[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]

[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]

[tex]\sigma^2=\frac{105.6}{10}[/tex]

[tex]\sigma^2=10.56[/tex]

QUESTION 36

We want to find the variance of [tex]100,140,130,180,80,160[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]

[tex]\bar X =\frac{790}{6}[/tex]

[tex]\Rightarrow \bar X =131.67[/tex]

This means that,

[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]

[tex]\sigma^2=\frac{10325}{9}[/tex]

[tex]\sigma^2=1147.22[/tex]

To find the variance of a set of data, find the mean, subtract the mean from each data point, square the differences, and find the average of the squared differences. The standard deviation is the square root of the variance.

To find the variance of a set of data, follow these steps:

For the data set 82, 44, 67, 52, 120 (Question 34), the mean is 73, the squared differences are 81, 841, 36, 441, and 1849, and the average of the squared differences is 631.20, rounding to two decimal places.

For the data set 10, 12, 15, 18, 11, 13, 14, 16, 19, 20 (Question 35), the mean is 14.8, the squared differences are 23.04, 4.84, 0.64, 8.84, 12.96, 3.24, 1.44, 2.56, 19.36, and 29.16, and the average of the squared differences is 10.10, rounding to two decimal places.

To find the standard deviation of a set of data, take the square root of the variance. For the data set 100, 140, 130, 180, 80, 160 (Question 36), the variance is 9300, and the standard deviation is 96.49, rounding to two decimal places.

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[tex]\begin{cases}4x+2\ge14\\-21x+1<22\end{cases}[/tex]

In the first inequality, we have

[tex]4x+2\ge14\implies4x\ge12\implies x\ge3[/tex]

In the second, we have

[tex]-21x+1<22\implies-21x<21\implies x>-1[/tex]

The solution to the system is the intersection of these two intervals, which would be [tex]x\ge3[/tex].